Average Error: 0.1 → 0.1
Time: 16.3s
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 r139805 = x;
        double r139806 = y;
        double r139807 = cos(r139806);
        double r139808 = r139805 * r139807;
        double r139809 = z;
        double r139810 = sin(r139806);
        double r139811 = r139809 * r139810;
        double r139812 = r139808 + r139811;
        return r139812;
}
↓
double f(double x, double y, double z) {
        double r139813 = x;
        double r139814 = y;
        double r139815 = cos(r139814);
        double r139816 = z;
        double r139817 = sin(r139814);
        double r139818 = r139816 * r139817;
        double r139819 = fma(r139813, r139815, r139818);
        return r139819;
}

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 2019208 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutY from diagrams-lib-1.3.0.3"
  :precision binary64
  (+ (* x (cos y)) (* z (sin y))))