Average Error: 0.0 → 0.1
Time: 7.2s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \left(\left(\sqrt[3]{\sqrt{\frac{\sinh y}{y}}} \cdot \sqrt[3]{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt[3]{\sqrt{\frac{\sinh y}{y}}}\right)\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \left(\left(\sqrt[3]{\sqrt{\frac{\sinh y}{y}}} \cdot \sqrt[3]{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt[3]{\sqrt{\frac{\sinh y}{y}}}\right)
double f(double x, double y) {
        double r132538 = x;
        double r132539 = sin(r132538);
        double r132540 = y;
        double r132541 = sinh(r132540);
        double r132542 = r132541 / r132540;
        double r132543 = r132539 * r132542;
        return r132543;
}
↓
double f(double x, double y) {
        double r132544 = x;
        double r132545 = sin(r132544);
        double r132546 = y;
        double r132547 = sinh(r132546);
        double r132548 = r132547 / r132546;
        double r132549 = sqrt(r132548);
        double r132550 = r132545 * r132549;
        double r132551 = cbrt(r132549);
        double r132552 = r132551 * r132551;
        double r132553 = r132552 * r132551;
        double r132554 = r132550 * r132553;
        return r132554;
}

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

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))