Average Error: 0.0 → 0.0
Time: 22.6s
Precision: 64
\[x \cdot y + \left(1 - x\right) \cdot z\]
↓
\[\mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)\]
x \cdot y + \left(1 - x\right) \cdot z
↓
\mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)
double f(double x, double y, double z) {
        double r15653341 = x;
        double r15653342 = y;
        double r15653343 = r15653341 * r15653342;
        double r15653344 = 1.0;
        double r15653345 = r15653344 - r15653341;
        double r15653346 = z;
        double r15653347 = r15653345 * r15653346;
        double r15653348 = r15653343 + r15653347;
        return r15653348;
}
↓
double f(double x, double y, double z) {
        double r15653349 = x;
        double r15653350 = y;
        double r15653351 = 1.0;
        double r15653352 = r15653351 - r15653349;
        double r15653353 = z;
        double r15653354 = r15653352 * r15653353;
        double r15653355 = fma(r15653349, r15653350, r15653354);
        return r15653355;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Derivation

  1. Initial program 0.0

    \[x \cdot y + \left(1 - x\right) \cdot z\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(x, y, \left(1 - x\right) \cdot z\right)\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y z)
  :name "Diagrams.Backend.Rasterific:$crender from diagrams-rasterific-1.3.1.3"
  (+ (* x y) (* (- 1.0 x) z)))