Average Error: 13.7 → 0.1
Time: 4.2s
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 r536119 = x;
        double r536120 = sin(r536119);
        double r536121 = y;
        double r536122 = sinh(r536121);
        double r536123 = r536120 * r536122;
        double r536124 = r536123 / r536119;
        return r536124;
}
↓
double f(double x, double y) {
        double r536125 = 1.0;
        double r536126 = x;
        double r536127 = sin(r536126);
        double r536128 = r536126 / r536127;
        double r536129 = r536125 / r536128;
        double r536130 = y;
        double r536131 = sinh(r536130);
        double r536132 = r536129 * r536131;
        return r536132;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Target

Original13.7
Target0.3
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.7

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

  3. Applied associate-/l*0.8

    \[\leadsto \color{blue}{\frac{\sin x}{\frac{x}{\sinh y}}}\]
  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 2020003 
(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))