Average Error: 46.3 → 45.6
Time: 18.3s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (((double) (x * ((double) cos(((double) (((double) (((double) (((double) (((double) (y * 2.0)) + 1.0)) * z)) * t)) / 16.0)))))) * ((double) cos(((double) (((double) (((double) (((double) (((double) (a * 2.0)) + 1.0)) * b)) * t)) / 16.0))))));
}

↓
double code(double x, double y, double z, double t, double a, double b) {
	return ((double) (x * ((double) (((double) cos(((double) (((double) cbrt(((double) (((double) (y * 2.0)) + 1.0)))) * ((double) (((double) cbrt(((double) (((double) (y * 2.0)) + 1.0)))) * ((double) (((double) cbrt(((double) (((double) (y * 2.0)) + 1.0)))) * ((double) (z * ((double) (t / 16.0)))))))))))) * ((double) cos(((double) (t * ((double) (b * 0.0625))))))))));
}

Error
Bits error versus x
Bits error versus y
Bits error versus z
Bits error versus t
Bits error versus a
Bits error versus b
Try it out
Your Program's Arguments
Results
Enter valid numbers for all inputs
Target
Original46.3
Target44.7
Herbie45.6
\[\]
Derivation
  1. Initial program 46.3
    \[\]
  2. Simplified46.0
    \[\leadsto \]
  3. Taylor expanded around inf 45.8
    \[\leadsto \]
  4. Simplified45.8
    \[\leadsto \]
  5. Using strategy rm
  6. Applied add-cube-cbrt45.8
    \[\leadsto \]
  7. Applied associate-*l*45.7
    \[\leadsto \]
  8. Simplified45.8
    \[\leadsto \]
  9. Using strategy rm
  10. Applied associate-*l*45.8
    \[\leadsto \]
  11. Simplified45.7
    \[\leadsto \]
  12. Taylor expanded around 0 45.6
    \[\leadsto \]
  13. Simplified45.6
    \[\leadsto \]
  14. Final simplification45.6
    \[\leadsto \]
Reproduce
herbie shell --seed 2020191 
(FPCore (x y z t a b)
  :name "Codec.Picture.Jpg.FastDct:referenceDct from JuicyPixels-3.2.6.1"
  :precision binary64

  :herbie-target
  (* x (cos (* (/ b 16.0) (/ t (+ (- 1.0 (* a 2.0)) (pow (* a 2.0) 2.0))))))

  (* (* x (cos (/ (* (* (+ (* y 2.0) 1.0) z) t) 16.0))) (cos (/ (* (* (+ (* a 2.0) 1.0) b) t) 16.0))))