Average Error: 0.0 → 0.0
Time: 4.1s
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 r815835 = x;
        double r815836 = y;
        double r815837 = z;
        double r815838 = r815836 - r815837;
        double r815839 = t;
        double r815840 = r815839 - r815835;
        double r815841 = r815838 * r815840;
        double r815842 = r815835 + r815841;
        return r815842;
}
↓
double f(double x, double y, double z, double t) {
        double r815843 = t;
        double r815844 = x;
        double r815845 = r815843 - r815844;
        double r815846 = y;
        double r815847 = z;
        double r815848 = r815846 - r815847;
        double r815849 = fma(r815845, r815848, r815844);
        return r815849;
}

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 2020033 +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))))