Average Error: 0.1 → 0.2
Time: 6.4s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\left(\sqrt[3]{\cosh x} \cdot \sqrt[3]{\cosh x}\right) \cdot \left(\sqrt[3]{\cosh x} \cdot \frac{\sin y}{y}\right)\]
\cosh x \cdot \frac{\sin y}{y}
↓
\left(\sqrt[3]{\cosh x} \cdot \sqrt[3]{\cosh x}\right) \cdot \left(\sqrt[3]{\cosh x} \cdot \frac{\sin y}{y}\right)
double f(double x, double y) {
        double r519462 = x;
        double r519463 = cosh(r519462);
        double r519464 = y;
        double r519465 = sin(r519464);
        double r519466 = r519465 / r519464;
        double r519467 = r519463 * r519466;
        return r519467;
}
↓
double f(double x, double y) {
        double r519468 = x;
        double r519469 = cosh(r519468);
        double r519470 = cbrt(r519469);
        double r519471 = r519470 * r519470;
        double r519472 = y;
        double r519473 = sin(r519472);
        double r519474 = r519473 / r519472;
        double r519475 = r519470 * r519474;
        double r519476 = r519471 * r519475;
        return r519476;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.1
Target0.1
Herbie0.2
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.1

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

  3. Applied add-cube-cbrt0.2

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

  4. Applied associate-*l*0.2

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

  5. Final simplification0.2

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

Reproduce

herbie shell --seed 2020036 
(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)))