Average Error: 0.0 → 0.0
Time: 37.2s
Precision: 64
\[x + \left(y - z\right) \cdot \left(t - x\right)\]
↓
\[\mathsf{fma}\left(y - z, t - x, x\right)\]
x + \left(y - z\right) \cdot \left(t - x\right)
↓
\mathsf{fma}\left(y - z, t - x, x\right)
double f(double x, double y, double z, double t) {
        double r497257 = x;
        double r497258 = y;
        double r497259 = z;
        double r497260 = r497258 - r497259;
        double r497261 = t;
        double r497262 = r497261 - r497257;
        double r497263 = r497260 * r497262;
        double r497264 = r497257 + r497263;
        return r497264;
}
↓
double f(double x, double y, double z, double t) {
        double r497265 = y;
        double r497266 = z;
        double r497267 = r497265 - r497266;
        double r497268 = t;
        double r497269 = x;
        double r497270 = r497268 - r497269;
        double r497271 = fma(r497267, r497270, r497269);
        return r497271;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original0.0
Target0.0
Herbie0.0
\[x + \left(t \cdot \left(y - z\right) + \left(-x\right) \cdot \left(y - z\right)\right)\]

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"
  :precision binary64

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

  (+ x (* (- y z) (- t x))))