Average Error: 0.1 → 0.4
Time: 16.5s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[x \cdot \sin y + \left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}\]
x \cdot \sin y + z \cdot \cos y
↓
x \cdot \sin y + \left(z \cdot \left(\sqrt[3]{\cos y} \cdot \sqrt[3]{\cos y}\right)\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r191438 = x;
        double r191439 = y;
        double r191440 = sin(r191439);
        double r191441 = r191438 * r191440;
        double r191442 = z;
        double r191443 = cos(r191439);
        double r191444 = r191442 * r191443;
        double r191445 = r191441 + r191444;
        return r191445;
}
↓
double f(double x, double y, double z) {
        double r191446 = x;
        double r191447 = y;
        double r191448 = sin(r191447);
        double r191449 = r191446 * r191448;
        double r191450 = z;
        double r191451 = cos(r191447);
        double r191452 = cbrt(r191451);
        double r191453 = r191452 * r191452;
        double r191454 = r191450 * r191453;
        double r191455 = r191454 * r191452;
        double r191456 = r191449 + r191455;
        return r191456;
}

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. Final simplification0.4

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

Reproduce

herbie shell --seed 2019350 
(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))))