Average Error: 0.1 → 0.3
Time: 6.0s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\sqrt[3]{{\left(\cosh x\right)}^{3}} \cdot \frac{\sin y}{y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\sqrt[3]{{\left(\cosh x\right)}^{3}} \cdot \frac{\sin y}{y}
double code(double x, double y) {
	return (cosh(x) * (sin(y) / y));
}
↓
double code(double x, double y) {
	return (cbrt(pow(cosh(x), 3.0)) * (sin(y) / y));
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.1
Target0.1
Herbie0.3
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.1

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

  3. Applied add-cbrt-cube0.3

    \[\leadsto \color{blue}{\sqrt[3]{\left(\cosh x \cdot \cosh x\right) \cdot \cosh x}} \cdot \frac{\sin y}{y}\]

  4. Simplified0.3

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\cosh x\right)}^{3}}} \cdot \frac{\sin y}{y}\]

  5. Final simplification0.3

    \[\leadsto \sqrt[3]{{\left(\cosh x\right)}^{3}} \cdot \frac{\sin y}{y}\]

Reproduce

herbie shell --seed 2020106 
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (/ (* (cosh x) (sin y)) y)

  (* (cosh x) (/ (sin y) y)))