Average Error: 0.0 → 0.0
Time: 38.3s
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 r606989 = x;
        double r606990 = y;
        double r606991 = z;
        double r606992 = r606990 - r606991;
        double r606993 = t;
        double r606994 = r606993 - r606989;
        double r606995 = r606992 * r606994;
        double r606996 = r606989 + r606995;
        return r606996;
}
↓
double f(double x, double y, double z, double t) {
        double r606997 = t;
        double r606998 = x;
        double r606999 = r606997 - r606998;
        double r607000 = y;
        double r607001 = z;
        double r607002 = r607000 - r607001;
        double r607003 = fma(r606999, r607002, r606998);
        return r607003;
}

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 2019179 +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))))