Average Error: 0.1 → 0.1
Time: 6.4s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\frac{1}{2} \cdot \left(\sin y \cdot e^{x}\right) + \frac{1}{2} \cdot \left(e^{-1 \cdot x} \cdot \sin y\right)}{y}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\frac{1}{2} \cdot \left(\sin y \cdot e^{x}\right) + \frac{1}{2} \cdot \left(e^{-1 \cdot x} \cdot \sin y\right)}{y}
double f(double x, double y) {
        double r602751 = x;
        double r602752 = cosh(r602751);
        double r602753 = y;
        double r602754 = sin(r602753);
        double r602755 = r602754 / r602753;
        double r602756 = r602752 * r602755;
        return r602756;
}
↓
double f(double x, double y) {
        double r602757 = 0.5;
        double r602758 = y;
        double r602759 = sin(r602758);
        double r602760 = x;
        double r602761 = exp(r602760);
        double r602762 = r602759 * r602761;
        double r602763 = r602757 * r602762;
        double r602764 = -1.0;
        double r602765 = r602764 * r602760;
        double r602766 = exp(r602765);
        double r602767 = r602766 * r602759;
        double r602768 = r602757 * r602767;
        double r602769 = r602763 + r602768;
        double r602770 = r602769 / r602758;
        return r602770;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Using strategy rm

  5. Applied div-inv0.3

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

  6. Applied associate-/r*0.3

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

  7. Taylor expanded around inf 0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020100 +o rules:numerics
(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)))