Average Error: 0.1 → 0.2
Time: 16.2s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot {\left({\left({\left(\cos y\right)}^{2}\right)}^{\frac{2}{3}} \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot {\left({\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}
double f(double x, double y, double z) {
        double r167907 = x;
        double r167908 = y;
        double r167909 = sin(r167908);
        double r167910 = r167907 * r167909;
        double r167911 = z;
        double r167912 = cos(r167908);
        double r167913 = r167911 * r167912;
        double r167914 = r167910 + r167913;
        return r167914;
}
↓
double f(double x, double y, double z) {
        double r167915 = x;
        double r167916 = y;
        double r167917 = sin(r167916);
        double r167918 = r167915 * r167917;
        double r167919 = z;
        double r167920 = cos(r167916);
        double r167921 = 2.0;
        double r167922 = pow(r167920, r167921);
        double r167923 = 0.6666666666666666;
        double r167924 = pow(r167922, r167923);
        double r167925 = cbrt(r167922);
        double r167926 = r167924 * r167925;
        double r167927 = 0.3333333333333333;
        double r167928 = pow(r167926, r167927);
        double r167929 = r167919 * r167928;
        double r167930 = cbrt(r167920);
        double r167931 = r167929 * r167930;
        double r167932 = r167918 + r167931;
        return r167932;
}

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

    \[x \cdot \sin y + z \cdot \cos y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied pow1/316.5

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

  7. Applied pow1/316.5

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

  8. Applied pow-prod-down0.2

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

  9. Simplified0.2

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

  11. Applied add-cube-cbrt0.3

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

  12. Simplified0.2

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

  13. Final simplification0.2

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

Reproduce

herbie shell --seed 2019212 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))