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 r120403 = x;
        double r120404 = sin(r120403);
        double r120405 = y;
        double r120406 = sinh(r120405);
        double r120407 = r120406 / r120405;
        double r120408 = r120404 * r120407;
        return r120408;
}
↓
double f(double x, double y) {
        double r120409 = x;
        double r120410 = sin(r120409);
        double r120411 = y;
        double r120412 = sinh(r120411);
        double r120413 = r120412 / r120411;
        double r120414 = cbrt(r120413);
        double r120415 = fabs(r120414);
        double r120416 = sqrt(r120414);
        double r120417 = r120415 * r120416;
        double r120418 = r120410 * r120417;
        double r120419 = sqrt(r120413);
        double r120420 = r120418 * r120419;
        return r120420;
}

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)))