Average Error: 0.1 → 0.1
Time: 5.0s
Precision: 64
\[\left(x + \sin y\right) + z \cdot \cos y\]
↓
\[\left(x + \sin y\right) + \left(z \cdot {\left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}} \cdot {\left(\sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{3}}\right)}^{\frac{1}{3}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]
\left(x + \sin y\right) + z \cdot \cos y
↓
\left(x + \sin y\right) + \left(z \cdot {\left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}} \cdot {\left(\sqrt[3]{{\left({\left(\cos y\right)}^{2}\right)}^{3}}\right)}^{\frac{1}{3}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r192300 = x;
        double r192301 = y;
        double r192302 = sin(r192301);
        double r192303 = r192300 + r192302;
        double r192304 = z;
        double r192305 = cos(r192301);
        double r192306 = r192304 * r192305;
        double r192307 = r192303 + r192306;
        return r192307;
}
↓
double f(double x, double y, double z) {
        double r192308 = x;
        double r192309 = y;
        double r192310 = sin(r192309);
        double r192311 = r192308 + r192310;
        double r192312 = z;
        double r192313 = cos(r192309);
        double r192314 = 2.0;
        double r192315 = pow(r192313, r192314);
        double r192316 = 0.6666666666666666;
        double r192317 = pow(r192315, r192316);
        double r192318 = 3.0;
        double r192319 = pow(r192315, r192318);
        double r192320 = cbrt(r192319);
        double r192321 = 0.3333333333333333;
        double r192322 = pow(r192320, r192321);
        double r192323 = r192317 * r192322;
        double r192324 = pow(r192323, r192321);
        double r192325 = r192312 * r192324;
        double r192326 = cbrt(r192313);
        double r192327 = r192325 * r192326;
        double r192328 = r192311 + r192327;
        return r192328;
}

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 pow1/316.4

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

  7. Applied pow1/316.4

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

  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-cube-cbrt0.2

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

  12. Simplified0.1

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

  13. Simplified0.1

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

  15. Applied add-cbrt-cube0.1

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

  16. Simplified0.1

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

  17. Final simplification0.1

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

Reproduce

herbie shell --seed 2020021 
(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))))