Average Error: 0.1 → 0.2
Time: 14.8s
Precision: 64
\[\left(x + \sin y\right) + z \cdot \cos y\]
↓
\[\left(x + \sin y\right) + \left(\left(\sqrt{\sqrt[3]{{\left(\cos y\right)}^{2}}} \cdot z\right) \cdot \sqrt{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y}\]
\left(x + \sin y\right) + z \cdot \cos y
↓
\left(x + \sin y\right) + \left(\left(\sqrt{\sqrt[3]{{\left(\cos y\right)}^{2}}} \cdot z\right) \cdot \sqrt{{\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}}\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r229385 = x;
        double r229386 = y;
        double r229387 = sin(r229386);
        double r229388 = r229385 + r229387;
        double r229389 = z;
        double r229390 = cos(r229386);
        double r229391 = r229389 * r229390;
        double r229392 = r229388 + r229391;
        return r229392;
}
↓
double f(double x, double y, double z) {
        double r229393 = x;
        double r229394 = y;
        double r229395 = sin(r229394);
        double r229396 = r229393 + r229395;
        double r229397 = cos(r229394);
        double r229398 = 2.0;
        double r229399 = pow(r229397, r229398);
        double r229400 = cbrt(r229399);
        double r229401 = sqrt(r229400);
        double r229402 = z;
        double r229403 = r229401 * r229402;
        double r229404 = 0.3333333333333333;
        double r229405 = pow(r229399, r229404);
        double r229406 = sqrt(r229405);
        double r229407 = r229403 * r229406;
        double r229408 = cbrt(r229397);
        double r229409 = r229407 * r229408;
        double r229410 = r229396 + r229409;
        return r229410;
}

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

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

  3. Applied add-cube-cbrt0.3

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

  4. Applied associate-*r*0.3

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

  6. Applied pow1/316.1

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

  7. Applied pow1/316.1

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

  8. Applied pow-prod-down0.1

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

  9. Simplified0.1

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

  11. Applied add-sqr-sqrt0.2

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

  12. Applied associate-*r*0.2

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

  13. Simplified0.2

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

  14. Final simplification0.2

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

Reproduce

herbie shell --seed 2020042 
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  :precision binary64
  (+ (+ x (sin y)) (* z (cos y))))