Average Error: 0.1 → 0.2
Time: 5.1s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\left(x \cdot {\left(\sqrt[3]{{\left(\cos y\right)}^{4}} \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]
x \cdot \cos y + z \cdot \sin y
↓
\left(x \cdot {\left(\sqrt[3]{{\left(\cos y\right)}^{4}} \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y
double f(double x, double y, double z) {
        double r278065 = x;
        double r278066 = y;
        double r278067 = cos(r278066);
        double r278068 = r278065 * r278067;
        double r278069 = z;
        double r278070 = sin(r278066);
        double r278071 = r278069 * r278070;
        double r278072 = r278068 + r278071;
        return r278072;
}
↓
double f(double x, double y, double z) {
        double r278073 = x;
        double r278074 = y;
        double r278075 = cos(r278074);
        double r278076 = 4.0;
        double r278077 = pow(r278075, r278076);
        double r278078 = cbrt(r278077);
        double r278079 = 2.0;
        double r278080 = pow(r278075, r278079);
        double r278081 = 0.3333333333333333;
        double r278082 = pow(r278080, r278081);
        double r278083 = r278078 * r278082;
        double r278084 = pow(r278083, r278081);
        double r278085 = r278073 * r278084;
        double r278086 = cbrt(r278075);
        double r278087 = r278085 * r278086;
        double r278088 = z;
        double r278089 = sin(r278074);
        double r278090 = r278088 * r278089;
        double r278091 = r278087 + r278090;
        return r278091;
}

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 pow1/316.4

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

  7. Applied pow1/316.4

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

  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-cube-cbrt0.3

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

  12. Simplified0.2

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

  13. Simplified0.2

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

  15. Applied add-cbrt-cube0.2

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

  16. Simplified0.2

    \[\leadsto \left(x \cdot {\left(\sqrt[3]{\color{blue}{{\left(\cos y\right)}^{4}}} \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]

  17. Final simplification0.2

    \[\leadsto \left(x \cdot {\left(\sqrt[3]{{\left(\cos y\right)}^{4}} \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} + z \cdot \sin y\]

Reproduce

herbie shell --seed 2020081 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))