Average Error: 0.0 → 0.0
Time: 22.7s
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 r844983 = x;
        double r844984 = y;
        double r844985 = z;
        double r844986 = r844984 - r844985;
        double r844987 = t;
        double r844988 = r844987 - r844983;
        double r844989 = r844986 * r844988;
        double r844990 = r844983 + r844989;
        return r844990;
}
↓
double f(double x, double y, double z, double t) {
        double r844991 = y;
        double r844992 = z;
        double r844993 = r844991 - r844992;
        double r844994 = t;
        double r844995 = x;
        double r844996 = r844994 - r844995;
        double r844997 = fma(r844993, r844996, r844995);
        return r844997;
}

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 2020043 +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))))