Average Error: 0.1 → 0.1
Time: 23.3s
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 r7880836 = x;
        double r7880837 = y;
        double r7880838 = sin(r7880837);
        double r7880839 = r7880836 * r7880838;
        double r7880840 = z;
        double r7880841 = cos(r7880837);
        double r7880842 = r7880840 * r7880841;
        double r7880843 = r7880839 + r7880842;
        return r7880843;
}
↓
double f(double x, double y, double z) {
        double r7880844 = y;
        double r7880845 = cos(r7880844);
        double r7880846 = z;
        double r7880847 = x;
        double r7880848 = sin(r7880844);
        double r7880849 = r7880847 * r7880848;
        double r7880850 = fma(r7880845, r7880846, r7880849);
        return r7880850;
}

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 2019172 +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))))