Average Error: 0.0 → 0.0
Time: 5.1s
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 r1068288 = x;
        double r1068289 = y;
        double r1068290 = z;
        double r1068291 = r1068289 - r1068290;
        double r1068292 = t;
        double r1068293 = r1068292 - r1068288;
        double r1068294 = r1068291 * r1068293;
        double r1068295 = r1068288 + r1068294;
        return r1068295;
}
↓
double f(double x, double y, double z, double t) {
        double r1068296 = t;
        double r1068297 = x;
        double r1068298 = r1068296 - r1068297;
        double r1068299 = y;
        double r1068300 = z;
        double r1068301 = r1068299 - r1068300;
        double r1068302 = fma(r1068298, r1068301, r1068297);
        return r1068302;
}

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 2020025 +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))))