Average Error: 0.0 → 0.1
Time: 16.2s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sin x \cdot \left(\left(\sqrt[3]{\sqrt{\frac{\sinh y}{y}}} \cdot \sqrt[3]{\sqrt{\frac{\sinh y}{y}}}\right) \cdot \sqrt[3]{\sqrt{\frac{\sinh y}{y}}}\right)\right) \cdot \sqrt{\frac{\sinh y}{y}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\sin x \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)\right) \cdot \sqrt{\frac{\sinh y}{y}}
double f(double x, double y) {
        double r172470 = x;
        double r172471 = sin(r172470);
        double r172472 = y;
        double r172473 = sinh(r172472);
        double r172474 = r172473 / r172472;
        double r172475 = r172471 * r172474;
        return r172475;
}
↓
double f(double x, double y) {
        double r172476 = x;
        double r172477 = sin(r172476);
        double r172478 = y;
        double r172479 = sinh(r172478);
        double r172480 = r172479 / r172478;
        double r172481 = sqrt(r172480);
        double r172482 = cbrt(r172481);
        double r172483 = r172482 * r172482;
        double r172484 = r172483 * r172482;
        double r172485 = r172477 * r172484;
        double r172486 = r172485 * r172481;
        return r172486;
}

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

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

  7. Final simplification0.1

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

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)))