Average Error: 0.0 → 0.0
Time: 8.9s
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 r965854 = x;
        double r965855 = y;
        double r965856 = z;
        double r965857 = r965855 - r965856;
        double r965858 = t;
        double r965859 = r965858 - r965854;
        double r965860 = r965857 * r965859;
        double r965861 = r965854 + r965860;
        return r965861;
}
↓
double f(double x, double y, double z, double t) {
        double r965862 = y;
        double r965863 = z;
        double r965864 = r965862 - r965863;
        double r965865 = t;
        double r965866 = x;
        double r965867 = r965865 - r965866;
        double r965868 = fma(r965864, r965867, r965866);
        return r965868;
}

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 2019305 +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))))