Average Error: 0.1 → 0.3
Time: 14.3s
Precision: 64
\[\cosh x \cdot \frac{\sin y}{y}\]
↓
\[\frac{\frac{\cosh x}{y}}{\frac{1}{\sin y}}\]
\cosh x \cdot \frac{\sin y}{y}
↓
\frac{\frac{\cosh x}{y}}{\frac{1}{\sin y}}
double f(double x, double y) {
        double r380328 = x;
        double r380329 = cosh(r380328);
        double r380330 = y;
        double r380331 = sin(r380330);
        double r380332 = r380331 / r380330;
        double r380333 = r380329 * r380332;
        return r380333;
}
↓
double f(double x, double y) {
        double r380334 = x;
        double r380335 = cosh(r380334);
        double r380336 = y;
        double r380337 = r380335 / r380336;
        double r380338 = 1.0;
        double r380339 = sin(r380336);
        double r380340 = r380338 / r380339;
        double r380341 = r380337 / r380340;
        return r380341;
}

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
Herbie0.3
\[\frac{\cosh x \cdot \sin y}{y}\]

Derivation

  1. Initial program 0.1

    \[\cosh x \cdot \frac{\sin y}{y}\]
  2. Using strategy rm

  3. Applied pow10.1

    \[\leadsto \cosh x \cdot \color{blue}{{\left(\frac{\sin y}{y}\right)}^{1}}\]

  4. Applied pow10.1

    \[\leadsto \color{blue}{{\left(\cosh x\right)}^{1}} \cdot {\left(\frac{\sin y}{y}\right)}^{1}\]

  5. Applied pow-prod-down0.1

    \[\leadsto \color{blue}{{\left(\cosh x \cdot \frac{\sin y}{y}\right)}^{1}}\]

  6. Simplified0.1

    \[\leadsto {\color{blue}{\left(\frac{\cosh x \cdot \sin y}{y}\right)}}^{1}\]
  7. Using strategy rm

  8. Applied associate-/l*0.2

    \[\leadsto {\color{blue}{\left(\frac{\cosh x}{\frac{y}{\sin y}}\right)}}^{1}\]
  9. Using strategy rm

  10. Applied div-inv0.3

    \[\leadsto {\left(\frac{\cosh x}{\color{blue}{y \cdot \frac{1}{\sin y}}}\right)}^{1}\]

  11. Applied associate-/r*0.3

    \[\leadsto {\color{blue}{\left(\frac{\frac{\cosh x}{y}}{\frac{1}{\sin y}}\right)}}^{1}\]

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019209 +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)))