Average Error: 0.1 → 0.6
Time: 5.6s
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 r210574 = x;
        double r210575 = y;
        double r210576 = sin(r210575);
        double r210577 = r210574 * r210576;
        double r210578 = z;
        double r210579 = cos(r210575);
        double r210580 = r210578 * r210579;
        double r210581 = r210577 + r210580;
        return r210581;
}
↓
double f(double x, double y, double z) {
        double r210582 = x;
        double r210583 = cbrt(r210582);
        double r210584 = r210583 * r210583;
        double r210585 = y;
        double r210586 = sin(r210585);
        double r210587 = r210583 * r210586;
        double r210588 = r210584 * r210587;
        double r210589 = z;
        double r210590 = cos(r210585);
        double r210591 = r210589 * r210590;
        double r210592 = r210588 + r210591;
        return r210592;
}

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 2019353 
(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))))