Average Error: 0.1 → 0.2
Time: 24.7s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(x \cdot {\left(\sqrt{\sqrt[3]{{\left(\cos y\right)}^{6}}} \cdot \sqrt{\sqrt[3]{{\left(\cos y\right)}^{6}}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(x \cdot {\left(\sqrt{\sqrt[3]{{\left(\cos y\right)}^{6}}} \cdot \sqrt{\sqrt[3]{{\left(\cos y\right)}^{6}}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y
double f(double x, double y, double z) {
        double r132116 = x;
        double r132117 = y;
        double r132118 = cos(r132117);
        double r132119 = r132116 * r132118;
        double r132120 = z;
        double r132121 = sin(r132117);
        double r132122 = r132120 * r132121;
        double r132123 = r132119 - r132122;
        return r132123;
}
↓
double f(double x, double y, double z) {
        double r132124 = x;
        double r132125 = y;
        double r132126 = cos(r132125);
        double r132127 = 6.0;
        double r132128 = pow(r132126, r132127);
        double r132129 = cbrt(r132128);
        double r132130 = sqrt(r132129);
        double r132131 = r132130 * r132130;
        double r132132 = 0.3333333333333333;
        double r132133 = pow(r132131, r132132);
        double r132134 = r132124 * r132133;
        double r132135 = cbrt(r132126);
        double r132136 = r132134 * r132135;
        double r132137 = z;
        double r132138 = sin(r132125);
        double r132139 = r132137 * r132138;
        double r132140 = r132136 - r132139;
        return r132140;
}

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 pow1/316.2

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

  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-cbrt-cube0.2

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

  12. Simplified0.2

    \[\leadsto \left(x \cdot {\left(\sqrt[3]{\color{blue}{{\left(\cos y\right)}^{6}}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]
  13. Using strategy rm

  14. Applied add-sqr-sqrt0.2

    \[\leadsto \left(x \cdot {\color{blue}{\left(\sqrt{\sqrt[3]{{\left(\cos y\right)}^{6}}} \cdot \sqrt{\sqrt[3]{{\left(\cos y\right)}^{6}}}\right)}}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

  15. Final simplification0.2

    \[\leadsto \left(x \cdot {\left(\sqrt{\sqrt[3]{{\left(\cos y\right)}^{6}}} \cdot \sqrt{\sqrt[3]{{\left(\cos y\right)}^{6}}}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y} - z \cdot \sin y\]

Reproduce

herbie shell --seed 2019323 
(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))))