Average Error: 0.1 → 0.3
Time: 16.2s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot \sqrt[3]{e^{\log \left({\left(\cos y\right)}^{2}\right)}}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot \sqrt[3]{e^{\log \left({\left(\cos y\right)}^{2}\right)}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r163625 = x;
        double r163626 = y;
        double r163627 = sin(r163626);
        double r163628 = r163625 * r163627;
        double r163629 = z;
        double r163630 = cos(r163626);
        double r163631 = r163629 * r163630;
        double r163632 = r163628 + r163631;
        return r163632;
}
↓
double f(double x, double y, double z) {
        double r163633 = x;
        double r163634 = y;
        double r163635 = sin(r163634);
        double r163636 = r163633 * r163635;
        double r163637 = z;
        double r163638 = cos(r163634);
        double r163639 = 2.0;
        double r163640 = pow(r163638, r163639);
        double r163641 = log(r163640);
        double r163642 = exp(r163641);
        double r163643 = cbrt(r163642);
        double r163644 = r163637 * r163643;
        double r163645 = cbrt(r163638);
        double r163646 = r163644 * r163645;
        double r163647 = r163636 + r163646;
        return r163647;
}

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-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied cbrt-unprod0.3

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

  7. Simplified0.3

    \[\leadsto x \cdot \sin y + \left(z \cdot \sqrt[3]{\color{blue}{{\left(\cos y\right)}^{2}}}\right) \cdot \sqrt[3]{\cos y}\]
  8. Using strategy rm

  9. Applied add-exp-log16.3

    \[\leadsto x \cdot \sin y + \left(z \cdot \sqrt[3]{{\color{blue}{\left(e^{\log \left(\cos y\right)}\right)}}^{2}}\right) \cdot \sqrt[3]{\cos y}\]

  10. Applied pow-exp16.3

    \[\leadsto x \cdot \sin y + \left(z \cdot \sqrt[3]{\color{blue}{e^{\log \left(\cos y\right) \cdot 2}}}\right) \cdot \sqrt[3]{\cos y}\]

  11. Simplified0.3

    \[\leadsto x \cdot \sin y + \left(z \cdot \sqrt[3]{e^{\color{blue}{\log \left({\left(\cos y\right)}^{2}\right)}}}\right) \cdot \sqrt[3]{\cos y}\]

  12. Final simplification0.3

    \[\leadsto x \cdot \sin y + \left(z \cdot \sqrt[3]{e^{\log \left({\left(\cos y\right)}^{2}\right)}}\right) \cdot \sqrt[3]{\cos y}\]

Reproduce

herbie shell --seed 2019294 
(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))))