Average Error: 0.0 → 0.0
Time: 1.4s
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 r695545 = x;
        double r695546 = y;
        double r695547 = z;
        double r695548 = r695546 - r695547;
        double r695549 = t;
        double r695550 = r695549 - r695545;
        double r695551 = r695548 * r695550;
        double r695552 = r695545 + r695551;
        return r695552;
}
↓
double f(double x, double y, double z, double t) {
        double r695553 = t;
        double r695554 = x;
        double r695555 = r695553 - r695554;
        double r695556 = y;
        double r695557 = z;
        double r695558 = r695556 - r695557;
        double r695559 = fma(r695555, r695558, r695554);
        return r695559;
}

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 2020001 +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))))