Average Error: 0.0 → 0.0
Time: 28.1s
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 r477981 = x;
        double r477982 = y;
        double r477983 = z;
        double r477984 = r477982 - r477983;
        double r477985 = t;
        double r477986 = r477985 - r477981;
        double r477987 = r477984 * r477986;
        double r477988 = r477981 + r477987;
        return r477988;
}
↓
double f(double x, double y, double z, double t) {
        double r477989 = y;
        double r477990 = z;
        double r477991 = r477989 - r477990;
        double r477992 = t;
        double r477993 = x;
        double r477994 = r477992 - r477993;
        double r477995 = fma(r477991, r477994, r477993);
        return r477995;
}

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 2020042 +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))))