Average Error: 0.1 → 0.1
Time: 4.8s
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 r411590 = x;
        double r411591 = cosh(r411590);
        double r411592 = y;
        double r411593 = sin(r411592);
        double r411594 = r411593 / r411592;
        double r411595 = r411591 * r411594;
        return r411595;
}
↓
double f(double x, double y) {
        double r411596 = x;
        double r411597 = cosh(r411596);
        double r411598 = y;
        double r411599 = sin(r411598);
        double r411600 = r411597 * r411599;
        double r411601 = r411600 / r411598;
        return r411601;
}

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. Using strategy rm

  5. Applied clear-num0.2

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

  6. Taylor expanded around inf 0.1

    \[\leadsto \color{blue}{\frac{\frac{1}{2} \cdot \left(\sin y \cdot e^{x}\right) + \frac{1}{2} \cdot \left(\sin y \cdot e^{-x}\right)}{y}}\]

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020024 
(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)))