Average Error: 0.1 → 0.3
Time: 26.8s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(\sqrt[3]{{\left(\cos y\right)}^{2}} \cdot z\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(\sqrt[3]{{\left(\cos y\right)}^{2}} \cdot z\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r162882 = x;
        double r162883 = y;
        double r162884 = sin(r162883);
        double r162885 = r162882 * r162884;
        double r162886 = z;
        double r162887 = cos(r162883);
        double r162888 = r162886 * r162887;
        double r162889 = r162885 + r162888;
        return r162889;
}
↓
double f(double x, double y, double z) {
        double r162890 = x;
        double r162891 = y;
        double r162892 = sin(r162891);
        double r162893 = r162890 * r162892;
        double r162894 = cos(r162891);
        double r162895 = 2.0;
        double r162896 = pow(r162894, r162895);
        double r162897 = cbrt(r162896);
        double r162898 = z;
        double r162899 = r162897 * r162898;
        double r162900 = cbrt(r162894);
        double r162901 = r162899 * r162900;
        double r162902 = r162893 + r162901;
        return r162902;
}

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 pow1/316.0

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

  7. Applied pow1/316.0

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

  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 *-un-lft-identity0.2

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

  12. Applied associate-*l*0.2

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

  13. Simplified0.3

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

  14. Final simplification0.3

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

Reproduce

herbie shell --seed 2019303 
(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))))