Average Error: 0.1 → 0.2
Time: 6.9s
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 r463723 = x;
        double r463724 = cosh(r463723);
        double r463725 = y;
        double r463726 = sin(r463725);
        double r463727 = r463726 / r463725;
        double r463728 = r463724 * r463727;
        return r463728;
}
↓
double f(double x, double y) {
        double r463729 = x;
        double r463730 = cosh(r463729);
        double r463731 = cbrt(r463730);
        double r463732 = r463731 * r463731;
        double r463733 = y;
        double r463734 = sin(r463733);
        double r463735 = r463734 / r463733;
        double r463736 = r463731 * r463735;
        double r463737 = r463732 * r463736;
        return r463737;
}

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)))