Average Error: 0.0 → 0.0
Time: 22.8s
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 r770608 = x;
        double r770609 = y;
        double r770610 = z;
        double r770611 = r770609 - r770610;
        double r770612 = t;
        double r770613 = r770612 - r770608;
        double r770614 = r770611 * r770613;
        double r770615 = r770608 + r770614;
        return r770615;
}
↓
double f(double x, double y, double z, double t) {
        double r770616 = t;
        double r770617 = x;
        double r770618 = r770616 - r770617;
        double r770619 = y;
        double r770620 = z;
        double r770621 = r770619 - r770620;
        double r770622 = fma(r770618, r770621, r770617);
        return r770622;
}

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 2019196 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"

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

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