Average Error: 0.0 → 0.0
Time: 14.6s
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 r345481 = x;
        double r345482 = y;
        double r345483 = z;
        double r345484 = r345482 - r345483;
        double r345485 = t;
        double r345486 = r345485 - r345481;
        double r345487 = r345484 * r345486;
        double r345488 = r345481 + r345487;
        return r345488;
}
↓
double f(double x, double y, double z, double t) {
        double r345489 = y;
        double r345490 = z;
        double r345491 = r345489 - r345490;
        double r345492 = t;
        double r345493 = x;
        double r345494 = r345492 - r345493;
        double r345495 = fma(r345491, r345494, r345493);
        return r345495;
}

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 2019209 +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))))