Average Error: 0.1 → 0.1
Time: 19.3s
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 r20606408 = x;
        double r20606409 = cosh(r20606408);
        double r20606410 = y;
        double r20606411 = sin(r20606410);
        double r20606412 = r20606411 / r20606410;
        double r20606413 = r20606409 * r20606412;
        return r20606413;
}
↓
double f(double x, double y) {
        double r20606414 = x;
        double r20606415 = cosh(r20606414);
        double r20606416 = y;
        double r20606417 = sin(r20606416);
        double r20606418 = r20606417 / r20606416;
        double r20606419 = r20606415 * r20606418;
        return r20606419;
}

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 2019171 +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)))