Average Error: 0.1 → 0.2
Time: 5.4s
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 r212148 = x;
        double r212149 = y;
        double r212150 = cos(r212149);
        double r212151 = r212148 * r212150;
        double r212152 = z;
        double r212153 = sin(r212149);
        double r212154 = r212152 * r212153;
        double r212155 = r212151 + r212154;
        return r212155;
}
↓
double f(double x, double y, double z) {
        double r212156 = x;
        double r212157 = y;
        double r212158 = cos(r212157);
        double r212159 = 2.0;
        double r212160 = pow(r212158, r212159);
        double r212161 = 0.3333333333333333;
        double r212162 = sqrt(r212161);
        double r212163 = pow(r212160, r212162);
        double r212164 = pow(r212163, r212162);
        double r212165 = r212156 * r212164;
        double r212166 = cbrt(r212158);
        double r212167 = r212165 * r212166;
        double r212168 = z;
        double r212169 = sin(r212157);
        double r212170 = r212168 * r212169;
        double r212171 = r212167 + r212170;
        return r212171;
}

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