Average Error: 0.0 → 0.0
Time: 26.9s
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 r49829 = x;
        double r49830 = y;
        double r49831 = z;
        double r49832 = r49830 - r49831;
        double r49833 = t;
        double r49834 = r49833 - r49829;
        double r49835 = r49832 * r49834;
        double r49836 = r49829 + r49835;
        return r49836;
}
↓
double f(double x, double y, double z, double t) {
        double r49837 = y;
        double r49838 = z;
        double r49839 = r49837 - r49838;
        double r49840 = t;
        double r49841 = x;
        double r49842 = r49840 - r49841;
        double r49843 = fma(r49839, r49842, r49841);
        return r49843;
}

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 2019310 +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))))