Average Error: 0.1 → 0.1
Time: 22.5s
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 r10207220 = x;
        double r10207221 = y;
        double r10207222 = cos(r10207221);
        double r10207223 = r10207220 * r10207222;
        double r10207224 = z;
        double r10207225 = sin(r10207221);
        double r10207226 = r10207224 * r10207225;
        double r10207227 = r10207223 + r10207226;
        return r10207227;
}
↓
double f(double x, double y, double z) {
        double r10207228 = y;
        double r10207229 = sin(r10207228);
        double r10207230 = z;
        double r10207231 = x;
        double r10207232 = cos(r10207228);
        double r10207233 = r10207231 * r10207232;
        double r10207234 = fma(r10207229, r10207230, r10207233);
        return r10207234;
}

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 2019163 +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))))