Average Error: 0.1 → 0.1
Time: 24.5s
Precision: 64
\[x \cdot \cos y + z \cdot \sin y\]
↓
\[\mathsf{fma}\left(\sin y, z, x \cdot \cos y\right)\]
x \cdot \cos y + z \cdot \sin y
↓
\mathsf{fma}\left(\sin y, z, x \cdot \cos y\right)
double f(double x, double y, double z) {
        double r8114000 = x;
        double r8114001 = y;
        double r8114002 = cos(r8114001);
        double r8114003 = r8114000 * r8114002;
        double r8114004 = z;
        double r8114005 = sin(r8114001);
        double r8114006 = r8114004 * r8114005;
        double r8114007 = r8114003 + r8114006;
        return r8114007;
}
↓
double f(double x, double y, double z) {
        double r8114008 = y;
        double r8114009 = sin(r8114008);
        double r8114010 = z;
        double r8114011 = x;
        double r8114012 = cos(r8114008);
        double r8114013 = r8114011 * r8114012;
        double r8114014 = fma(r8114009, r8114010, r8114013);
        return r8114014;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 +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))))