Average Error: 0.1 → 0.1
Time: 5.4s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\mathsf{fma}\left(x, \sin y, z \cdot \cos y\right)\]
x \cdot \sin y + z \cdot \cos y
↓
\mathsf{fma}\left(x, \sin y, z \cdot \cos y\right)
double f(double x, double y, double z) {
        double r173323 = x;
        double r173324 = y;
        double r173325 = sin(r173324);
        double r173326 = r173323 * r173325;
        double r173327 = z;
        double r173328 = cos(r173324);
        double r173329 = r173327 * r173328;
        double r173330 = r173326 + r173329;
        return r173330;
}
↓
double f(double x, double y, double z) {
        double r173331 = x;
        double r173332 = y;
        double r173333 = sin(r173332);
        double r173334 = z;
        double r173335 = cos(r173332);
        double r173336 = r173334 * r173335;
        double r173337 = fma(r173331, r173333, r173336);
        return r173337;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.1

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

  2. Simplified0.1

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019353 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  :precision binary64
  (+ (* x (sin y)) (* z (cos y))))