Average Error: 10.4 → 0.2
Time: 20.7s
Precision: binary64
\[\frac{x}{y \cdot y}\]
↓
\[\frac{\frac{\sqrt[3]{1} \cdot x}{y}}{y}\]
\frac{x}{y \cdot y}
↓
\frac{\frac{\sqrt[3]{1} \cdot x}{y}}{y}
(FPCore (x y) :precision binary64 (/ x (* y y)))
↓
(FPCore (x y) :precision binary64 (/ (/ (* (cbrt 1.0) x) y) y))
double code(double x, double y) {
	return x / (y * y);
}
↓
double code(double x, double y) {
	return ((cbrt(1.0) * x) / y) / y;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original10.4
Target0.2
Herbie0.2
\[\frac{\frac{x}{y}}{y}\]

Derivation

  1. Initial program 10.4

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

  3. Applied clear-num_binary64_1269410.6

    \[\leadsto \color{blue}{\frac{1}{\frac{y \cdot y}{x}}}\]

  4. Simplified0.6

    \[\leadsto \frac{1}{\color{blue}{\frac{y}{\frac{x}{y}}}}\]
  5. Using strategy rm

  6. Applied associate-/r/_binary64_126410.6

    \[\leadsto \frac{1}{\color{blue}{\frac{y}{x} \cdot y}}\]

  7. Applied associate-/r*_binary64_126390.2

    \[\leadsto \color{blue}{\frac{\frac{1}{\frac{y}{x}}}{y}}\]

  8. Simplified0.2

    \[\leadsto \frac{\color{blue}{\frac{\sqrt[3]{1} \cdot x}{y}}}{y}\]

  9. Final simplification0.2

    \[\leadsto \frac{\frac{\sqrt[3]{1} \cdot x}{y}}{y}\]

Reproduce

herbie shell --seed 2021176 
(FPCore (x y)
  :name "Physics.ForceLayout:coulombForce from force-layout-0.4.0.2"
  :precision binary64

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

  (/ x (* y y)))