Average Error: 0.1 → 0.9
Time: 5.4s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(\left(\sqrt[3]{x \cdot \cos y} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{x \cdot \cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(\left(\sqrt[3]{x \cdot \cos y} \cdot \sqrt[3]{x}\right) \cdot \sqrt[3]{\cos y}\right) \cdot \sqrt[3]{x \cdot \cos y} + z \cdot \sin y
double f(double x, double y, double z) {
        double r183812 = x;
        double r183813 = y;
        double r183814 = cos(r183813);
        double r183815 = r183812 * r183814;
        double r183816 = z;
        double r183817 = sin(r183813);
        double r183818 = r183816 * r183817;
        double r183819 = r183815 + r183818;
        return r183819;
}
↓
double f(double x, double y, double z) {
        double r183820 = x;
        double r183821 = y;
        double r183822 = cos(r183821);
        double r183823 = r183820 * r183822;
        double r183824 = cbrt(r183823);
        double r183825 = cbrt(r183820);
        double r183826 = r183824 * r183825;
        double r183827 = cbrt(r183822);
        double r183828 = r183826 * r183827;
        double r183829 = r183828 * r183824;
        double r183830 = z;
        double r183831 = sin(r183821);
        double r183832 = r183830 * r183831;
        double r183833 = r183829 + r183832;
        return r183833;
}

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-cbrt0.9

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

  5. Applied cbrt-prod0.9

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

  6. Applied associate-*r*0.9

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

  7. Final simplification0.9

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

Reproduce

herbie shell --seed 2020018 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))