Average Error: 0.0 → 0.0
Time: 3.3s
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 r794255 = x;
        double r794256 = y;
        double r794257 = z;
        double r794258 = r794256 - r794257;
        double r794259 = t;
        double r794260 = r794259 - r794255;
        double r794261 = r794258 * r794260;
        double r794262 = r794255 + r794261;
        return r794262;
}
↓
double f(double x, double y, double z, double t) {
        double r794263 = t;
        double r794264 = x;
        double r794265 = r794263 - r794264;
        double r794266 = y;
        double r794267 = z;
        double r794268 = r794266 - r794267;
        double r794269 = fma(r794265, r794268, r794264);
        return r794269;
}

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 2020089 +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))))