Average Error: 0.1 → 0.1
Time: 13.4s
Precision: 64
\[\left(x + \cos y\right) - z \cdot \sin y\]
↓
\[\cos y + \mathsf{fma}\left(-z, \sin y, x\right)\]
\left(x + \cos y\right) - z \cdot \sin y
↓
\cos y + \mathsf{fma}\left(-z, \sin y, x\right)
double f(double x, double y, double z) {
        double r111080 = x;
        double r111081 = y;
        double r111082 = cos(r111081);
        double r111083 = r111080 + r111082;
        double r111084 = z;
        double r111085 = sin(r111081);
        double r111086 = r111084 * r111085;
        double r111087 = r111083 - r111086;
        return r111087;
}
↓
double f(double x, double y, double z) {
        double r111088 = y;
        double r111089 = cos(r111088);
        double r111090 = z;
        double r111091 = -r111090;
        double r111092 = sin(r111088);
        double r111093 = x;
        double r111094 = fma(r111091, r111092, r111093);
        double r111095 = r111089 + r111094;
        return r111095;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

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

  4. Applied associate--l+0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y z)
  :name "Graphics.Rasterific.Svg.PathConverter:segmentToBezier from rasterific-svg-0.2.3.1, B"
  (- (+ x (cos y)) (* z (sin y))))