Average Error: 0.1 → 0.1
Time: 27.3s
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 r413186 = x;
        double r413187 = cosh(r413186);
        double r413188 = y;
        double r413189 = sin(r413188);
        double r413190 = r413189 / r413188;
        double r413191 = r413187 * r413190;
        return r413191;
}
↓
double f(double x, double y) {
        double r413192 = x;
        double r413193 = cosh(r413192);
        double r413194 = y;
        double r413195 = sin(r413194);
        double r413196 = r413193 * r413195;
        double r413197 = r413196 / r413194;
        return r413197;
}

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

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

Reproduce

herbie shell --seed 2019323 
(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)))