Average Error: 0.1 → 0.4
Time: 6.9s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot {\left(\log \left(e^{{\left(\cos y\right)}^{2}}\right)\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot {\left(\log \left(e^{{\left(\cos y\right)}^{2}}\right)\right)}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r166142 = x;
        double r166143 = y;
        double r166144 = sin(r166143);
        double r166145 = r166142 * r166144;
        double r166146 = z;
        double r166147 = cos(r166143);
        double r166148 = r166146 * r166147;
        double r166149 = r166145 + r166148;
        return r166149;
}
↓
double f(double x, double y, double z) {
        double r166150 = x;
        double r166151 = y;
        double r166152 = sin(r166151);
        double r166153 = r166150 * r166152;
        double r166154 = z;
        double r166155 = cos(r166151);
        double r166156 = 2.0;
        double r166157 = pow(r166155, r166156);
        double r166158 = exp(r166157);
        double r166159 = log(r166158);
        double r166160 = 0.3333333333333333;
        double r166161 = pow(r166159, r166160);
        double r166162 = r166154 * r166161;
        double r166163 = cbrt(r166155);
        double r166164 = r166162 * r166163;
        double r166165 = r166153 + r166164;
        return r166165;
}

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

    \[x \cdot \sin y + z \cdot \cos y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

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

  4. Applied associate-*r*0.4

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

  6. Applied pow1/316.2

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

  7. Applied pow1/316.1

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

  8. Applied pow-prod-down0.2

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

  9. Simplified0.2

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

  11. Applied add-log-exp0.4

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

  12. Final simplification0.4

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

Reproduce

herbie shell --seed 2019322 
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))