Average Error: 13.9 → 0.2
Time: 27.4s
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 r320113 = x;
        double r320114 = sin(r320113);
        double r320115 = y;
        double r320116 = sinh(r320115);
        double r320117 = r320114 * r320116;
        double r320118 = r320117 / r320113;
        return r320118;
}
↓
double f(double x, double y) {
        double r320119 = x;
        double r320120 = sin(r320119);
        double r320121 = y;
        double r320122 = sinh(r320121);
        double r320123 = r320122 / r320119;
        double r320124 = r320120 * r320123;
        return r320124;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original13.9
Target0.2
Herbie0.2
\[\sin x \cdot \frac{\sinh y}{x}\]

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-frac0.2

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

  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 2019347 +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))