Average Error: 0.1 → 0.1
Time: 5.6s
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 r244523 = x;
        double r244524 = y;
        double r244525 = cos(r244524);
        double r244526 = r244523 * r244525;
        double r244527 = z;
        double r244528 = sin(r244524);
        double r244529 = r244527 * r244528;
        double r244530 = r244526 + r244529;
        return r244530;
}
↓
double f(double x, double y, double z) {
        double r244531 = x;
        double r244532 = y;
        double r244533 = cos(r244532);
        double r244534 = z;
        double r244535 = sin(r244532);
        double r244536 = r244534 * r244535;
        double r244537 = fma(r244531, r244533, r244536);
        return r244537;
}

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 2020057 +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))))