Average Error: 0.1 → 0.1
Time: 2.8s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double y, double z) {
	return ((double) (((double) (((double) (((double) (x * y)) + ((double) (z * z)))) + ((double) (z * z)))) + ((double) (z * z))));
}

↓
double code(double x, double y, double z) {
	return ((double) (((double) (x * y)) + ((double) (((double) cbrt(((double) sqrt(3.0)))) * ((double) (z * ((double) (z * ((double) (((double) pow(((double) cbrt(3.0)), 2.0)) * ((double) cbrt(((double) sqrt(3.0))))))))))))));
}

Error
Bits error versus x
Bits error versus y
Bits error versus z
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original0.1
Target0.1
Herbie0.1
\[\]
Derivation
  1. Initial program 0.1
    \[\]
  2. Simplified0.1
    \[\leadsto \]
  3. Using strategy rm
  4. Applied associate-*r*0.1
    \[\leadsto \]
  5. Using strategy rm
  6. Applied add-cube-cbrt0.1
    \[\leadsto \]
  7. Applied associate-*r*0.2
    \[\leadsto \]
  8. Simplified0.2
    \[\leadsto \]
  9. Using strategy rm
  10. Applied add-sqr-sqrt0.2
    \[\leadsto \]
  11. Applied cbrt-prod0.2
    \[\leadsto \]
  12. Applied associate-*r*0.2
    \[\leadsto \]
  13. Simplified0.1
    \[\leadsto \]
  14. Final simplification0.1
    \[\leadsto \]
Reproduce
herbie shell --seed 2020180 
(FPCore (x y z)
  :name "Linear.Quaternion:$c/ from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (+ (* (* 3.0 z) z) (* y x))

  (+ (+ (+ (* x y) (* z z)) (* z z)) (* z z)))