Average Error: 0.0 → 0.0
Time: 7.2s
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 r22881268 = x;
        double r22881269 = y;
        double r22881270 = z;
        double r22881271 = r22881269 - r22881270;
        double r22881272 = t;
        double r22881273 = r22881272 - r22881268;
        double r22881274 = r22881271 * r22881273;
        double r22881275 = r22881268 + r22881274;
        return r22881275;
}
↓
double f(double x, double y, double z, double t) {
        double r22881276 = t;
        double r22881277 = x;
        double r22881278 = r22881276 - r22881277;
        double r22881279 = y;
        double r22881280 = z;
        double r22881281 = r22881279 - r22881280;
        double r22881282 = fma(r22881278, r22881281, r22881277);
        return r22881282;
}

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 2019172 +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))))