Average Error: 0.0 → 0.0
Time: 13.6s
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 r680252 = x;
        double r680253 = y;
        double r680254 = z;
        double r680255 = r680253 - r680254;
        double r680256 = t;
        double r680257 = r680256 - r680252;
        double r680258 = r680255 * r680257;
        double r680259 = r680252 + r680258;
        return r680259;
}
↓
double f(double x, double y, double z, double t) {
        double r680260 = y;
        double r680261 = z;
        double r680262 = r680260 - r680261;
        double r680263 = t;
        double r680264 = x;
        double r680265 = r680263 - r680264;
        double r680266 = fma(r680262, r680265, r680264);
        return r680266;
}

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 2019351 +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))))