Average Error: 0.1 → 0.1
Time: 38.4s
Precision: 64
\[x \cdot \sin y + z \cdot \cos y\]
↓
\[\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)\]
x \cdot \sin y + z \cdot \cos y
↓
\mathsf{fma}\left(\cos y, z, x \cdot \sin y\right)
double f(double x, double y, double z) {
        double r11167391 = x;
        double r11167392 = y;
        double r11167393 = sin(r11167392);
        double r11167394 = r11167391 * r11167393;
        double r11167395 = z;
        double r11167396 = cos(r11167392);
        double r11167397 = r11167395 * r11167396;
        double r11167398 = r11167394 + r11167397;
        return r11167398;
}
↓
double f(double x, double y, double z) {
        double r11167399 = y;
        double r11167400 = cos(r11167399);
        double r11167401 = z;
        double r11167402 = x;
        double r11167403 = sin(r11167399);
        double r11167404 = r11167402 * r11167403;
        double r11167405 = fma(r11167400, r11167401, r11167404);
        return r11167405;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2019168 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.ThreeD.Transform:aboutX from diagrams-lib-1.3.0.3, B"
  (+ (* x (sin y)) (* z (cos y))))