Average Error: 0.1 → 0.2
Time: 15.0s
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 r434558 = x;
        double r434559 = cosh(r434558);
        double r434560 = y;
        double r434561 = sin(r434560);
        double r434562 = r434561 / r434560;
        double r434563 = r434559 * r434562;
        return r434563;
}
↓
double f(double x, double y) {
        double r434564 = x;
        double r434565 = cosh(r434564);
        double r434566 = 1.0;
        double r434567 = y;
        double r434568 = sin(r434567);
        double r434569 = r434567 / r434568;
        double r434570 = r434566 / r434569;
        double r434571 = r434565 * r434570;
        return r434571;
}

Error

Bits error versus x

Bits error versus y

Try it out

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Results

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Target

Original0.1
Target0.1
Herbie0.2
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.1

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

  3. Applied 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 2020045 
(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)))