Average Error: 0.1 → 0.3
Time: 5.2s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot \sqrt[3]{{\left(\cos y\right)}^{2}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r147217 = x;
        double r147218 = y;
        double r147219 = sin(r147218);
        double r147220 = r147217 * r147219;
        double r147221 = z;
        double r147222 = cos(r147218);
        double r147223 = r147221 * r147222;
        double r147224 = r147220 + r147223;
        return r147224;
}
↓
double f(double x, double y, double z) {
        double r147225 = x;
        double r147226 = y;
        double r147227 = sin(r147226);
        double r147228 = r147225 * r147227;
        double r147229 = z;
        double r147230 = cos(r147226);
        double r147231 = 2.0;
        double r147232 = pow(r147230, r147231);
        double r147233 = cbrt(r147232);
        double r147234 = r147229 * r147233;
        double r147235 = cbrt(r147230);
        double r147236 = r147234 * r147235;
        double r147237 = r147228 + r147236;
        return r147237;
}

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 cbrt-unprod0.3

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

  7. Simplified0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2020024 
(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))))