Average Error: 33.6 → 1.1
Time: 5.9s
Precision: binary64
\[\]
↓
\[\]
↓
double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (x * x)) / ((double) (y * y)))) + ((double) (((double) (z * z)) / ((double) (t * t))))));
}

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

Error
Bits error versus x
Bits error versus y
Bits error versus z
Bits error versus t
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Results
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Target
Original33.6
Target0.4
Herbie1.1
\[\]
Derivation
  1. Initial program 33.6
    \[\]
  2. Simplified24.9
    \[\leadsto \]
  3. Using strategy rm
  4. Applied add-sqr-sqrt44.0
    \[\leadsto \]
  5. Applied times-frac40.0
    \[\leadsto \]
  6. Applied add-sqr-sqrt40.0
    \[\leadsto \]
  7. Applied unswap-sqr38.2
    \[\leadsto \]
  8. Simplified38.1
    \[\leadsto \]
  9. Simplified13.3
    \[\leadsto \]
  10. Using strategy rm
  11. Applied add-sqr-sqrt38.6
    \[\leadsto \]
  12. Applied times-frac34.2
    \[\leadsto \]
  13. Applied add-sqr-sqrt34.3
    \[\leadsto \]
  14. Applied unswap-sqr32.1
    \[\leadsto \]
  15. Simplified32.1
    \[\leadsto \]
  16. Simplified0.4
    \[\leadsto \]
  17. Using strategy rm
  18. Applied add-cube-cbrt0.8
    \[\leadsto \]
  19. Applied add-sqr-sqrt31.9
    \[\leadsto \]
  20. Applied times-frac31.9
    \[\leadsto \]
  21. Applied add-cube-cbrt32.0
    \[\leadsto \]
  22. Applied add-sqr-sqrt32.0
    \[\leadsto \]
  23. Applied times-frac32.0
    \[\leadsto \]
  24. Applied swap-sqr32.0
    \[\leadsto \]
  25. Simplified32.0
    \[\leadsto \]
  26. Simplified1.1
    \[\leadsto \]
  27. Final simplification1.1
    \[\leadsto \]
Reproduce
herbie shell --seed 2020190 
(FPCore (x y z t)
  :name "Graphics.Rasterific.Svg.PathConverter:arcToSegments from rasterific-svg-0.2.3.1"
  :precision binary64

  :herbie-target
  (+ (pow (/ x y) 2.0) (pow (/ z t) 2.0))

  (+ (/ (* x x) (* y y)) (/ (* z z) (* t t))))