Average Error: 0.1 → 0.1
Time: 25.1s
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 r16776942 = x;
        double r16776943 = cosh(r16776942);
        double r16776944 = y;
        double r16776945 = sin(r16776944);
        double r16776946 = r16776945 / r16776944;
        double r16776947 = r16776943 * r16776946;
        return r16776947;
}
↓
double f(double x, double y) {
        double r16776948 = x;
        double r16776949 = cosh(r16776948);
        double r16776950 = y;
        double r16776951 = sin(r16776950);
        double r16776952 = r16776951 / r16776950;
        double r16776953 = r16776949 * r16776952;
        return r16776953;
}

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 clear-num0.2

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

  4. Taylor expanded around inf 0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019170 +o rules:numerics
(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)))