Average Error: 0.1 → 0.6
Time: 5.8s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\left(\sqrt[3]{x \cdot \sin y} \cdot \sqrt[3]{x \cdot \sin y}\right) \cdot \sqrt[3]{x \cdot \sin y} + z \cdot \cos y\]
x \cdot \sin y + z \cdot \cos y
↓
\left(\sqrt[3]{x \cdot \sin y} \cdot \sqrt[3]{x \cdot \sin y}\right) \cdot \sqrt[3]{x \cdot \sin y} + z \cdot \cos y
double f(double x, double y, double z) {
        double r201999 = x;
        double r202000 = y;
        double r202001 = sin(r202000);
        double r202002 = r201999 * r202001;
        double r202003 = z;
        double r202004 = cos(r202000);
        double r202005 = r202003 * r202004;
        double r202006 = r202002 + r202005;
        return r202006;
}
↓
double f(double x, double y, double z) {
        double r202007 = x;
        double r202008 = y;
        double r202009 = sin(r202008);
        double r202010 = r202007 * r202009;
        double r202011 = cbrt(r202010);
        double r202012 = r202011 * r202011;
        double r202013 = r202012 * r202011;
        double r202014 = z;
        double r202015 = cos(r202008);
        double r202016 = r202014 * r202015;
        double r202017 = r202013 + r202016;
        return r202017;
}

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. Final simplification0.6

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

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(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))))