Average Error: 0.1 → 0.4
Time: 4.9s
Precision: 64
\[\left(x + \cos y\right) - z \cdot \sin y\]
↓
\[\left(x + \cos y\right) - \left(\left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}} \cdot \sqrt[3]{\sqrt[3]{\sin y}}\right)\right) \cdot \sqrt[3]{z \cdot \sin y}\]
\left(x + \cos y\right) - z \cdot \sin y
↓
\left(x + \cos y\right) - \left(\left(\sqrt[3]{z \cdot \sin y} \cdot \sqrt[3]{z}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\sin y} \cdot \sqrt[3]{\sin y}} \cdot \sqrt[3]{\sqrt[3]{\sin y}}\right)\right) \cdot \sqrt[3]{z \cdot \sin y}
double f(double x, double y, double z) {
        double r161349 = x;
        double r161350 = y;
        double r161351 = cos(r161350);
        double r161352 = r161349 + r161351;
        double r161353 = z;
        double r161354 = sin(r161350);
        double r161355 = r161353 * r161354;
        double r161356 = r161352 - r161355;
        return r161356;
}
↓
double f(double x, double y, double z) {
        double r161357 = x;
        double r161358 = y;
        double r161359 = cos(r161358);
        double r161360 = r161357 + r161359;
        double r161361 = z;
        double r161362 = sin(r161358);
        double r161363 = r161361 * r161362;
        double r161364 = cbrt(r161363);
        double r161365 = cbrt(r161361);
        double r161366 = r161364 * r161365;
        double r161367 = cbrt(r161362);
        double r161368 = r161367 * r161367;
        double r161369 = cbrt(r161368);
        double r161370 = cbrt(r161367);
        double r161371 = r161369 * r161370;
        double r161372 = r161366 * r161371;
        double r161373 = r161372 * r161364;
        double r161374 = r161360 - r161373;
        return r161374;
}

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

    \[\left(x + \cos y\right) - z \cdot \sin y\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.4

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

  5. Applied cbrt-prod0.3

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

  6. Applied associate-*r*0.3

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

  8. Applied add-cube-cbrt0.3

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

  9. Applied cbrt-prod0.4

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

  10. Final simplification0.4

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  :precision binary64
  (- (+ x (cos y)) (* z (sin y))))