diff --git a/examples/interval/bouncing_particle_v_slope.hydla b/examples/interval/bouncing_particle_v_slope.hydla
index c9358da6..54c12da1 100644
--- a/examples/interval/bouncing_particle_v_slope.hydla
+++ b/examples/interval/bouncing_particle_v_slope.hydla
@@ -22,4 +22,6 @@ BOUNCE_PLUS <=> [](y- = tan(s) * x- =>
 
 INIT, A << (BOUNCE_PLUS,BOUNCE_MINUS).
 
-//#hylagi -p10 --fnd --finterval --fdump_in_progress --guards_to_interval_newton y-=tan[s]*x-,y-=(-tan[s])*x-
+//#hylagi -p10 --fnd --finterval --guards_to_interval_newton y-=Tan[s]*x-,y-=-Tan[s]*x-
+//#hylagi -p10 --fnd --finterval --guards_to_interval_newton y-=Tan[s]*x-,y-=-Tan[s]*x- --faffine
+//#hylagi -p5 --fnd 
diff --git a/examples/interval/circle.hydla b/examples/interval/circle.hydla
index 391df4ae..126fee28 100644
--- a/examples/interval/circle.hydla
+++ b/examples/interval/circle.hydla
@@ -9,4 +9,6 @@ BOUNCE <=> []((x-)^2 + (y-)^2 = 1 => cont = 0 &
 ).
 INIT, RUN, [](cont = 1) << BOUNCE.
 
-//#hylagi -p15 --fnd --guards_to_interval_newton x-^2+y-^2=1 --finterval --fstep_by_step --approximation_step 1 --vars_to_approximate x,y,x',y'
+//#hylagi -p15 --guards_to_interval_newton x-^2+y-^2=1 --finterval --fstep_by_step --approximation_step 1 --vars_to_approximate x,y,x',y' 
+//#hylagi -p15 --guards_to_interval_newton x-^2+y-^2=1 --finterval --fstep_by_step --approximation_step 1 --vars_to_approximate x,y,x',y' --faffine 
+
diff --git a/examples/interval/half_circle.hydla b/examples/interval/half_circle.hydla
index c5801595..841b5a69 100644
--- a/examples/interval/half_circle.hydla
+++ b/examples/interval/half_circle.hydla
@@ -5,4 +5,4 @@ CONSTDIR <=> [](c' = 0).
 
 INIT, CONSTDIR << BOUNCE, CIRCLE.
 
-//#hylagi -p 30 --fnd --finterval --approximation_step 1 --vars_to_approximate x,y
+//#hylagi -p 30 --fnd --finterval --approximation_step 1 --vars_to_approximate x,y --guards_to_interval_newton x-=y-
diff --git a/examples/interval/planet_tunnel_easy.hydla b/examples/interval/planet_tunnel_easy.hydla
index c628a5c4..297f7f58 100644
--- a/examples/interval/planet_tunnel_easy.hydla
+++ b/examples/interval/planet_tunnel_easy.hydla
@@ -7,3 +7,4 @@ FORCE3 <=> [](x- < -1 => x''=4/3*Pi*r*g).
 INIT(0.5), CONST, FORCE1 << (FORCE2, FORCE3).
 
 //#hylagi -p18 --finterval --fnd --approximation_step 1 --vars_to_approximate x' --guards_to_interval_newton x->1,x-<-1
+//This program cannot be executed using the above command.Currently, the executable commands for this program are unknown.
\ No newline at end of file
diff --git a/examples/interval/simplified_inverted_pendulum.hydla b/examples/interval/simplified_inverted_pendulum.hydla
index f4154991..84e8c839 100644
--- a/examples/interval/simplified_inverted_pendulum.hydla
+++ b/examples/interval/simplified_inverted_pendulum.hydla
@@ -16,4 +16,6 @@ LAW(1,1,1,10,0),
 SCONST << (SR, SL),
 FORCE(1, 15), FORCE(2, -15), FORCE(0, 0).
 
-// #hylagi -p10 --fignore_warnings --finterval --guards_to_interval_newton angle-=threshold,angle-=-threshold --fdump_in_progress --fstep_by_step
+//#hylagi -p9 --fignore_warnings --finterval --guards_to_interval_newton angle-=threshold,angle-=-threshold --fdump_in_progress --fstep_by_step
+//#hylagi -p10 --fignore_warnings --finterval --guards_to_interval_newton angle-=threshold,angle-=-threshold --fdump_in_progress --fstep_by_step --faffine 
+//#hylagi -p10 --fignore_warnings 
diff --git a/examples/interval/trampoline.hydla b/examples/interval/trampoline.hydla
index 1ac216cc..5f415e62 100644
--- a/examples/interval/trampoline.hydla
+++ b/examples/interval/trampoline.hydla
@@ -2,4 +2,8 @@ INIT <=> x = 10 &  x' = 0 & [](g = 9.8) & [](m = 60) & [](k = 100).
 FALL <=> [](x'' = -m*g).
 TRAMPOLINE <=> [](x < 0 => x'' = -k*x - m*g).
 
-INIT, FALL<<TRAMPOLINE.
\ No newline at end of file
+INIT, FALL<<TRAMPOLINE.
+
+//#hylagi -p7 --finterval --fstep_by_step --guards_to_interval_newton x<0 --vars_to_approximate x x' --approximation_step 1
+//#hylagi -p5 --finterval --fstep_by_step --guards_to_interval_newton x<0 --vars_to_approximate x x' --approximation_step 1 --faffine
+//#hylagi -p3
\ No newline at end of file
diff --git a/examples/interval/two_tanks.hydla b/examples/interval/two_tanks.hydla
index 5d00e32c..23837b15 100644
--- a/examples/interval/two_tanks.hydla
+++ b/examples/interval/two_tanks.hydla
@@ -11,4 +11,5 @@ X2 <=> []((v2 = 0 => x2' = x1) & (v2 = 1 => x2' = x1 - x2 - 5)).
 
 INIT, (V1_CONST, V2_CONST) << (V1_OFF2ON, V1_ON2OFF, V2_OFF2ON, V2_ON2OFF), X1, X2.
 
-//#hylagi --fnd  --finterval --guards_to_interval_newton x1-=-1,x1-=1,x2-=1,x2-=0 --fstep_by_step -p 60
+//#hylagi --fnd  --finterval --guards_to_interval_newton x1-=-1,x1-=1,x2-=1,x2-=0 --fstep_by_step -p21
+//#hylagi --fnd  --finterval --guards_to_interval_newton x1-=-1,x1-=1,x2-=1,x2-=0 --fstep_by_step -p60 --faffine