Average Error: 0.1 → 0.1
Time: 12.6s
Precision: 64
\[\left(x + \sin y\right) + z \cdot \cos y\]
↓
\[\left(x + \sin y\right) + z \cdot \left({\left({\left(\cos y\right)}^{2}\right)}^{\left(\frac{1}{3}\right)} \cdot \sqrt[3]{\cos y}\right)\]
\left(x + \sin y\right) + z \cdot \cos y
↓
\left(x + \sin y\right) + z \cdot \left({\left({\left(\cos y\right)}^{2}\right)}^{\left(\frac{1}{3}\right)} \cdot \sqrt[3]{\cos y}\right)
double f(double x, double y, double z) {
        double r122652 = x;
        double r122653 = y;
        double r122654 = sin(r122653);
        double r122655 = r122652 + r122654;
        double r122656 = z;
        double r122657 = cos(r122653);
        double r122658 = r122656 * r122657;
        double r122659 = r122655 + r122658;
        return r122659;
}
↓
double f(double x, double y, double z) {
        double r122660 = x;
        double r122661 = y;
        double r122662 = sin(r122661);
        double r122663 = r122660 + r122662;
        double r122664 = z;
        double r122665 = cos(r122661);
        double r122666 = 2.0;
        double r122667 = pow(r122665, r122666);
        double r122668 = 1.0;
        double r122669 = 3.0;
        double r122670 = r122668 / r122669;
        double r122671 = pow(r122667, r122670);
        double r122672 = cbrt(r122665);
        double r122673 = r122671 * r122672;
        double r122674 = r122664 * r122673;
        double r122675 = r122663 + r122674;
        return r122675;
}

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*0.2

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

  5. Taylor expanded around inf 0.1

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

  6. Simplified0.1

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

  8. Applied associate-*l*0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(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))))