Average Error: 0.1 → 0.1
Time: 6.6s
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 r495254 = x;
        double r495255 = cosh(r495254);
        double r495256 = y;
        double r495257 = sin(r495256);
        double r495258 = r495257 / r495256;
        double r495259 = r495255 * r495258;
        return r495259;
}
↓
double f(double x, double y) {
        double r495260 = x;
        double r495261 = cosh(r495260);
        double r495262 = y;
        double r495263 = sin(r495262);
        double r495264 = r495263 / r495262;
        double r495265 = r495261 * r495264;
        return r495265;
}

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 2020065 +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)))