Average Error: 0.1 → 0.2
Time: 24.8s
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 r132604 = x;
        double r132605 = y;
        double r132606 = cos(r132605);
        double r132607 = r132604 * r132606;
        double r132608 = z;
        double r132609 = sin(r132605);
        double r132610 = r132608 * r132609;
        double r132611 = r132607 + r132610;
        return r132611;
}
↓
double f(double x, double y, double z) {
        double r132612 = x;
        double r132613 = y;
        double r132614 = cos(r132613);
        double r132615 = 6.0;
        double r132616 = pow(r132614, r132615);
        double r132617 = cbrt(r132616);
        double r132618 = sqrt(r132617);
        double r132619 = r132618 * r132618;
        double r132620 = 0.3333333333333333;
        double r132621 = pow(r132619, r132620);
        double r132622 = r132612 * r132621;
        double r132623 = cbrt(r132614);
        double r132624 = r132622 * r132623;
        double r132625 = z;
        double r132626 = sin(r132613);
        double r132627 = r132625 * r132626;
        double r132628 = r132624 + r132627;
        return r132628;
}

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))))