Average Error: 0.1 → 0.3
Time: 19.5s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r157337 = x;
        double r157338 = y;
        double r157339 = sin(r157338);
        double r157340 = r157337 * r157339;
        double r157341 = z;
        double r157342 = cos(r157338);
        double r157343 = r157341 * r157342;
        double r157344 = r157340 + r157343;
        return r157344;
}
↓
double f(double x, double y, double z) {
        double r157345 = x;
        double r157346 = y;
        double r157347 = sin(r157346);
        double r157348 = r157345 * r157347;
        double r157349 = z;
        double r157350 = cos(r157346);
        double r157351 = 2.0;
        double r157352 = pow(r157350, r157351);
        double r157353 = cbrt(r157352);
        double r157354 = r157349 * r157353;
        double r157355 = cbrt(r157350);
        double r157356 = r157354 * r157355;
        double r157357 = r157348 + r157356;
        return r157357;
}

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

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

  3. Applied add-cube-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  5. Simplified0.4

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

  6. Taylor expanded around inf 0.2

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

  7. Simplified0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019194 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))