Average Error: 0.0 → 0.1
Time: 6.4s
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 r132280 = x;
        double r132281 = sin(r132280);
        double r132282 = y;
        double r132283 = sinh(r132282);
        double r132284 = r132283 / r132282;
        double r132285 = r132281 * r132284;
        return r132285;
}
↓
double f(double x, double y) {
        double r132286 = x;
        double r132287 = sin(r132286);
        double r132288 = y;
        double r132289 = sinh(r132288);
        double r132290 = r132289 / r132288;
        double r132291 = sqrt(r132290);
        double r132292 = r132287 * r132291;
        double r132293 = 3.0;
        double r132294 = pow(r132291, r132293);
        double r132295 = cbrt(r132294);
        double r132296 = r132292 * r132295;
        return r132296;
}

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 2020036 
(FPCore (x y)
  :name "Linear.Quaternion:$ccos from linear-1.19.1.3"
  :precision binary64
  (* (sin x) (/ (sinh y) y)))