Average Error: 0.1 → 0.6
Time: 8.3s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[x \cdot \cos y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)\]
x \cdot \cos y + z \cdot \sin y
↓
x \cdot \cos y + \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{z} \cdot \sin y\right)
double f(double x, double y, double z) {
        double r180557 = x;
        double r180558 = y;
        double r180559 = cos(r180558);
        double r180560 = r180557 * r180559;
        double r180561 = z;
        double r180562 = sin(r180558);
        double r180563 = r180561 * r180562;
        double r180564 = r180560 + r180563;
        return r180564;
}
↓
double f(double x, double y, double z) {
        double r180565 = x;
        double r180566 = y;
        double r180567 = cos(r180566);
        double r180568 = r180565 * r180567;
        double r180569 = z;
        double r180570 = cbrt(r180569);
        double r180571 = r180570 * r180570;
        double r180572 = sin(r180566);
        double r180573 = r180570 * r180572;
        double r180574 = r180571 * r180573;
        double r180575 = r180568 + r180574;
        return r180575;
}

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-cbrt0.6

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

  4. Applied associate-*l*0.6

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2019322 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))