Average Error: 0.1 → 0.2
Time: 17.7s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r137419 = x;
        double r137420 = y;
        double r137421 = sin(r137420);
        double r137422 = r137419 * r137421;
        double r137423 = z;
        double r137424 = cos(r137420);
        double r137425 = r137423 * r137424;
        double r137426 = r137422 + r137425;
        return r137426;
}
↓
double f(double x, double y, double z) {
        double r137427 = x;
        double r137428 = y;
        double r137429 = sin(r137428);
        double r137430 = r137427 * r137429;
        double r137431 = z;
        double r137432 = cos(r137428);
        double r137433 = 2.0;
        double r137434 = pow(r137432, r137433);
        double r137435 = 0.3333333333333333;
        double r137436 = pow(r137434, r137435);
        double r137437 = r137431 * r137436;
        double r137438 = cbrt(r137432);
        double r137439 = r137437 * r137438;
        double r137440 = r137430 + r137439;
        return r137440;
}

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. Using strategy rm

  9. Applied pow1/30.2

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

  10. Final simplification0.2

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

Reproduce

herbie shell --seed 2019195 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))