Average Error: 0.2 → 0.2
Time: 5.2s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\cosh x \cdot \frac{1}{\frac{y}{\sin y}}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\cosh x \cdot \frac{1}{\frac{y}{\sin y}}
double f(double x, double y) {
        double r461376 = x;
        double r461377 = cosh(r461376);
        double r461378 = y;
        double r461379 = sin(r461378);
        double r461380 = r461379 / r461378;
        double r461381 = r461377 * r461380;
        return r461381;
}
↓
double f(double x, double y) {
        double r461382 = x;
        double r461383 = cosh(r461382);
        double r461384 = 1.0;
        double r461385 = y;
        double r461386 = sin(r461385);
        double r461387 = r461385 / r461386;
        double r461388 = r461384 / r461387;
        double r461389 = r461383 * r461388;
        return r461389;
}

Error

Bits error versus x

Bits error versus y

Try it out

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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. Using strategy rm

  3. Applied clear-num0.2

    \[\leadsto \cosh x \cdot \color{blue}{\frac{1}{\frac{y}{\sin y}}}\]

  4. Final simplification0.2

    \[\leadsto \cosh x \cdot \frac{1}{\frac{y}{\sin y}}\]

Reproduce

herbie shell --seed 2020062 
(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)))