Average Error: 0.1 → 0.1
Time: 11.1s
Precision: 64
\[\left(x + \sin y\right) + z \cdot \cos y\]
↓
\[\cos y \cdot z + \left(x + \sin y\right)\]
\left(x + \sin y\right) + z \cdot \cos y
↓
\cos y \cdot z + \left(x + \sin y\right)
double f(double x, double y, double z) {
        double r180704 = x;
        double r180705 = y;
        double r180706 = sin(r180705);
        double r180707 = r180704 + r180706;
        double r180708 = z;
        double r180709 = cos(r180705);
        double r180710 = r180708 * r180709;
        double r180711 = r180707 + r180710;
        return r180711;
}
↓
double f(double x, double y, double z) {
        double r180712 = y;
        double r180713 = cos(r180712);
        double r180714 = z;
        double r180715 = r180713 * r180714;
        double r180716 = x;
        double r180717 = sin(r180712);
        double r180718 = r180716 + r180717;
        double r180719 = r180715 + r180718;
        return r180719;
}

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. Simplified0.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(\cos y, z, x + \sin y\right)}\]
  3. Using strategy rm

  4. Applied fma-udef0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019209 +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))))