Average Error: 0.1 → 0.6
Time: 41.3s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[x \cdot \cos y - \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sin y \cdot \sqrt[3]{z}\right)\]
x \cdot \cos y - z \cdot \sin y
↓
x \cdot \cos y - \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) \cdot \left(\sin y \cdot \sqrt[3]{z}\right)
double f(double x, double y, double z) {
        double r9830005 = x;
        double r9830006 = y;
        double r9830007 = cos(r9830006);
        double r9830008 = r9830005 * r9830007;
        double r9830009 = z;
        double r9830010 = sin(r9830006);
        double r9830011 = r9830009 * r9830010;
        double r9830012 = r9830008 - r9830011;
        return r9830012;
}
↓
double f(double x, double y, double z) {
        double r9830013 = x;
        double r9830014 = y;
        double r9830015 = cos(r9830014);
        double r9830016 = r9830013 * r9830015;
        double r9830017 = z;
        double r9830018 = cbrt(r9830017);
        double r9830019 = r9830018 * r9830018;
        double r9830020 = sin(r9830014);
        double r9830021 = r9830020 * r9830018;
        double r9830022 = r9830019 * r9830021;
        double r9830023 = r9830016 - r9830022;
        return r9830023;
}

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

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  (- (* x (cos y)) (* z (sin y))))