Average Error: 0.0 → 0.0
Time: 13.2s
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 r37147981 = x;
        double r37147982 = y;
        double r37147983 = z;
        double r37147984 = r37147982 - r37147983;
        double r37147985 = t;
        double r37147986 = r37147985 - r37147981;
        double r37147987 = r37147984 * r37147986;
        double r37147988 = r37147981 + r37147987;
        return r37147988;
}
↓
double f(double x, double y, double z, double t) {
        double r37147989 = t;
        double r37147990 = x;
        double r37147991 = r37147989 - r37147990;
        double r37147992 = y;
        double r37147993 = z;
        double r37147994 = r37147992 - r37147993;
        double r37147995 = fma(r37147991, r37147994, r37147990);
        return r37147995;
}

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 2019168 +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))))