Average Error: 5.9 → 1.1
Time: 5.0s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double y, double z) {
	return ((double) (x + ((double) (((double) exp(((double) (y * ((double) log(((double) (y / ((double) (z + y)))))))))) / y))));
}

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

Error
Bits error versus x
Bits error versus y
Bits error versus z
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Results
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Target
Original5.9
Target1.1
Herbie1.1
\[\]
Derivation
  1. Initial program 5.9
    \[\]
  2. Simplified5.9
    \[\leadsto \]
  3. Using strategy rm
  4. Applied add-cube-cbrt19.7
    \[\leadsto \]
  5. Applied add-cube-cbrt5.9
    \[\leadsto \]
  6. Applied times-frac5.9
    \[\leadsto \]
  7. Applied unpow-prod-down2.2
    \[\leadsto \]
  8. Simplified2.2
    \[\leadsto \]
  9. Using strategy rm
  10. Applied pow12.2
    \[\leadsto \]
  11. Applied pow12.2
    \[\leadsto \]
  12. Applied pow-prod-up2.2
    \[\leadsto \]
  13. Applied pow-pow1.1
    \[\leadsto \]
  14. Simplified1.1
    \[\leadsto \]
  15. Final simplification1.1
    \[\leadsto \]
Reproduce
herbie shell --seed 2020190 
(FPCore (x y z)
  :name "Numeric.SpecFunctions:invIncompleteBetaWorker from math-functions-0.1.5.2, G"
  :precision binary64

  :herbie-target
  (if (< (/ y (+ z y)) 7.1154157597908e-315) (+ x (/ (exp (/ -1.0 z)) y)) (+ x (/ (exp (log (pow (/ y (+ y z)) y))) y)))

  (+ x (/ (exp (* y (log (/ y (+ z y))))) y)))