Average Error: 0.1 → 0.1
Time: 11.0s
Precision: 64
\[\left(x + \sin y\right) + z \cdot \cos y\]
↓
\[\sin y + \mathsf{fma}\left(z, \cos y, x\right)\]
\left(x + \sin y\right) + z \cdot \cos y
↓
\sin y + \mathsf{fma}\left(z, \cos y, x\right)
double f(double x, double y, double z) {
        double r3583503 = x;
        double r3583504 = y;
        double r3583505 = sin(r3583504);
        double r3583506 = r3583503 + r3583505;
        double r3583507 = z;
        double r3583508 = cos(r3583504);
        double r3583509 = r3583507 * r3583508;
        double r3583510 = r3583506 + r3583509;
        return r3583510;
}
↓
double f(double x, double y, double z) {
        double r3583511 = y;
        double r3583512 = sin(r3583511);
        double r3583513 = z;
        double r3583514 = cos(r3583511);
        double r3583515 = x;
        double r3583516 = fma(r3583513, r3583514, r3583515);
        double r3583517 = r3583512 + r3583516;
        return r3583517;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

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

  2. Simplified0.0

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

  3. Taylor expanded around inf 0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

    \[\leadsto \sin y + \mathsf{fma}\left(z, \cos y, x\right)\]

Reproduce

herbie shell --seed 2019156 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, C"
  (+ (+ x (sin y)) (* z (cos y))))