Average Error: 14.0 → 0.1
Time: 14.1s
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 r446181 = x;
        double r446182 = sin(r446181);
        double r446183 = y;
        double r446184 = sinh(r446183);
        double r446185 = r446182 * r446184;
        double r446186 = r446185 / r446181;
        return r446186;
}
↓
double f(double x, double y) {
        double r446187 = y;
        double r446188 = sinh(r446187);
        double r446189 = x;
        double r446190 = sin(r446189);
        double r446191 = r446189 / r446190;
        double r446192 = r446188 / r446191;
        return r446192;
}

Error

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Bits error versus y

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Results

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Target

Original14.0
Target0.2
Herbie0.1
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.0

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

  2. Simplified0.1

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

  4. Applied clear-num0.1

    \[\leadsto \sinh y \cdot \color{blue}{\frac{1}{\frac{x}{\sin x}}}\]
  5. Using strategy rm

  6. Applied un-div-inv0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019179 +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))