Average Error: 14.4 → 0.2
Time: 4.6s
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 r489920 = x;
        double r489921 = sin(r489920);
        double r489922 = y;
        double r489923 = sinh(r489922);
        double r489924 = r489921 * r489923;
        double r489925 = r489924 / r489920;
        return r489925;
}
↓
double f(double x, double y) {
        double r489926 = x;
        double r489927 = sin(r489926);
        double r489928 = y;
        double r489929 = sinh(r489928);
        double r489930 = r489929 / r489926;
        double r489931 = r489927 * r489930;
        return r489931;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.4
Target0.2
Herbie0.2
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.4

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

  3. Applied *-un-lft-identity14.4

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

  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 2020046 +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))