Average Error: 0.0 → 0.0
Time: 5.0s
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 r22602250 = x;
        double r22602251 = y;
        double r22602252 = z;
        double r22602253 = r22602251 - r22602252;
        double r22602254 = t;
        double r22602255 = r22602254 - r22602250;
        double r22602256 = r22602253 * r22602255;
        double r22602257 = r22602250 + r22602256;
        return r22602257;
}
↓
double f(double x, double y, double z, double t) {
        double r22602258 = t;
        double r22602259 = x;
        double r22602260 = r22602258 - r22602259;
        double r22602261 = y;
        double r22602262 = z;
        double r22602263 = r22602261 - r22602262;
        double r22602264 = fma(r22602260, r22602263, r22602259);
        return r22602264;
}

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 2019174 +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))))