Average Error: 0.0 → 0.1
Time: 26.7s
Precision: 64
\[\sin x \cdot \frac{\sinh y}{y}\]
↓
\[\left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt[3]{{\left(\sqrt{\frac{\sinh y}{y}}\right)}^{3}}\]
\sin x \cdot \frac{\sinh y}{y}
↓
\left(\sin x \cdot \sqrt{\frac{\sinh y}{y}}\right) \cdot \sqrt[3]{{\left(\sqrt{\frac{\sinh y}{y}}\right)}^{3}}
double f(double x, double y) {
        double r163465 = x;
        double r163466 = sin(r163465);
        double r163467 = y;
        double r163468 = sinh(r163467);
        double r163469 = r163468 / r163467;
        double r163470 = r163466 * r163469;
        return r163470;
}
↓
double f(double x, double y) {
        double r163471 = x;
        double r163472 = sin(r163471);
        double r163473 = y;
        double r163474 = sinh(r163473);
        double r163475 = r163474 / r163473;
        double r163476 = sqrt(r163475);
        double r163477 = r163472 * r163476;
        double r163478 = 3.0;
        double r163479 = pow(r163476, r163478);
        double r163480 = cbrt(r163479);
        double r163481 = r163477 * r163480;
        return r163481;
}

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

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))