Average Error: 0.2 → 0.2
Time: 11.8s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\cosh x}{\frac{y}{\sin y}}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\cosh x}{\frac{y}{\sin y}}
double f(double x, double y) {
        double r604025 = x;
        double r604026 = cosh(r604025);
        double r604027 = y;
        double r604028 = sin(r604027);
        double r604029 = r604028 / r604027;
        double r604030 = r604026 * r604029;
        return r604030;
}
↓
double f(double x, double y) {
        double r604031 = x;
        double r604032 = cosh(r604031);
        double r604033 = y;
        double r604034 = sin(r604033);
        double r604035 = r604033 / r604034;
        double r604036 = r604032 / r604035;
        return r604036;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.2

    \[\cosh x \cdot \frac{\sin y}{y}\]

  2. Taylor expanded around inf 0.2

    \[\leadsto \color{blue}{\frac{\frac{1}{2} \cdot \left(\sin y \cdot e^{x}\right) + \frac{1}{2} \cdot \left(\sin y \cdot e^{-x}\right)}{y}}\]

  3. Simplified0.2

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

  4. Final simplification0.2

    \[\leadsto \frac{\cosh x}{\frac{y}{\sin y}}\]

Reproduce

herbie shell --seed 2020047 +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)))