Average Error: 0.1 → 0.6
Time: 18.7s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \sin y\right) + z \cdot \cos y\]
x \cdot \sin y + z \cdot \cos y
↓
\left(\sqrt[3]{x} \cdot \sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} \cdot \sin y\right) + z \cdot \cos y
double f(double x, double y, double z) {
        double r184631 = x;
        double r184632 = y;
        double r184633 = sin(r184632);
        double r184634 = r184631 * r184633;
        double r184635 = z;
        double r184636 = cos(r184632);
        double r184637 = r184635 * r184636;
        double r184638 = r184634 + r184637;
        return r184638;
}
↓
double f(double x, double y, double z) {
        double r184639 = x;
        double r184640 = cbrt(r184639);
        double r184641 = r184640 * r184640;
        double r184642 = y;
        double r184643 = sin(r184642);
        double r184644 = r184640 * r184643;
        double r184645 = r184641 * r184644;
        double r184646 = z;
        double r184647 = cos(r184642);
        double r184648 = r184646 * r184647;
        double r184649 = r184645 + r184648;
        return r184649;
}

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

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

  4. Applied associate-*l*0.6

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

  5. Final simplification0.6

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

Reproduce

herbie shell --seed 2019198 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))