Average Error: 0.1 → 0.2
Time: 5.0s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot {\left(e^{\log \left({\left(\cos y\right)}^{2}\right)}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot {\left(e^{\log \left({\left(\cos y\right)}^{2}\right)}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y
double f(double x, double y, double z) {
        double r219657 = x;
        double r219658 = y;
        double r219659 = cos(r219658);
        double r219660 = r219657 * r219659;
        double r219661 = z;
        double r219662 = sin(r219658);
        double r219663 = r219661 * r219662;
        double r219664 = r219660 - r219663;
        return r219664;
}
↓
double f(double x, double y, double z) {
        double r219665 = x;
        double r219666 = y;
        double r219667 = cos(r219666);
        double r219668 = 2.0;
        double r219669 = pow(r219667, r219668);
        double r219670 = log(r219669);
        double r219671 = exp(r219670);
        double r219672 = 0.3333333333333333;
        double r219673 = pow(r219671, r219672);
        double r219674 = r219665 * r219673;
        double r219675 = cbrt(r219667);
        double r219676 = r219674 * r219675;
        double r219677 = z;
        double r219678 = sin(r219666);
        double r219679 = r219677 * r219678;
        double r219680 = r219676 - r219679;
        return r219680;
}

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 pow1/316.1

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

  7. Applied pow1/316.1

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

  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-exp-log16.1

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

  12. Applied pow-exp16.1

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

  13. Simplified0.2

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

  14. Final simplification0.2

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

Reproduce

herbie shell --seed 2020062 
(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))))