Average Error: 0.0 → 0.0
Time: 1.6s
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 r759189 = x;
        double r759190 = y;
        double r759191 = z;
        double r759192 = r759190 - r759191;
        double r759193 = t;
        double r759194 = r759193 - r759189;
        double r759195 = r759192 * r759194;
        double r759196 = r759189 + r759195;
        return r759196;
}
↓
double f(double x, double y, double z, double t) {
        double r759197 = t;
        double r759198 = x;
        double r759199 = r759197 - r759198;
        double r759200 = y;
        double r759201 = z;
        double r759202 = r759200 - r759201;
        double r759203 = fma(r759199, r759202, r759198);
        return r759203;
}

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 2020081 +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))))