Average Error: 0.0 → 0.0
Time: 1.3s
Precision: 64
\[x + \left(y - z\right) \cdot \left(t - x\right)\]
↓
\[\mathsf{fma}\left(t - x, y - z, x\right)\]
x + \left(y - z\right) \cdot \left(t - x\right)
↓
\mathsf{fma}\left(t - x, y - z, x\right)
double f(double x, double y, double z, double t) {
        double r808318 = x;
        double r808319 = y;
        double r808320 = z;
        double r808321 = r808319 - r808320;
        double r808322 = t;
        double r808323 = r808322 - r808318;
        double r808324 = r808321 * r808323;
        double r808325 = r808318 + r808324;
        return r808325;
}
↓
double f(double x, double y, double z, double t) {
        double r808326 = t;
        double r808327 = x;
        double r808328 = r808326 - r808327;
        double r808329 = y;
        double r808330 = z;
        double r808331 = r808329 - r808330;
        double r808332 = fma(r808328, r808331, r808327);
        return r808332;
}

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

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020065 +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))))