Average Error: 0.0 → 0.0
Time: 2.4s
Precision: 64
\[x + \left(y - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(z, y - x, x\right)\]
x + \left(y - x\right) \cdot z
↓
\mathsf{fma}\left(z, y - x, x\right)
double f(double x, double y, double z) {
        double r193230 = x;
        double r193231 = y;
        double r193232 = r193231 - r193230;
        double r193233 = z;
        double r193234 = r193232 * r193233;
        double r193235 = r193230 + r193234;
        return r193235;
}
↓
double f(double x, double y, double z) {
        double r193236 = z;
        double r193237 = y;
        double r193238 = x;
        double r193239 = r193237 - r193238;
        double r193240 = fma(r193236, r193239, r193238);
        return r193240;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x + \left(y - x\right) \cdot z\]

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

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