Average Error: 0.0 → 0.0
Time: 22.7s
Precision: 64
\[x + \left(y - z\right) \cdot \left(t - x\right)\]
↓
\[\mathsf{fma}\left(y - z, t - x, x\right)\]
x + \left(y - z\right) \cdot \left(t - x\right)
↓
\mathsf{fma}\left(y - z, t - x, x\right)
double f(double x, double y, double z, double t) {
        double r549259 = x;
        double r549260 = y;
        double r549261 = z;
        double r549262 = r549260 - r549261;
        double r549263 = t;
        double r549264 = r549263 - r549259;
        double r549265 = r549262 * r549264;
        double r549266 = r549259 + r549265;
        return r549266;
}
↓
double f(double x, double y, double z, double t) {
        double r549267 = y;
        double r549268 = z;
        double r549269 = r549267 - r549268;
        double r549270 = t;
        double r549271 = x;
        double r549272 = r549270 - r549271;
        double r549273 = fma(r549269, r549272, r549271);
        return r549273;
}

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

    \[\leadsto \color{blue}{\mathsf{fma}\left(y - z, t - x, x\right)}\]

  3. Final simplification0.0

    \[\leadsto \mathsf{fma}\left(y - z, t - x, x\right)\]

Reproduce

herbie shell --seed 2019199 +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))))