Average Error: 14.1 → 0.3
Time: 4.2s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sin x \cdot \left(\sinh y \cdot \frac{1}{x}\right)\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sin x \cdot \left(\sinh y \cdot \frac{1}{x}\right)
double f(double x, double y) {
        double r560260 = x;
        double r560261 = sin(r560260);
        double r560262 = y;
        double r560263 = sinh(r560262);
        double r560264 = r560261 * r560263;
        double r560265 = r560264 / r560260;
        return r560265;
}
↓
double f(double x, double y) {
        double r560266 = x;
        double r560267 = sin(r560266);
        double r560268 = y;
        double r560269 = sinh(r560268);
        double r560270 = 1.0;
        double r560271 = r560270 / r560266;
        double r560272 = r560269 * r560271;
        double r560273 = r560267 * r560272;
        return r560273;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.1
Target0.2
Herbie0.3
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.1

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

  3. Applied *-un-lft-identity14.1

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

  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. Using strategy rm

  7. Applied div-inv0.3

    \[\leadsto \sin x \cdot \color{blue}{\left(\sinh y \cdot \frac{1}{x}\right)}\]

  8. Final simplification0.3

    \[\leadsto \sin x \cdot \left(\sinh y \cdot \frac{1}{x}\right)\]

Reproduce

herbie shell --seed 2020049 
(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))