Average Error: 0.1 → 0.1
Time: 31.7s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\mathsf{fma}\left(x, \cos y, z \cdot \sin y\right)\]
x \cdot \cos y + z \cdot \sin y
↓
\mathsf{fma}\left(x, \cos y, z \cdot \sin y\right)
double f(double x, double y, double z) {
        double r145000 = x;
        double r145001 = y;
        double r145002 = cos(r145001);
        double r145003 = r145000 * r145002;
        double r145004 = z;
        double r145005 = sin(r145001);
        double r145006 = r145004 * r145005;
        double r145007 = r145003 + r145006;
        return r145007;
}
↓
double f(double x, double y, double z) {
        double r145008 = x;
        double r145009 = y;
        double r145010 = cos(r145009);
        double r145011 = z;
        double r145012 = sin(r145009);
        double r145013 = r145011 * r145012;
        double r145014 = fma(r145008, r145010, r145013);
        return r145014;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019199 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  (+ (* x (cos y)) (* z (sin y))))