Average Error: 0.1 → 0.5
Time: 9.5s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\left(\sqrt[3]{x} \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{x \cdot \sin y}\right)\right) \cdot \sqrt[3]{x \cdot \sin y} + z \cdot \cos y\]
x \cdot \sin y + z \cdot \cos y
↓
\left(\sqrt[3]{x} \cdot \left(\sqrt[3]{\sin y} \cdot \sqrt[3]{x \cdot \sin y}\right)\right) \cdot \sqrt[3]{x \cdot \sin y} + z \cdot \cos y
double f(double x, double y, double z) {
        double r149621 = x;
        double r149622 = y;
        double r149623 = sin(r149622);
        double r149624 = r149621 * r149623;
        double r149625 = z;
        double r149626 = cos(r149622);
        double r149627 = r149625 * r149626;
        double r149628 = r149624 + r149627;
        return r149628;
}
↓
double f(double x, double y, double z) {
        double r149629 = x;
        double r149630 = cbrt(r149629);
        double r149631 = y;
        double r149632 = sin(r149631);
        double r149633 = cbrt(r149632);
        double r149634 = r149629 * r149632;
        double r149635 = cbrt(r149634);
        double r149636 = r149633 * r149635;
        double r149637 = r149630 * r149636;
        double r149638 = r149637 * r149635;
        double r149639 = z;
        double r149640 = cos(r149631);
        double r149641 = r149639 * r149640;
        double r149642 = r149638 + r149641;
        return r149642;
}

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

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

  6. Applied associate-*l*0.5

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

  7. Final simplification0.5

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

Reproduce

herbie shell --seed 2019304 
(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))))