Average Error: 13.5 → 0.1
Time: 4.3s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\frac{1}{\frac{x}{\sin x}} \cdot \sinh y\]
\frac{\sin x \cdot \sinh y}{x}
↓
\frac{1}{\frac{x}{\sin x}} \cdot \sinh y
double f(double x, double y) {
        double r509034 = x;
        double r509035 = sin(r509034);
        double r509036 = y;
        double r509037 = sinh(r509036);
        double r509038 = r509035 * r509037;
        double r509039 = r509038 / r509034;
        return r509039;
}
↓
double f(double x, double y) {
        double r509040 = 1.0;
        double r509041 = x;
        double r509042 = sin(r509041);
        double r509043 = r509041 / r509042;
        double r509044 = r509040 / r509043;
        double r509045 = y;
        double r509046 = sinh(r509045);
        double r509047 = r509044 * r509046;
        return r509047;
}

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

Original13.5
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.5

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

  3. Applied associate-/l*0.6

    \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{\sinh y}}}\]
  4. Using strategy rm

  5. Applied associate-/r/0.1

    \[\leadsto \color{blue}{\frac{\sin x}{x} \cdot \sinh y}\]
  6. Using strategy rm

  7. Applied clear-num0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020034 
(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))