Average Error: 0.1 → 0.2
Time: 23.4s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left({\left(\sqrt{\cos y \cdot \cos y}\right)}^{\frac{1}{3}} \cdot \left(z \cdot {\left(\sqrt{\cos y \cdot \cos y}\right)}^{\frac{1}{3}}\right)\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left({\left(\sqrt{\cos y \cdot \cos y}\right)}^{\frac{1}{3}} \cdot \left(z \cdot {\left(\sqrt{\cos y \cdot \cos y}\right)}^{\frac{1}{3}}\right)\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r19814828 = x;
        double r19814829 = y;
        double r19814830 = sin(r19814829);
        double r19814831 = r19814828 * r19814830;
        double r19814832 = z;
        double r19814833 = cos(r19814829);
        double r19814834 = r19814832 * r19814833;
        double r19814835 = r19814831 + r19814834;
        return r19814835;
}
↓
double f(double x, double y, double z) {
        double r19814836 = x;
        double r19814837 = y;
        double r19814838 = sin(r19814837);
        double r19814839 = r19814836 * r19814838;
        double r19814840 = cos(r19814837);
        double r19814841 = r19814840 * r19814840;
        double r19814842 = sqrt(r19814841);
        double r19814843 = 0.3333333333333333;
        double r19814844 = pow(r19814842, r19814843);
        double r19814845 = z;
        double r19814846 = r19814845 * r19814844;
        double r19814847 = r19814844 * r19814846;
        double r19814848 = cbrt(r19814840);
        double r19814849 = r19814847 * r19814848;
        double r19814850 = r19814839 + r19814849;
        return r19814850;
}

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 pow1/315.4

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

  7. Applied pow1/315.4

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

  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. Using strategy rm

  10. Applied add-sqr-sqrt0.2

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

  11. Applied unpow-prod-down0.2

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

  12. Applied associate-*r*0.2

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

  13. Final simplification0.2

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

Reproduce

herbie shell --seed 2019158 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))