Average Error: 13.5 → 0.3
Time: 16.6s
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 r384953 = x;
        double r384954 = sin(r384953);
        double r384955 = y;
        double r384956 = sinh(r384955);
        double r384957 = r384954 * r384956;
        double r384958 = r384957 / r384953;
        return r384958;
}
↓
double f(double x, double y) {
        double r384959 = x;
        double r384960 = sin(r384959);
        double r384961 = y;
        double r384962 = sinh(r384961);
        double r384963 = r384962 / r384959;
        double r384964 = r384960 * r384963;
        return r384964;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original13.5
Target0.3
Herbie0.3
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 13.5

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

  3. Applied *-un-lft-identity13.5

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

  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 2019209 
(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))