Average Error: 0.0 → 0.0
Time: 11.5s
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 r35465861 = x;
        double r35465862 = y;
        double r35465863 = z;
        double r35465864 = r35465862 - r35465863;
        double r35465865 = t;
        double r35465866 = r35465865 - r35465861;
        double r35465867 = r35465864 * r35465866;
        double r35465868 = r35465861 + r35465867;
        return r35465868;
}
↓
double f(double x, double y, double z, double t) {
        double r35465869 = t;
        double r35465870 = x;
        double r35465871 = r35465869 - r35465870;
        double r35465872 = y;
        double r35465873 = z;
        double r35465874 = r35465872 - r35465873;
        double r35465875 = fma(r35465871, r35465874, r35465870);
        return r35465875;
}

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 2019172 +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))))