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 r492755 = x;
        double r492756 = cosh(r492755);
        double r492757 = y;
        double r492758 = sin(r492757);
        double r492759 = r492758 / r492757;
        double r492760 = r492756 * r492759;
        return r492760;
}
↓
double f(double x, double y) {
        double r492761 = x;
        double r492762 = cosh(r492761);
        double r492763 = cbrt(r492762);
        double r492764 = r492763 * r492763;
        double r492765 = y;
        double r492766 = sin(r492765);
        double r492767 = r492766 / r492765;
        double r492768 = r492763 * r492767;
        double r492769 = r492764 * r492768;
        return r492769;
}

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 +o rules:numerics
(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)))