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 r797616 = x;
        double r797617 = y;
        double r797618 = z;
        double r797619 = r797617 - r797618;
        double r797620 = t;
        double r797621 = r797620 - r797616;
        double r797622 = r797619 * r797621;
        double r797623 = r797616 + r797622;
        return r797623;
}
↓
double f(double x, double y, double z, double t) {
        double r797624 = t;
        double r797625 = x;
        double r797626 = r797624 - r797625;
        double r797627 = y;
        double r797628 = z;
        double r797629 = r797627 - r797628;
        double r797630 = fma(r797626, r797629, r797625);
        return r797630;
}

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 2020056 +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))))