Average Error: 0.1 → 0.4
Time: 5.6s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y
double f(double x, double y, double z) {
        double r196592 = x;
        double r196593 = y;
        double r196594 = cos(r196593);
        double r196595 = r196592 * r196594;
        double r196596 = z;
        double r196597 = sin(r196593);
        double r196598 = r196596 * r196597;
        double r196599 = r196595 - r196598;
        return r196599;
}
↓
double f(double x, double y, double z) {
        double r196600 = x;
        double r196601 = y;
        double r196602 = cos(r196601);
        double r196603 = cbrt(r196602);
        double r196604 = r196603 * r196603;
        double r196605 = r196600 * r196604;
        double r196606 = r196605 * r196603;
        double r196607 = z;
        double r196608 = sin(r196601);
        double r196609 = r196607 * r196608;
        double r196610 = r196606 - r196609;
        return r196610;
}

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-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  5. Final simplification0.4

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

Reproduce

herbie shell --seed 2020083 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))