Average Error: 0.1 → 0.1
Time: 4.6s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\sin x \cdot e^{\log \left(\frac{\sinh y}{y}\right)}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\sin x \cdot e^{\log \left(\frac{\sinh y}{y}\right)}
double f(double x, double y) {
        double r122652 = x;
        double r122653 = sin(r122652);
        double r122654 = y;
        double r122655 = sinh(r122654);
        double r122656 = r122655 / r122654;
        double r122657 = r122653 * r122656;
        return r122657;
}
↓
double f(double x, double y) {
        double r122658 = x;
        double r122659 = sin(r122658);
        double r122660 = y;
        double r122661 = sinh(r122660);
        double r122662 = r122661 / r122660;
        double r122663 = log(r122662);
        double r122664 = exp(r122663);
        double r122665 = r122659 * r122664;
        return r122665;
}

Error

Bits error versus x

Bits error versus y

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Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  3. Applied add-exp-log34.8

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

  4. Applied add-exp-log32.0

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

  5. Applied div-exp32.0

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))