Average Error: 0.0 → 0.0
Time: 15.4s
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 r34415828 = x;
        double r34415829 = y;
        double r34415830 = z;
        double r34415831 = r34415829 - r34415830;
        double r34415832 = t;
        double r34415833 = r34415832 - r34415828;
        double r34415834 = r34415831 * r34415833;
        double r34415835 = r34415828 + r34415834;
        return r34415835;
}
↓
double f(double x, double y, double z, double t) {
        double r34415836 = t;
        double r34415837 = x;
        double r34415838 = r34415836 - r34415837;
        double r34415839 = y;
        double r34415840 = z;
        double r34415841 = r34415839 - r34415840;
        double r34415842 = fma(r34415838, r34415841, r34415837);
        return r34415842;
}

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 2019169 +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))))