Average Error: 0.1 → 0.1
Time: 17.2s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\cosh x \cdot \frac{-\sin y}{-y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\cosh x \cdot \frac{-\sin y}{-y}
double f(double x, double y) {
        double r375215 = x;
        double r375216 = cosh(r375215);
        double r375217 = y;
        double r375218 = sin(r375217);
        double r375219 = r375218 / r375217;
        double r375220 = r375216 * r375219;
        return r375220;
}
↓
double f(double x, double y) {
        double r375221 = x;
        double r375222 = cosh(r375221);
        double r375223 = y;
        double r375224 = sin(r375223);
        double r375225 = -r375224;
        double r375226 = -r375223;
        double r375227 = r375225 / r375226;
        double r375228 = r375222 * r375227;
        return r375228;
}

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 frac-2neg0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019235 
(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)))