Average Error: 0.1 → 0.2
Time: 25.7s
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 r134478 = x;
        double r134479 = y;
        double r134480 = cos(r134479);
        double r134481 = r134478 * r134480;
        double r134482 = z;
        double r134483 = sin(r134479);
        double r134484 = r134482 * r134483;
        double r134485 = r134481 + r134484;
        return r134485;
}
↓
double f(double x, double y, double z) {
        double r134486 = x;
        double r134487 = y;
        double r134488 = cos(r134487);
        double r134489 = 6.0;
        double r134490 = pow(r134488, r134489);
        double r134491 = cbrt(r134490);
        double r134492 = sqrt(r134491);
        double r134493 = r134492 * r134492;
        double r134494 = 0.3333333333333333;
        double r134495 = pow(r134493, r134494);
        double r134496 = r134486 * r134495;
        double r134497 = cbrt(r134488);
        double r134498 = r134496 * r134497;
        double r134499 = z;
        double r134500 = sin(r134487);
        double r134501 = r134499 * r134500;
        double r134502 = r134498 + r134501;
        return r134502;
}

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))))