Average Error: 0.1 → 0.3
Time: 5.1s
Precision: 64
\[x \cdot \cos y - z \cdot \sin y\]
↓
\[\left(\left(x \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{{\left(\sqrt[3]{\cos y}\right)}^{2}}\right) \cdot \sqrt[3]{\sqrt[3]{\cos y}} - z \cdot \sin y\]
x \cdot \cos y - z \cdot \sin y
↓
\left(\left(x \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{{\left(\sqrt[3]{\cos y}\right)}^{2}}\right) \cdot \sqrt[3]{\sqrt[3]{\cos y}} - z \cdot \sin y
double f(double x, double y, double z) {
        double r254196 = x;
        double r254197 = y;
        double r254198 = cos(r254197);
        double r254199 = r254196 * r254198;
        double r254200 = z;
        double r254201 = sin(r254197);
        double r254202 = r254200 * r254201;
        double r254203 = r254199 - r254202;
        return r254203;
}
↓
double f(double x, double y, double z) {
        double r254204 = x;
        double r254205 = y;
        double r254206 = cos(r254205);
        double r254207 = 2.0;
        double r254208 = pow(r254206, r254207);
        double r254209 = 0.3333333333333333;
        double r254210 = pow(r254208, r254209);
        double r254211 = r254204 * r254210;
        double r254212 = cbrt(r254206);
        double r254213 = pow(r254212, r254207);
        double r254214 = cbrt(r254213);
        double r254215 = r254211 * r254214;
        double r254216 = cbrt(r254212);
        double r254217 = r254215 * r254216;
        double r254218 = z;
        double r254219 = sin(r254205);
        double r254220 = r254218 * r254219;
        double r254221 = r254217 - r254220;
        return r254221;
}

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 cbrt-unprod0.3

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

  7. Simplified0.3

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

  9. Applied add-cube-cbrt0.3

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

  10. Applied cbrt-prod0.3

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

  11. Applied associate-*r*0.3

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

  12. Simplified0.3

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

  13. Final simplification0.3

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

Reproduce

herbie shell --seed 2020021 
(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))))