Average Error: 0.0 → 0.1
Time: 19.0s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[e^{\log \left(\frac{\sinh y}{y}\right)} \cdot \sin x\]
\sin x \cdot \frac{\sinh y}{y}
↓
e^{\log \left(\frac{\sinh y}{y}\right)} \cdot \sin x
double f(double x, double y) {
        double r105976 = x;
        double r105977 = sin(r105976);
        double r105978 = y;
        double r105979 = sinh(r105978);
        double r105980 = r105979 / r105978;
        double r105981 = r105977 * r105980;
        return r105981;
}
↓
double f(double x, double y) {
        double r105982 = y;
        double r105983 = sinh(r105982);
        double r105984 = r105983 / r105982;
        double r105985 = log(r105984);
        double r105986 = exp(r105985);
        double r105987 = x;
        double r105988 = sin(r105987);
        double r105989 = r105986 * r105988;
        return r105989;
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.0

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

  3. Applied add-exp-log34.5

    \[\leadsto \sin x \cdot \frac{\sinh y}{\color{blue}{e^{\log y}}}\]

  4. Applied add-exp-log31.7

    \[\leadsto \sin x \cdot \frac{\color{blue}{e^{\log \left(\sinh y\right)}}}{e^{\log y}}\]

  5. Applied div-exp31.7

    \[\leadsto \sin x \cdot \color{blue}{e^{\log \left(\sinh y\right) - \log y}}\]

  6. Simplified0.1

    \[\leadsto \sin x \cdot e^{\color{blue}{\log \left(\frac{\sinh y}{y}\right)}}\]

  7. Final simplification0.1

    \[\leadsto e^{\log \left(\frac{\sinh y}{y}\right)} \cdot \sin x\]

Reproduce

herbie shell --seed 2019196 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  (* (sin x) (/ (sinh y) y)))