Average Error: 0.1 → 0.1
Time: 4.8s
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 r523380 = x;
        double r523381 = cosh(r523380);
        double r523382 = y;
        double r523383 = sin(r523382);
        double r523384 = r523383 / r523382;
        double r523385 = r523381 * r523384;
        return r523385;
}
↓
double f(double x, double y) {
        double r523386 = x;
        double r523387 = cosh(r523386);
        double r523388 = y;
        double r523389 = sin(r523388);
        double r523390 = r523389 / r523388;
        double r523391 = r523387 * r523390;
        return r523391;
}

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 2019353 +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)))