Average Error: 0.1 → 0.1
Time: 28.7s
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 r20379392 = x;
        double r20379393 = cosh(r20379392);
        double r20379394 = y;
        double r20379395 = sin(r20379394);
        double r20379396 = r20379395 / r20379394;
        double r20379397 = r20379393 * r20379396;
        return r20379397;
}
↓
double f(double x, double y) {
        double r20379398 = x;
        double r20379399 = cosh(r20379398);
        double r20379400 = y;
        double r20379401 = sin(r20379400);
        double r20379402 = r20379401 / r20379400;
        double r20379403 = r20379399 * r20379402;
        return r20379403;
}

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 2019162 +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)))