Average Error: 0.2 → 0.2
Time: 17.8s
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 r21225550 = x;
        double r21225551 = cosh(r21225550);
        double r21225552 = y;
        double r21225553 = sin(r21225552);
        double r21225554 = r21225553 / r21225552;
        double r21225555 = r21225551 * r21225554;
        return r21225555;
}
↓
double f(double x, double y) {
        double r21225556 = x;
        double r21225557 = cosh(r21225556);
        double r21225558 = y;
        double r21225559 = sin(r21225558);
        double r21225560 = r21225559 / r21225558;
        double r21225561 = r21225557 * r21225560;
        return r21225561;
}

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 2019179 +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)))