Average Error: 0.0 → 0.0
Time: 12.4s
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 r520467 = x;
        double r520468 = y;
        double r520469 = z;
        double r520470 = r520468 - r520469;
        double r520471 = t;
        double r520472 = r520471 - r520467;
        double r520473 = r520470 * r520472;
        double r520474 = r520467 + r520473;
        return r520474;
}
↓
double f(double x, double y, double z, double t) {
        double r520475 = y;
        double r520476 = z;
        double r520477 = r520475 - r520476;
        double r520478 = t;
        double r520479 = x;
        double r520480 = r520478 - r520479;
        double r520481 = fma(r520477, r520480, r520479);
        return r520481;
}

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 2019208 +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))))