Average Error: 0.1 → 0.2
Time: 4.9s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(x \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \log \left(e^{\sqrt[3]{\cos y}}\right) + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(x \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \log \left(e^{\sqrt[3]{\cos y}}\right) + z \cdot \sin y
double f(double x, double y, double z) {
        double r176340 = x;
        double r176341 = y;
        double r176342 = cos(r176341);
        double r176343 = r176340 * r176342;
        double r176344 = z;
        double r176345 = sin(r176341);
        double r176346 = r176344 * r176345;
        double r176347 = r176343 + r176346;
        return r176347;
}
↓
double f(double x, double y, double z) {
        double r176348 = x;
        double r176349 = y;
        double r176350 = cos(r176349);
        double r176351 = 2.0;
        double r176352 = pow(r176350, r176351);
        double r176353 = 0.3333333333333333;
        double r176354 = pow(r176352, r176353);
        double r176355 = r176348 * r176354;
        double r176356 = cbrt(r176350);
        double r176357 = exp(r176356);
        double r176358 = log(r176357);
        double r176359 = r176355 * r176358;
        double r176360 = z;
        double r176361 = sin(r176349);
        double r176362 = r176360 * r176361;
        double r176363 = r176359 + r176362;
        return r176363;
}

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 pow1/316.5

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

  7. Applied pow1/316.5

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

  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-exp0.2

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

  12. Final simplification0.2

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

Reproduce

herbie shell --seed 2020003 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))