Average Error: 0.5 → 0.5
Time: 7.7s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double a1, double a2, double th) {
	return ((double) (((double) (((double) (((double) cos(th)) / ((double) sqrt(2.0)))) * ((double) (a1 * a1)))) + ((double) (((double) (((double) cos(th)) / ((double) sqrt(2.0)))) * ((double) (a2 * a2))))));
}

↓
double code(double a1, double a2, double th) {
	return ((double) (((double) cos(th)) * ((double) (((double) (((double) (((double) (a1 * a1)) + ((double) (a2 * a2)))) / ((double) (((double) cbrt(((double) sqrt(2.0)))) * ((double) cbrt(((double) sqrt(2.0)))))))) / ((double) cbrt(((double) sqrt(2.0))))))));
}

Error
Bits error versus a1
Bits error versus a2
Bits error versus th
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Derivation
  1. Initial program 0.5
    \[\]
  2. Simplified0.5
    \[\leadsto \]
  3. Using strategy rm
  4. Applied add-cube-cbrt0.5
    \[\leadsto \]
  5. Applied associate-/r*0.5
    \[\leadsto \]
  6. Final simplification0.5
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (a1 a2 th)
  :name "Migdal et al, Equation (64)"
  :precision binary64
  (+ (* (/ (cos th) (sqrt 2.0)) (* a1 a1)) (* (/ (cos th) (sqrt 2.0)) (* a2 a2))))