Average Error: 0.1 → 0.3
Time: 9.5s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[z \cdot \left(\sqrt[3]{{\left(\cos y\right)}^{2}} \cdot \sqrt[3]{\cos y}\right) + x \cdot \sin y\]
x \cdot \sin y + z \cdot \cos y
↓
z \cdot \left(\sqrt[3]{{\left(\cos y\right)}^{2}} \cdot \sqrt[3]{\cos y}\right) + x \cdot \sin y
double f(double x, double y, double z) {
        double r124253 = x;
        double r124254 = y;
        double r124255 = sin(r124254);
        double r124256 = r124253 * r124255;
        double r124257 = z;
        double r124258 = cos(r124254);
        double r124259 = r124257 * r124258;
        double r124260 = r124256 + r124259;
        return r124260;
}
↓
double f(double x, double y, double z) {
        double r124261 = z;
        double r124262 = y;
        double r124263 = cos(r124262);
        double r124264 = 2.0;
        double r124265 = pow(r124263, r124264);
        double r124266 = cbrt(r124265);
        double r124267 = cbrt(r124263);
        double r124268 = r124266 * r124267;
        double r124269 = r124261 * r124268;
        double r124270 = x;
        double r124271 = sin(r124262);
        double r124272 = r124270 * r124271;
        double r124273 = r124269 + r124272;
        return r124273;
}

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. Using strategy rm

  9. Applied add-log-exp0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 1978988140 
(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))))