Average Error: 0.1 → 0.1
Time: 26.6s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\sin y \cdot \cosh x}{y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\sin y \cdot \cosh x}{y}
double f(double x, double y) {
        double r35656230 = x;
        double r35656231 = cosh(r35656230);
        double r35656232 = y;
        double r35656233 = sin(r35656232);
        double r35656234 = r35656233 / r35656232;
        double r35656235 = r35656231 * r35656234;
        return r35656235;
}
↓
double f(double x, double y) {
        double r35656236 = y;
        double r35656237 = sin(r35656236);
        double r35656238 = x;
        double r35656239 = cosh(r35656238);
        double r35656240 = r35656237 * r35656239;
        double r35656241 = r35656240 / r35656236;
        return r35656241;
}

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. Using strategy rm

  3. Applied associate-*r/0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 
(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)))