Average Error: 0.1 → 0.4
Time: 4.9s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot \left(\left(\sqrt[3]{\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right) \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot \left(\left(\sqrt[3]{\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}} \cdot \sqrt[3]{\sqrt[3]{\cos y}}\right) \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 r265052 = x;
        double r265053 = y;
        double r265054 = cos(r265053);
        double r265055 = r265052 * r265054;
        double r265056 = z;
        double r265057 = sin(r265053);
        double r265058 = r265056 * r265057;
        double r265059 = r265055 - r265058;
        return r265059;
}
↓
double f(double x, double y, double z) {
        double r265060 = x;
        double r265061 = y;
        double r265062 = cos(r265061);
        double r265063 = cbrt(r265062);
        double r265064 = r265063 * r265063;
        double r265065 = cbrt(r265064);
        double r265066 = cbrt(r265063);
        double r265067 = r265065 * r265066;
        double r265068 = r265067 * r265063;
        double r265069 = r265060 * r265068;
        double r265070 = r265069 * r265063;
        double r265071 = z;
        double r265072 = sin(r265061);
        double r265073 = r265071 * r265072;
        double r265074 = r265070 - r265073;
        return r265074;
}

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. Using strategy rm

  6. Applied add-cube-cbrt0.4

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

  7. Applied cbrt-prod0.4

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

  8. Final simplification0.4

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

Reproduce

herbie shell --seed 2020056 
(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))))