Average Error: 0.1 → 0.1
Time: 4.3s
Precision: 64
\[\left(x + \sin y\right) + z \cdot \cos y\]
↓
\[\left(x + \sin y\right) + \left(z \cdot \left(1 \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right)\right) \cdot \sqrt[3]{\cos y}\]
\left(x + \sin y\right) + z \cdot \cos y
↓
\left(x + \sin y\right) + \left(z \cdot \left(1 \cdot {\left({\left(\cos y\right)}^{2}\right)}^{\frac{1}{3}}\right)\right) \cdot \sqrt[3]{\cos y}
double f(double x, double y, double z) {
        double r152036 = x;
        double r152037 = y;
        double r152038 = sin(r152037);
        double r152039 = r152036 + r152038;
        double r152040 = z;
        double r152041 = cos(r152037);
        double r152042 = r152040 * r152041;
        double r152043 = r152039 + r152042;
        return r152043;
}
↓
double f(double x, double y, double z) {
        double r152044 = x;
        double r152045 = y;
        double r152046 = sin(r152045);
        double r152047 = r152044 + r152046;
        double r152048 = z;
        double r152049 = 1.0;
        double r152050 = cos(r152045);
        double r152051 = 2.0;
        double r152052 = pow(r152050, r152051);
        double r152053 = 0.3333333333333333;
        double r152054 = pow(r152052, r152053);
        double r152055 = r152049 * r152054;
        double r152056 = r152048 * r152055;
        double r152057 = cbrt(r152050);
        double r152058 = r152056 * r152057;
        double r152059 = r152047 + r152058;
        return r152059;
}

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-cbrt0.2

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

  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 cbrt-unprod0.2

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

  7. Simplified0.2

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

  9. Applied *-un-lft-identity0.2

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

  10. Applied unpow-prod-down0.2

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

  11. Applied cbrt-prod0.2

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

  12. Simplified0.2

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

  13. Simplified0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2019362 
(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))))