Average Error: 0.1 → 0.1
Time: 14.2s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\cosh x \cdot \frac{\sin y}{y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\cosh x \cdot \frac{\sin y}{y}
double f(double x, double y) {
        double r320905 = x;
        double r320906 = cosh(r320905);
        double r320907 = y;
        double r320908 = sin(r320907);
        double r320909 = r320908 / r320907;
        double r320910 = r320906 * r320909;
        return r320910;
}
↓
double f(double x, double y) {
        double r320911 = x;
        double r320912 = cosh(r320911);
        double r320913 = y;
        double r320914 = sin(r320913);
        double r320915 = r320914 / r320913;
        double r320916 = r320912 * r320915;
        return r320916;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.1
Target0.1
Herbie0.1
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.1

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

  2. Final simplification0.1

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

Reproduce

herbie shell --seed 2019208 +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)))