Average Error: 0.0 → 0.0
Time: 22.2s
Precision: 64
\[\cos x \cdot \frac{\sinh y}{y}\]
↓
\[\cos x \cdot e^{\log \left(\frac{\sinh y}{y}\right)}\]
\cos x \cdot \frac{\sinh y}{y}
↓
\cos x \cdot e^{\log \left(\frac{\sinh y}{y}\right)}
double f(double x, double y) {
        double r110692 = x;
        double r110693 = cos(r110692);
        double r110694 = y;
        double r110695 = sinh(r110694);
        double r110696 = r110695 / r110694;
        double r110697 = r110693 * r110696;
        return r110697;
}
↓
double f(double x, double y) {
        double r110698 = x;
        double r110699 = cos(r110698);
        double r110700 = y;
        double r110701 = sinh(r110700);
        double r110702 = r110701 / r110700;
        double r110703 = log(r110702);
        double r110704 = exp(r110703);
        double r110705 = r110699 * r110704;
        return r110705;
}

Error

Bits error versus x

Bits error versus y

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Results

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Derivation

  1. Initial program 0.0

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

  3. Applied add-exp-log35.1

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

  4. Applied add-exp-log32.3

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

  5. Applied div-exp32.3

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

  6. Simplified0.0

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

  7. Final simplification0.0

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

Reproduce

herbie shell --seed 2019350 +o rules:numerics
(FPCore (x y)
  :name "Linear.Quaternion:$csin from linear-1.19.1.3"
  :precision binary64
  (* (cos x) (/ (sinh y) y)))