Average Error: 0.1 → 0.3
Time: 19.0s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\cosh x \cdot \left(\sin y \cdot \frac{1}{y}\right)\]
\cosh x \cdot \frac{\sin y}{y}
↓
\cosh x \cdot \left(\sin y \cdot \frac{1}{y}\right)
double f(double x, double y) {
        double r397408 = x;
        double r397409 = cosh(r397408);
        double r397410 = y;
        double r397411 = sin(r397410);
        double r397412 = r397411 / r397410;
        double r397413 = r397409 * r397412;
        return r397413;
}
↓
double f(double x, double y) {
        double r397414 = x;
        double r397415 = cosh(r397414);
        double r397416 = y;
        double r397417 = sin(r397416);
        double r397418 = 1.0;
        double r397419 = r397418 / r397416;
        double r397420 = r397417 * r397419;
        double r397421 = r397415 * r397420;
        return r397421;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original0.1
Target0.1
Herbie0.3
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.1

    \[\cosh x \cdot \frac{\sin y}{y}\]
  2. Using strategy rm

  3. Applied div-inv0.3

    \[\leadsto \cosh x \cdot \color{blue}{\left(\sin y \cdot \frac{1}{y}\right)}\]

  4. Final simplification0.3

    \[\leadsto \cosh x \cdot \left(\sin y \cdot \frac{1}{y}\right)\]

Reproduce

herbie shell --seed 2019351 +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)))