Average Error: 0.1 → 0.2
Time: 1.1m
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}} \cdot z\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left({\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}} \cdot z\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r9773421 = x;
        double r9773422 = y;
        double r9773423 = sin(r9773422);
        double r9773424 = r9773421 * r9773423;
        double r9773425 = z;
        double r9773426 = cos(r9773422);
        double r9773427 = r9773425 * r9773426;
        double r9773428 = r9773424 + r9773427;
        return r9773428;
}
↓
double f(double x, double y, double z) {
        double r9773429 = x;
        double r9773430 = y;
        double r9773431 = sin(r9773430);
        double r9773432 = r9773429 * r9773431;
        double r9773433 = cos(r9773430);
        double r9773434 = r9773433 * r9773433;
        double r9773435 = 0.3333333333333333;
        double r9773436 = pow(r9773434, r9773435);
        double r9773437 = z;
        double r9773438 = r9773436 * r9773437;
        double r9773439 = cbrt(r9773433);
        double r9773440 = r9773438 * r9773439;
        double r9773441 = r9773432 + r9773440;
        return r9773441;
}

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. Using strategy rm

  6. Applied pow1/316.2

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

  7. Applied pow1/316.2

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

  8. Applied pow-prod-down0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019200 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))