Average Error: 0.1 → 0.3
Time: 20.9s
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 r175540 = x;
        double r175541 = y;
        double r175542 = sin(r175541);
        double r175543 = r175540 * r175542;
        double r175544 = z;
        double r175545 = cos(r175541);
        double r175546 = r175544 * r175545;
        double r175547 = r175543 + r175546;
        return r175547;
}
↓
double f(double x, double y, double z) {
        double r175548 = x;
        double r175549 = y;
        double r175550 = sin(r175549);
        double r175551 = r175548 * r175550;
        double r175552 = z;
        double r175553 = cos(r175549);
        double r175554 = 2.0;
        double r175555 = pow(r175553, r175554);
        double r175556 = cbrt(r175555);
        double r175557 = r175552 * r175556;
        double r175558 = cbrt(r175553);
        double r175559 = r175557 * r175558;
        double r175560 = r175551 + r175559;
        return r175560;
}

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))))