Average Error: 14.5 → 0.2
Time: 31.2s
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 r394457 = x;
        double r394458 = sin(r394457);
        double r394459 = y;
        double r394460 = sinh(r394459);
        double r394461 = r394458 * r394460;
        double r394462 = r394461 / r394457;
        return r394462;
}
↓
double f(double x, double y) {
        double r394463 = x;
        double r394464 = sin(r394463);
        double r394465 = y;
        double r394466 = sinh(r394465);
        double r394467 = r394466 / r394463;
        double r394468 = r394464 * r394467;
        return r394468;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.5
Target0.2
Herbie0.2
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.5

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

  3. Applied *-un-lft-identity14.5

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

  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. Final simplification0.2

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(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))