Average Error: 10.1 → 1.3
Time: 2.3s
Precision: binary64
\[\frac{x}{y \cdot y} \]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -7.865606214009272 \cdot 10^{+265}:\\ \;\;\;\;x \cdot \sqrt[3]{{\left({y}^{-2}\right)}^{3}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{y}\\ \end{array} \]
\frac{x}{y \cdot y}
↓
\begin{array}{l}
\mathbf{if}\;x \leq -7.865606214009272 \cdot 10^{+265}:\\
\;\;\;\;x \cdot \sqrt[3]{{\left({y}^{-2}\right)}^{3}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\frac{x}{y}}{y}\\


\end{array}

(FPCore (x y) :precision binary64 (/ x (* y y)))
↓
(FPCore (x y)
 :precision binary64
 (if (<= x -7.865606214009272e+265)
   (* x (cbrt (pow (pow y -2.0) 3.0)))
   (/ (/ x y) y)))
double code(double x, double y) {
	return x / (y * y);
}
↓
double code(double x, double y) {
	double tmp;
	if (x <= -7.865606214009272e+265) {
		tmp = x * cbrt(pow(pow(y, -2.0), 3.0));
	} else {
		tmp = (x / y) / y;
	}
	return tmp;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original10.1
Target0.2
Herbie1.3
\[\frac{\frac{x}{y}}{y} \]

Derivation

  1. Split input into 2 regimes

  2. if x < -7.8656062140092724e265

    1. Initial program 24.1

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

    2. Applied egg-rr24.2

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

    3. Applied egg-rr49.5

      \[\leadsto x \cdot \color{blue}{\sqrt[3]{{\left({y}^{-2}\right)}^{3}}} \]

    if -7.8656062140092724e265 < x

    1. Initial program 9.8

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

    2. Applied egg-rr10.2

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

    3. Applied egg-rr0.2

      \[\leadsto \color{blue}{\frac{\frac{x}{y}}{y}} \]
  3. Recombined 2 regimes into one program.

  4. Final simplification1.3

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.865606214009272 \cdot 10^{+265}:\\ \;\;\;\;x \cdot \sqrt[3]{{\left({y}^{-2}\right)}^{3}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\frac{x}{y}}{y}\\ \end{array} \]

Reproduce

herbie shell --seed 2022127 
(FPCore (x y)
  :name "Physics.ForceLayout:coulombForce from force-layout-0.4.0.2"
  :precision binary64

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

  (/ x (* y y)))