Average Error: 10.3 → 0.2
Time: 1.4s
Precision: binary64
\[\frac{x}{y \cdot y}\]
↓
\[\frac{\frac{x}{y}}{y}\]
\frac{x}{y \cdot y}
↓
\frac{\frac{x}{y}}{y}
(FPCore (x y) :precision binary64 (/ x (* y y)))
↓
(FPCore (x y) :precision binary64 (/ (/ x y) y))
double code(double x, double y) {
	return x / (y * y);
}
↓
double code(double x, double y) {
	return (x / y) / y;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original10.3
Target0.2
Herbie0.2
\[\frac{\frac{x}{y}}{y}\]

Derivation

  1. Initial program 10.3

    \[\frac{x}{y \cdot y}\]
  2. Using strategy rm

  3. Applied associate-/r*_binary640.2

    \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}}\]

  4. Final simplification0.2

    \[\leadsto \frac{\frac{x}{y}}{y}\]

Reproduce

herbie shell --seed 2020233 
(FPCore (x y)
  :name "Physics.ForceLayout:coulombForce from force-layout-0.4.0.2"
  :precision binary64

  :herbie-target
  (/ (/ x y) y)

  (/ x (* y y)))