Average Error: 0.1 → 0.2
Time: 5.8s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\frac{\sin y}{\frac{1}{2}} \cdot \cosh x}{2 \cdot y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\frac{\sin y}{\frac{1}{2}} \cdot \cosh x}{2 \cdot y}
double f(double x, double y) {
        double r508717 = x;
        double r508718 = cosh(r508717);
        double r508719 = y;
        double r508720 = sin(r508719);
        double r508721 = r508720 / r508719;
        double r508722 = r508718 * r508721;
        return r508722;
}
↓
double f(double x, double y) {
        double r508723 = y;
        double r508724 = sin(r508723);
        double r508725 = 0.5;
        double r508726 = r508724 / r508725;
        double r508727 = x;
        double r508728 = cosh(r508727);
        double r508729 = r508726 * r508728;
        double r508730 = 2.0;
        double r508731 = r508730 * r508723;
        double r508732 = r508729 / r508731;
        return r508732;
}

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 cosh-def0.1

    \[\leadsto \color{blue}{\frac{e^{x} + e^{-x}}{2}} \cdot \frac{\sin y}{y}\]

  4. Applied frac-times0.2

    \[\leadsto \color{blue}{\frac{\left(e^{x} + e^{-x}\right) \cdot \sin y}{2 \cdot y}}\]

  5. Simplified0.2

    \[\leadsto \frac{\color{blue}{\frac{\sin y}{\frac{1}{2}} \cdot \cosh x}}{2 \cdot y}\]

  6. Final simplification0.2

    \[\leadsto \frac{\frac{\sin y}{\frac{1}{2}} \cdot \cosh x}{2 \cdot y}\]

Reproduce

herbie shell --seed 2020024 +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)))