Average Error: 0.1 → 0.2
Time: 14.7s
Precision: 64
\[\left(x + \sin y\right) + z \cdot \cos y\]
↓
\[\left(x + \sin y\right) + \left(\left(\sqrt{\sqrt[3]{{\left(\cos y\right)}^{2}}} \cdot z\right) \cdot \sqrt{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y}\]
\left(x + \sin y\right) + z \cdot \cos y
↓
\left(x + \sin y\right) + \left(\left(\sqrt{\sqrt[3]{{\left(\cos y\right)}^{2}}} \cdot z\right) \cdot \sqrt{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r243280 = x;
        double r243281 = y;
        double r243282 = sin(r243281);
        double r243283 = r243280 + r243282;
        double r243284 = z;
        double r243285 = cos(r243281);
        double r243286 = r243284 * r243285;
        double r243287 = r243283 + r243286;
        return r243287;
}
↓
double f(double x, double y, double z) {
        double r243288 = x;
        double r243289 = y;
        double r243290 = sin(r243289);
        double r243291 = r243288 + r243290;
        double r243292 = cos(r243289);
        double r243293 = 2.0;
        double r243294 = pow(r243292, r243293);
        double r243295 = cbrt(r243294);
        double r243296 = sqrt(r243295);
        double r243297 = z;
        double r243298 = r243296 * r243297;
        double r243299 = 0.3333333333333333;
        double r243300 = pow(r243294, r243299);
        double r243301 = sqrt(r243300);
        double r243302 = r243298 * r243301;
        double r243303 = cbrt(r243292);
        double r243304 = r243302 * r243303;
        double r243305 = r243291 + r243304;
        return r243305;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(x + \sin y\right) + z \cdot \cos y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.3

    \[\leadsto \left(x + \sin y\right) + z \cdot \color{blue}{\left(\left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{\cos y}\right)}\]

  4. Applied associate-*r*0.3

    \[\leadsto \left(x + \sin y\right) + \color{blue}{\left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}}\]
  5. Using strategy rm

  6. Applied pow1/316.1

    \[\leadsto \left(x + \sin y\right) + \left(z \cdot \left(\sqrt[3]{\cos y} \cdot \color{blue}{{\left(\cos y\right)}^{\frac{1}{3}}}\right)\right) \cdot \sqrt[3]{\cos y}\]

  7. Applied pow1/316.1

    \[\leadsto \left(x + \sin y\right) + \left(z \cdot \left(\color{blue}{{\left(\cos y\right)}^{\frac{1}{3}}} \cdot {\left(\cos y\right)}^{\frac{1}{3}}\right)\right) \cdot \sqrt[3]{\cos y}\]

  8. Applied pow-prod-down0.1

    \[\leadsto \left(x + \sin y\right) + \left(z \cdot \color{blue}{{\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y}\]

  9. Simplified0.1

    \[\leadsto \left(x + \sin y\right) + \left(z \cdot {\color{blue}{\left({\left(\cos y\right)}^{2}\right)}}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]
  10. Using strategy rm

  11. Applied add-sqr-sqrt0.2

    \[\leadsto \left(x + \sin y\right) + \left(z \cdot \color{blue}{\left(\sqrt{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}} \cdot \sqrt{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right)}\right) \cdot \sqrt[3]{\cos y}\]

  12. Applied associate-*r*0.2

    \[\leadsto \left(x + \sin y\right) + \color{blue}{\left(\left(z \cdot \sqrt{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right) \cdot \sqrt{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right)} \cdot \sqrt[3]{\cos y}\]

  13. Simplified0.2

    \[\leadsto \left(x + \sin y\right) + \left(\color{blue}{\left(\sqrt{\sqrt[3]{{\left(\cos y\right)}^{2}}} \cdot z\right)} \cdot \sqrt{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y}\]

  14. Final simplification0.2

    \[\leadsto \left(x + \sin y\right) + \left(\left(\sqrt{\sqrt[3]{{\left(\cos y\right)}^{2}}} \cdot z\right) \cdot \sqrt{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y}\]

Reproduce

herbie shell --seed 2020042 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))