Average Error: 0.1 → 0.1
Time: 17.4s
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 r438151 = x;
        double r438152 = cosh(r438151);
        double r438153 = y;
        double r438154 = sin(r438153);
        double r438155 = r438154 / r438153;
        double r438156 = r438152 * r438155;
        return r438156;
}
↓
double f(double x, double y) {
        double r438157 = x;
        double r438158 = cosh(r438157);
        double r438159 = y;
        double r438160 = sin(r438159);
        double r438161 = r438160 / r438159;
        double r438162 = r438158 * r438161;
        return r438162;
}

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 2020046 +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)))