Average Error: 0.1 → 0.2
Time: 51.3s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[z \cdot \sin y + \sqrt[3]{\cos y} \cdot \left({\left(e^{\log \left(\cos y \cdot \cos y\right)}\right)}^{\frac{1}{3}} \cdot x\right)\]
x \cdot \cos y + z \cdot \sin y
↓
z \cdot \sin y + \sqrt[3]{\cos y} \cdot \left({\left(e^{\log \left(\cos y \cdot \cos y\right)}\right)}^{\frac{1}{3}} \cdot x\right)
double f(double x, double y, double z) {
        double r8689153 = x;
        double r8689154 = y;
        double r8689155 = cos(r8689154);
        double r8689156 = r8689153 * r8689155;
        double r8689157 = z;
        double r8689158 = sin(r8689154);
        double r8689159 = r8689157 * r8689158;
        double r8689160 = r8689156 + r8689159;
        return r8689160;
}
↓
double f(double x, double y, double z) {
        double r8689161 = z;
        double r8689162 = y;
        double r8689163 = sin(r8689162);
        double r8689164 = r8689161 * r8689163;
        double r8689165 = cos(r8689162);
        double r8689166 = cbrt(r8689165);
        double r8689167 = r8689165 * r8689165;
        double r8689168 = log(r8689167);
        double r8689169 = exp(r8689168);
        double r8689170 = 0.3333333333333333;
        double r8689171 = pow(r8689169, r8689170);
        double r8689172 = x;
        double r8689173 = r8689171 * r8689172;
        double r8689174 = r8689166 * r8689173;
        double r8689175 = r8689164 + r8689174;
        return r8689175;
}

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 pow1/316.8

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

  7. Applied pow1/316.8

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

  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. Using strategy rm

  10. Applied add-exp-log0.2

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

  11. Final simplification0.2

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

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))