Average Error: 0.2 → 0.2
Time: 4.7s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\cosh x \cdot \sin y}{y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\cosh x \cdot \sin y}{y}
double f(double x, double y) {
        double r574252 = x;
        double r574253 = cosh(r574252);
        double r574254 = y;
        double r574255 = sin(r574254);
        double r574256 = r574255 / r574254;
        double r574257 = r574253 * r574256;
        return r574257;
}
↓
double f(double x, double y) {
        double r574258 = x;
        double r574259 = cosh(r574258);
        double r574260 = y;
        double r574261 = sin(r574260);
        double r574262 = r574259 * r574261;
        double r574263 = r574262 / r574260;
        return r574263;
}

Error

Bits error versus x

Bits error versus y

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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 associate-*r/0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020027 
(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)))