Average Error: 0.1 → 0.5
Time: 15.3s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\left(\sqrt[3]{x \cdot \sin y} \cdot \sqrt[3]{x \cdot \sin y}\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{\sin y}\right) + z \cdot \cos y\]
x \cdot \sin y + z \cdot \cos y
↓
\left(\sqrt[3]{x \cdot \sin y} \cdot \sqrt[3]{x \cdot \sin y}\right) \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{\sin y}\right) + z \cdot \cos y
double f(double x, double y, double z) {
        double r174825 = x;
        double r174826 = y;
        double r174827 = sin(r174826);
        double r174828 = r174825 * r174827;
        double r174829 = z;
        double r174830 = cos(r174826);
        double r174831 = r174829 * r174830;
        double r174832 = r174828 + r174831;
        return r174832;
}
↓
double f(double x, double y, double z) {
        double r174833 = x;
        double r174834 = y;
        double r174835 = sin(r174834);
        double r174836 = r174833 * r174835;
        double r174837 = cbrt(r174836);
        double r174838 = r174837 * r174837;
        double r174839 = cbrt(r174833);
        double r174840 = cbrt(r174835);
        double r174841 = r174839 * r174840;
        double r174842 = r174838 * r174841;
        double r174843 = z;
        double r174844 = cos(r174834);
        double r174845 = r174843 * r174844;
        double r174846 = r174842 + r174845;
        return r174846;
}

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

    \[x \cdot \sin y + z \cdot \cos y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.6

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

  5. Applied cbrt-prod0.5

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

  6. Final simplification0.5

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

Reproduce

herbie shell --seed 2019209 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))