Average Error: 0.0 → 0.0
Time: 933.0ms
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 r887280 = x;
        double r887281 = y;
        double r887282 = z;
        double r887283 = r887281 - r887282;
        double r887284 = t;
        double r887285 = r887284 - r887280;
        double r887286 = r887283 * r887285;
        double r887287 = r887280 + r887286;
        return r887287;
}
↓
double f(double x, double y, double z, double t) {
        double r887288 = t;
        double r887289 = x;
        double r887290 = r887288 - r887289;
        double r887291 = y;
        double r887292 = z;
        double r887293 = r887291 - r887292;
        double r887294 = fma(r887290, r887293, r887289);
        return r887294;
}

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 2020024 +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))))