Average Error: 0.1 → 0.6
Time: 5.5s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\left(\sqrt[3]{x \cdot \sin y} \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \sqrt[3]{x \cdot \sin y} + z \cdot \cos y\]
x \cdot \sin y + z \cdot \cos y
↓
\left(\sqrt[3]{x \cdot \sin y} \cdot \left(\sqrt[3]{x} \cdot \sqrt[3]{\sin y}\right)\right) \cdot \sqrt[3]{x \cdot \sin y} + z \cdot \cos y
double f(double x, double y, double z) {
        double r223001 = x;
        double r223002 = y;
        double r223003 = sin(r223002);
        double r223004 = r223001 * r223003;
        double r223005 = z;
        double r223006 = cos(r223002);
        double r223007 = r223005 * r223006;
        double r223008 = r223004 + r223007;
        return r223008;
}
↓
double f(double x, double y, double z) {
        double r223009 = x;
        double r223010 = y;
        double r223011 = sin(r223010);
        double r223012 = r223009 * r223011;
        double r223013 = cbrt(r223012);
        double r223014 = cbrt(r223009);
        double r223015 = cbrt(r223011);
        double r223016 = r223014 * r223015;
        double r223017 = r223013 * r223016;
        double r223018 = r223017 * r223013;
        double r223019 = z;
        double r223020 = cos(r223010);
        double r223021 = r223019 * r223020;
        double r223022 = r223018 + r223021;
        return r223022;
}

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-prod0.6

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

  6. Final simplification0.6

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

Reproduce

herbie shell --seed 2020027 
(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))))