Average Error: 0.0 → 0.0
Time: 2.6s
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 r1090748 = x;
        double r1090749 = y;
        double r1090750 = z;
        double r1090751 = r1090749 - r1090750;
        double r1090752 = t;
        double r1090753 = r1090752 - r1090748;
        double r1090754 = r1090751 * r1090753;
        double r1090755 = r1090748 + r1090754;
        return r1090755;
}
↓
double f(double x, double y, double z, double t) {
        double r1090756 = t;
        double r1090757 = x;
        double r1090758 = r1090756 - r1090757;
        double r1090759 = y;
        double r1090760 = z;
        double r1090761 = r1090759 - r1090760;
        double r1090762 = fma(r1090758, r1090761, r1090757);
        return r1090762;
}

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 2020034 +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))))