Average Error: 14.6 → 0.2
Time: 12.2s
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 r587887 = x;
        double r587888 = sin(r587887);
        double r587889 = y;
        double r587890 = sinh(r587889);
        double r587891 = r587888 * r587890;
        double r587892 = r587891 / r587887;
        return r587892;
}
↓
double f(double x, double y) {
        double r587893 = x;
        double r587894 = sin(r587893);
        double r587895 = y;
        double r587896 = sinh(r587895);
        double r587897 = r587896 / r587893;
        double r587898 = r587894 * r587897;
        return r587898;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original14.6
Target0.2
Herbie0.2
\[\sin x \cdot \frac{\sinh y}{x}\]

Derivation

  1. Initial program 14.6

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

  3. Applied *-un-lft-identity14.6

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

  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 2020047 +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))