Average Error: 0.0 → 0.0
Time: 1.2s
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 r903837 = x;
        double r903838 = y;
        double r903839 = z;
        double r903840 = r903838 - r903839;
        double r903841 = t;
        double r903842 = r903841 - r903837;
        double r903843 = r903840 * r903842;
        double r903844 = r903837 + r903843;
        return r903844;
}
↓
double f(double x, double y, double z, double t) {
        double r903845 = t;
        double r903846 = x;
        double r903847 = r903845 - r903846;
        double r903848 = y;
        double r903849 = z;
        double r903850 = r903848 - r903849;
        double r903851 = fma(r903847, r903850, r903846);
        return r903851;
}

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 2020018 +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))))