Average Error: 0.1 → 0.7
Time: 15.3s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \left(z \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}} \cdot \sqrt[3]{\sqrt[3]{\sin y}}\right)\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \left(z \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}} \cdot \sqrt[3]{\sqrt[3]{\sin y}}\right)
double f(double x, double y, double z) {
        double r184405 = x;
        double r184406 = y;
        double r184407 = cos(r184406);
        double r184408 = r184405 * r184407;
        double r184409 = z;
        double r184410 = sin(r184406);
        double r184411 = r184409 * r184410;
        double r184412 = r184408 - r184411;
        return r184412;
}
↓
double f(double x, double y, double z) {
        double r184413 = x;
        double r184414 = y;
        double r184415 = cos(r184414);
        double r184416 = r184413 * r184415;
        double r184417 = z;
        double r184418 = sin(r184414);
        double r184419 = cbrt(r184418);
        double r184420 = r184419 * r184419;
        double r184421 = r184417 * r184420;
        double r184422 = cbrt(r184420);
        double r184423 = cbrt(r184419);
        double r184424 = r184422 * r184423;
        double r184425 = r184421 * r184424;
        double r184426 = r184416 - r184425;
        return r184426;
}

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

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

  4. Applied associate-*r*0.6

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

  6. Applied add-cube-cbrt0.6

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

  7. Applied cbrt-prod0.7

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

  8. Final simplification0.7

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

Reproduce

herbie shell --seed 2019298 
(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))))