Average Error: 0.1 → 0.3
Time: 5.4s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot \log \left(e^{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot \log \left(e^{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y
double f(double x, double y, double z) {
        double r217604 = x;
        double r217605 = y;
        double r217606 = cos(r217605);
        double r217607 = r217604 * r217606;
        double r217608 = z;
        double r217609 = sin(r217605);
        double r217610 = r217608 * r217609;
        double r217611 = r217607 - r217610;
        return r217611;
}
↓
double f(double x, double y, double z) {
        double r217612 = x;
        double r217613 = y;
        double r217614 = cos(r217613);
        double r217615 = 2.0;
        double r217616 = pow(r217614, r217615);
        double r217617 = 0.3333333333333333;
        double r217618 = pow(r217616, r217617);
        double r217619 = exp(r217618);
        double r217620 = log(r217619);
        double r217621 = r217612 * r217620;
        double r217622 = cbrt(r217614);
        double r217623 = r217621 * r217622;
        double r217624 = z;
        double r217625 = sin(r217613);
        double r217626 = r217624 * r217625;
        double r217627 = r217623 - r217626;
        return r217627;
}

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

    \[x \cdot \cos y - z \cdot \sin y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied pow1/316.7

    \[\leadsto \left(x \cdot \left(\sqrt[3]{\cos y} \cdot \color{blue}{{\left(\cos y\right)}^{\frac{1}{3}}}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

  7. Applied pow1/316.7

    \[\leadsto \left(x \cdot \left(\color{blue}{{\left(\cos y\right)}^{\frac{1}{3}}} \cdot {\left(\cos y\right)}^{\frac{1}{3}}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

  8. Applied pow-prod-down0.2

    \[\leadsto \left(x \cdot \color{blue}{{\left(\cos y \cdot \cos y\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

  9. Simplified0.2

    \[\leadsto \left(x \cdot {\color{blue}{\left({\left(\cos y\right)}^{2}\right)}}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
  10. Using strategy rm

  11. Applied add-log-exp0.3

    \[\leadsto \left(x \cdot \color{blue}{\log \left(e^{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right)}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

  12. Final simplification0.3

    \[\leadsto \left(x \cdot \log \left(e^{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right)\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

Reproduce

herbie shell --seed 2020002 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, A"
  :precision binary64
  (- (* x (cos y)) (* z (sin y))))