Average Error: 13.9 → 0.1
Time: 45.7s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\frac{\sinh y}{\frac{x}{\sin x}}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\frac{\sinh y}{\frac{x}{\sin x}}
double f(double x, double y) {
        double r23594504 = x;
        double r23594505 = sin(r23594504);
        double r23594506 = y;
        double r23594507 = sinh(r23594506);
        double r23594508 = r23594505 * r23594507;
        double r23594509 = r23594508 / r23594504;
        return r23594509;
}
↓
double f(double x, double y) {
        double r23594510 = y;
        double r23594511 = sinh(r23594510);
        double r23594512 = x;
        double r23594513 = sin(r23594512);
        double r23594514 = r23594512 / r23594513;
        double r23594515 = r23594511 / r23594514;
        return r23594515;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original13.9
Target0.3
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.9

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

  2. Taylor expanded around inf 43.4

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

  3. Simplified0.1

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

  4. Final simplification0.1

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

Reproduce

herbie shell --seed 2019165 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccosh from linear-1.19.1.3"

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

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