Average Error: 0.1 → 0.1
Time: 12.5s
Precision: 64
\[\left(x + \sin y\right) + z \cdot \cos y\]
↓
\[\left(x + \sin y\right) + z \cdot \cos y\]
\left(x + \sin y\right) + z \cdot \cos y
↓
\left(x + \sin y\right) + z \cdot \cos y
double f(double x, double y, double z) {
        double r180263 = x;
        double r180264 = y;
        double r180265 = sin(r180264);
        double r180266 = r180263 + r180265;
        double r180267 = z;
        double r180268 = cos(r180264);
        double r180269 = r180267 * r180268;
        double r180270 = r180266 + r180269;
        return r180270;
}
↓
double f(double x, double y, double z) {
        double r180271 = x;
        double r180272 = y;
        double r180273 = sin(r180272);
        double r180274 = r180271 + r180273;
        double r180275 = z;
        double r180276 = cos(r180272);
        double r180277 = r180275 * r180276;
        double r180278 = r180274 + r180277;
        return r180278;
}

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 expm1-log1p-u0.1

    \[\leadsto \left(x + \sin y\right) + \left(z \cdot {\color{blue}{\left(\mathsf{expm1}\left(\mathsf{log1p}\left({\left(\cos y\right)}^{2}\right)\right)\right)}}^{\frac{1}{3}}\right) \cdot \sqrt[3]{\cos y}\]

  12. Taylor expanded around inf 0.1

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

  13. Final simplification0.1

    \[\leadsto \left(x + \sin y\right) + z \cdot \cos y\]

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(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))))