Average Error: 13.9 → 0.3
Time: 41.3s
Precision: 64
\[\frac{\sin x \cdot \sinh y}{x}\]
↓
\[\sin x \cdot \frac{\sinh y}{x}\]
\frac{\sin x \cdot \sinh y}{x}
↓
\sin x \cdot \frac{\sinh y}{x}
double f(double x, double y) {
        double r21386045 = x;
        double r21386046 = sin(r21386045);
        double r21386047 = y;
        double r21386048 = sinh(r21386047);
        double r21386049 = r21386046 * r21386048;
        double r21386050 = r21386049 / r21386045;
        return r21386050;
}
↓
double f(double x, double y) {
        double r21386051 = x;
        double r21386052 = sin(r21386051);
        double r21386053 = y;
        double r21386054 = sinh(r21386053);
        double r21386055 = r21386054 / r21386051;
        double r21386056 = r21386052 * r21386055;
        return r21386056;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

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

Derivation

  1. Initial program 13.9

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

  3. Applied *-un-lft-identity13.9

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

  4. Applied times-frac0.3

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

  5. Simplified0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019165 
(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))