Average Error: 0.1 → 0.3
Time: 5.2s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(x \cdot {\left(\log \left(e^{{\left(\cos y\right)}^{2}}\right)\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(x \cdot {\left(\log \left(e^{{\left(\cos y\right)}^{2}}\right)\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y
double f(double x, double y, double z) {
        double r226252 = x;
        double r226253 = y;
        double r226254 = cos(r226253);
        double r226255 = r226252 * r226254;
        double r226256 = z;
        double r226257 = sin(r226253);
        double r226258 = r226256 * r226257;
        double r226259 = r226255 + r226258;
        return r226259;
}
↓
double f(double x, double y, double z) {
        double r226260 = x;
        double r226261 = y;
        double r226262 = cos(r226261);
        double r226263 = 2.0;
        double r226264 = pow(r226262, r226263);
        double r226265 = exp(r226264);
        double r226266 = log(r226265);
        double r226267 = 0.3333333333333333;
        double r226268 = pow(r226266, r226267);
        double r226269 = r226260 * r226268;
        double r226270 = cbrt(r226262);
        double r226271 = r226269 * r226270;
        double r226272 = z;
        double r226273 = sin(r226261);
        double r226274 = r226272 * r226273;
        double r226275 = r226271 + r226274;
        return r226275;
}

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 pow1/316.2

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

  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-log-exp0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2020035 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))