Average Error: 0.1 → 0.4
Time: 18.6s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[z \cdot \sin y + \sqrt[3]{\cos y} \cdot \left(\left(x \cdot \sqrt[3]{\cos y}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot \left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right)\right)\right)\]
x \cdot \cos y + z \cdot \sin y
↓
z \cdot \sin y + \sqrt[3]{\cos y} \cdot \left(\left(x \cdot \sqrt[3]{\cos y}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot \left(\sqrt[3]{\sqrt[3]{\cos y}} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right)\right)\right)
double f(double x, double y, double z) {
        double r190672 = x;
        double r190673 = y;
        double r190674 = cos(r190673);
        double r190675 = r190672 * r190674;
        double r190676 = z;
        double r190677 = sin(r190673);
        double r190678 = r190676 * r190677;
        double r190679 = r190675 + r190678;
        return r190679;
}
↓
double f(double x, double y, double z) {
        double r190680 = z;
        double r190681 = y;
        double r190682 = sin(r190681);
        double r190683 = r190680 * r190682;
        double r190684 = cos(r190681);
        double r190685 = cbrt(r190684);
        double r190686 = x;
        double r190687 = r190686 * r190685;
        double r190688 = cbrt(r190685);
        double r190689 = r190688 * r190688;
        double r190690 = r190688 * r190689;
        double r190691 = r190687 * r190690;
        double r190692 = r190685 * r190691;
        double r190693 = r190683 + r190692;
        return r190693;
}

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. Simplified0.4

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

  7. Applied add-cube-cbrt0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2019179 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))