Average Error: 0.1 → 0.3
Time: 4.9s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{1}{y} \cdot \left(\cosh x \cdot \sin y\right)\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{1}{y} \cdot \left(\cosh x \cdot \sin y\right)
double f(double x, double y) {
        double r484408 = x;
        double r484409 = cosh(r484408);
        double r484410 = y;
        double r484411 = sin(r484410);
        double r484412 = r484411 / r484410;
        double r484413 = r484409 * r484412;
        return r484413;
}
↓
double f(double x, double y) {
        double r484414 = 1.0;
        double r484415 = y;
        double r484416 = r484414 / r484415;
        double r484417 = x;
        double r484418 = cosh(r484417);
        double r484419 = sin(r484415);
        double r484420 = r484418 * r484419;
        double r484421 = r484416 * r484420;
        return r484421;
}

Error

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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 associate-*r/0.1

    \[\leadsto \color{blue}{\frac{\cosh x \cdot \sin y}{y}}\]
  4. Using strategy rm

  5. Applied clear-num0.2

    \[\leadsto \color{blue}{\frac{1}{\frac{y}{\cosh x \cdot \sin y}}}\]
  6. Using strategy rm

  7. Applied div-inv0.3

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

  8. Applied add-cube-cbrt0.3

    \[\leadsto \frac{\color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{1}\right) \cdot \sqrt[3]{1}}}{y \cdot \frac{1}{\cosh x \cdot \sin y}}\]

  9. Applied times-frac0.3

    \[\leadsto \color{blue}{\frac{\sqrt[3]{1} \cdot \sqrt[3]{1}}{y} \cdot \frac{\sqrt[3]{1}}{\frac{1}{\cosh x \cdot \sin y}}}\]

  10. Simplified0.3

    \[\leadsto \color{blue}{\frac{1}{y}} \cdot \frac{\sqrt[3]{1}}{\frac{1}{\cosh x \cdot \sin y}}\]

  11. Simplified0.3

    \[\leadsto \frac{1}{y} \cdot \color{blue}{\left(\cosh x \cdot \sin y\right)}\]

  12. Final simplification0.3

    \[\leadsto \frac{1}{y} \cdot \left(\cosh x \cdot \sin y\right)\]

Reproduce

herbie shell --seed 2020081 +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)))