Average Error: 0.1 → 0.5
Time: 6.4s
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 r270593 = x;
        double r270594 = y;
        double r270595 = sin(r270594);
        double r270596 = r270593 * r270595;
        double r270597 = z;
        double r270598 = cos(r270594);
        double r270599 = r270597 * r270598;
        double r270600 = r270596 + r270599;
        return r270600;
}
↓
double f(double x, double y, double z) {
        double r270601 = x;
        double r270602 = y;
        double r270603 = sin(r270602);
        double r270604 = r270601 * r270603;
        double r270605 = cbrt(r270604);
        double r270606 = r270605 * r270605;
        double r270607 = cbrt(r270601);
        double r270608 = cbrt(r270603);
        double r270609 = r270607 * r270608;
        double r270610 = r270606 * r270609;
        double r270611 = z;
        double r270612 = cos(r270602);
        double r270613 = r270611 * r270612;
        double r270614 = r270610 + r270613;
        return r270614;
}

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 2020035 
(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))))