Average Error: 0.1 → 0.1
Time: 18.7s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)\]
x \cdot \sin y + z \cdot \cos y
↓
\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)
double f(double x, double y, double z) {
        double r142217 = x;
        double r142218 = y;
        double r142219 = sin(r142218);
        double r142220 = r142217 * r142219;
        double r142221 = z;
        double r142222 = cos(r142218);
        double r142223 = r142221 * r142222;
        double r142224 = r142220 + r142223;
        return r142224;
}
↓
double f(double x, double y, double z) {
        double r142225 = y;
        double r142226 = cos(r142225);
        double r142227 = z;
        double r142228 = x;
        double r142229 = sin(r142225);
        double r142230 = r142228 * r142229;
        double r142231 = fma(r142226, r142227, r142230);
        return r142231;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

    \[x \cdot \sin y + z \cdot \cos y\]

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019196 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))