Average Error: 0.1 → 0.1
Time: 4.1s
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 r165168 = x;
        double r165169 = y;
        double r165170 = sin(r165169);
        double r165171 = r165168 + r165170;
        double r165172 = z;
        double r165173 = cos(r165169);
        double r165174 = r165172 * r165173;
        double r165175 = r165171 + r165174;
        return r165175;
}
↓
double f(double x, double y, double z) {
        double r165176 = x;
        double r165177 = y;
        double r165178 = sin(r165177);
        double r165179 = r165176 + r165178;
        double r165180 = z;
        double r165181 = cos(r165177);
        double r165182 = r165180 * r165181;
        double r165183 = r165179 + r165182;
        return r165183;
}

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 pow1/316.0

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

  7. Applied pow1/316.0

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

  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. Taylor expanded around inf 0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019347 +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))))