Average Error: 14.3 → 0.2
Time: 32.0s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sin x \cdot \frac{\sinh y}{x}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sin x \cdot \frac{\sinh y}{x}
double f(double x, double y) {
        double r279112 = x;
        double r279113 = sin(r279112);
        double r279114 = y;
        double r279115 = sinh(r279114);
        double r279116 = r279113 * r279115;
        double r279117 = r279116 / r279112;
        return r279117;
}
↓
double f(double x, double y) {
        double r279118 = x;
        double r279119 = sin(r279118);
        double r279120 = y;
        double r279121 = sinh(r279120);
        double r279122 = r279121 / r279118;
        double r279123 = r279119 * r279122;
        return r279123;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original14.3
Target0.2
Herbie0.2
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.3

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

  3. Applied *-un-lft-identity14.3

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

  4. Applied times-frac0.2

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

  5. Simplified0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"
  :precision binary64

  :herbie-target
  (* (sin x) (/ (sinh y) x))

  (/ (* (sin x) (sinh y)) x))