Average Error: 0.0 → 0.1
Time: 7.2s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sin x \cdot \sqrt[3]{{\left(\sqrt{\frac{\sinh y}{y}}\right)}^{3}}\right) \cdot \sqrt{\frac{\sinh y}{y}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\sin x \cdot \sqrt[3]{{\left(\sqrt{\frac{\sinh y}{y}}\right)}^{3}}\right) \cdot \sqrt{\frac{\sinh y}{y}}
double f(double x, double y) {
        double r121772 = x;
        double r121773 = sin(r121772);
        double r121774 = y;
        double r121775 = sinh(r121774);
        double r121776 = r121775 / r121774;
        double r121777 = r121773 * r121776;
        return r121777;
}
↓
double f(double x, double y) {
        double r121778 = x;
        double r121779 = sin(r121778);
        double r121780 = y;
        double r121781 = sinh(r121780);
        double r121782 = r121781 / r121780;
        double r121783 = sqrt(r121782);
        double r121784 = 3.0;
        double r121785 = pow(r121783, r121784);
        double r121786 = cbrt(r121785);
        double r121787 = r121779 * r121786;
        double r121788 = r121787 * r121783;
        return r121788;
}

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-sqr-sqrt0.0

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

  4. Applied associate-*r*0.0

    \[\leadsto \color{blue}{\left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\frac{\sinh y}{y}}}\]
  5. Using strategy rm

  6. Applied add-cbrt-cube0.1

    \[\leadsto \left(\sin x \cdot \color{blue}{\sqrt[3]{\left(\sqrt{\frac{\sinh y}{y}} \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt{\frac{\sinh y}{y}}}}\right) \cdot \sqrt{\frac{\sinh y}{y}}\]

  7. Simplified0.1

    \[\leadsto \left(\sin x \cdot \sqrt[3]{\color{blue}{{\left(\sqrt{\frac{\sinh y}{y}}\right)}^{3}}}\right) \cdot \sqrt{\frac{\sinh y}{y}}\]

  8. Final simplification0.1

    \[\leadsto \left(\sin x \cdot \sqrt[3]{{\left(\sqrt{\frac{\sinh y}{y}}\right)}^{3}}\right) \cdot \sqrt{\frac{\sinh y}{y}}\]

Reproduce

herbie shell --seed 2020036 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))