Average Error: 0.2 → 0.2
Time: 25.5s
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 r21140408 = x;
        double r21140409 = cosh(r21140408);
        double r21140410 = y;
        double r21140411 = sin(r21140410);
        double r21140412 = r21140411 / r21140410;
        double r21140413 = r21140409 * r21140412;
        return r21140413;
}
↓
double f(double x, double y) {
        double r21140414 = x;
        double r21140415 = cosh(r21140414);
        double r21140416 = y;
        double r21140417 = sin(r21140416);
        double r21140418 = r21140417 / r21140416;
        double r21140419 = r21140415 * r21140418;
        return r21140419;
}

Error

Bits error versus x

Bits error versus y

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Results

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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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csinh from linear-1.19.1.3"

  :herbie-target
  (/ (* (cosh x) (sin y)) y)

  (* (cosh x) (/ (sin y) y)))