Average Error: 13.5 → 0.2
Time: 25.5s
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 r553973 = x;
        double r553974 = sin(r553973);
        double r553975 = y;
        double r553976 = sinh(r553975);
        double r553977 = r553974 * r553976;
        double r553978 = r553977 / r553973;
        return r553978;
}
↓
double f(double x, double y) {
        double r553979 = x;
        double r553980 = sin(r553979);
        double r553981 = y;
        double r553982 = sinh(r553981);
        double r553983 = r553982 / r553979;
        double r553984 = r553980 * r553983;
        return r553984;
}

Error

Bits error versus x

Bits error versus y

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Results

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Target

Original13.5
Target0.2
Herbie0.2
\[\sin x \cdot \frac{\sinh y}{x}\]

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-frac0.2

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

  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 2020043 +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))