Average Error: 0.0 → 0.0
Time: 30.3s
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 r993675 = x;
        double r993676 = y;
        double r993677 = z;
        double r993678 = r993676 - r993677;
        double r993679 = t;
        double r993680 = r993679 - r993675;
        double r993681 = r993678 * r993680;
        double r993682 = r993675 + r993681;
        return r993682;
}
↓
double f(double x, double y, double z, double t) {
        double r993683 = y;
        double r993684 = z;
        double r993685 = r993683 - r993684;
        double r993686 = t;
        double r993687 = x;
        double r993688 = r993686 - r993687;
        double r993689 = fma(r993685, r993688, r993687);
        return r993689;
}

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 2020042 +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))))