Average Error: 0.1 → 0.2
Time: 23.7s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(x \cdot {\left(\sqrt{\sqrt[3]{{\left(\cos y\right)}^{6}}} \cdot \sqrt{\sqrt[3]{{\left(\cos y\right)}^{6}}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(x \cdot {\left(\sqrt{\sqrt[3]{{\left(\cos y\right)}^{6}}} \cdot \sqrt{\sqrt[3]{{\left(\cos y\right)}^{6}}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y
double f(double x, double y, double z) {
        double r175351 = x;
        double r175352 = y;
        double r175353 = cos(r175352);
        double r175354 = r175351 * r175353;
        double r175355 = z;
        double r175356 = sin(r175352);
        double r175357 = r175355 * r175356;
        double r175358 = r175354 + r175357;
        return r175358;
}
↓
double f(double x, double y, double z) {
        double r175359 = x;
        double r175360 = y;
        double r175361 = cos(r175360);
        double r175362 = 6.0;
        double r175363 = pow(r175361, r175362);
        double r175364 = cbrt(r175363);
        double r175365 = sqrt(r175364);
        double r175366 = r175365 * r175365;
        double r175367 = 0.3333333333333333;
        double r175368 = pow(r175366, r175367);
        double r175369 = r175359 * r175368;
        double r175370 = cbrt(r175361);
        double r175371 = r175369 * r175370;
        double r175372 = z;
        double r175373 = sin(r175360);
        double r175374 = r175372 * r175373;
        double r175375 = r175371 + r175374;
        return r175375;
}

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

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

  3. Applied add-cube-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied pow1/316.3

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

  7. Applied pow1/316.2

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

  8. Applied pow-prod-down0.2

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

  9. Simplified0.2

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

  11. Applied add-cbrt-cube0.2

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

  12. Simplified0.2

    \[\leadsto \left(x \cdot {\left(\sqrt[3]{\color{blue}{{\left(\cos y\right)}^{6}}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
  13. Using strategy rm

  14. Applied add-sqr-sqrt0.2

    \[\leadsto \left(x \cdot {\color{blue}{\left(\sqrt{\sqrt[3]{{\left(\cos y\right)}^{6}}} \cdot \sqrt{\sqrt[3]{{\left(\cos y\right)}^{6}}}\right)}}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]

  15. Final simplification0.2

    \[\leadsto \left(x \cdot {\left(\sqrt{\sqrt[3]{{\left(\cos y\right)}^{6}}} \cdot \sqrt{\sqrt[3]{{\left(\cos y\right)}^{6}}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]

Reproduce

herbie shell --seed 2019323 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))