Average Error: 0.1 → 0.2
Time: 5.5s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(x \cdot {\left({\left({\left(\cos y\right)}^{2}\right)}^{\left(\sqrt{\frac{1}{3}}\right)}\right)}^{\left(\sqrt{\frac{1}{3}}\right)}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(x \cdot {\left({\left({\left(\cos y\right)}^{2}\right)}^{\left(\sqrt{\frac{1}{3}}\right)}\right)}^{\left(\sqrt{\frac{1}{3}}\right)}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y
double f(double x, double y, double z) {
        double r196712 = x;
        double r196713 = y;
        double r196714 = cos(r196713);
        double r196715 = r196712 * r196714;
        double r196716 = z;
        double r196717 = sin(r196713);
        double r196718 = r196716 * r196717;
        double r196719 = r196715 + r196718;
        return r196719;
}
↓
double f(double x, double y, double z) {
        double r196720 = x;
        double r196721 = y;
        double r196722 = cos(r196721);
        double r196723 = 2.0;
        double r196724 = pow(r196722, r196723);
        double r196725 = 0.3333333333333333;
        double r196726 = sqrt(r196725);
        double r196727 = pow(r196724, r196726);
        double r196728 = pow(r196727, r196726);
        double r196729 = r196720 * r196728;
        double r196730 = cbrt(r196722);
        double r196731 = r196729 * r196730;
        double r196732 = z;
        double r196733 = sin(r196721);
        double r196734 = r196732 * r196733;
        double r196735 = r196731 + r196734;
        return r196735;
}

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 pow1/316.3

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

  7. Applied pow1/316.3

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

  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-sqr-sqrt0.2

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

  12. Applied pow-unpow0.2

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

  13. Final simplification0.2

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))