Average Error: 0.0 → 0.1
Time: 6.1s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sin x \cdot \left(\left|\sqrt[3]{\frac{\sinh y}{y}}\right| \cdot \sqrt{\sqrt[3]{\frac{\sinh y}{y}}}\right)\right) \cdot \sqrt{\frac{\sinh y}{y}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\sin x \cdot \left(\left|\sqrt[3]{\frac{\sinh y}{y}}\right| \cdot \sqrt{\sqrt[3]{\frac{\sinh y}{y}}}\right)\right) \cdot \sqrt{\frac{\sinh y}{y}}
double f(double x, double y) {
        double r192620 = x;
        double r192621 = sin(r192620);
        double r192622 = y;
        double r192623 = sinh(r192622);
        double r192624 = r192623 / r192622;
        double r192625 = r192621 * r192624;
        return r192625;
}
↓
double f(double x, double y) {
        double r192626 = x;
        double r192627 = sin(r192626);
        double r192628 = y;
        double r192629 = sinh(r192628);
        double r192630 = r192629 / r192628;
        double r192631 = cbrt(r192630);
        double r192632 = fabs(r192631);
        double r192633 = sqrt(r192631);
        double r192634 = r192632 * r192633;
        double r192635 = r192627 * r192634;
        double r192636 = sqrt(r192630);
        double r192637 = r192635 * r192636;
        return r192637;
}

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-cube-cbrt0.1

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

  7. Applied sqrt-prod0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020001 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))