Average Error: 0.0 → 0.0
Time: 26.0s
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 r670814 = x;
        double r670815 = y;
        double r670816 = z;
        double r670817 = r670815 - r670816;
        double r670818 = t;
        double r670819 = r670818 - r670814;
        double r670820 = r670817 * r670819;
        double r670821 = r670814 + r670820;
        return r670821;
}
↓
double f(double x, double y, double z, double t) {
        double r670822 = y;
        double r670823 = z;
        double r670824 = r670822 - r670823;
        double r670825 = t;
        double r670826 = x;
        double r670827 = r670825 - r670826;
        double r670828 = fma(r670824, r670827, r670826);
        return r670828;
}

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 2019323 +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))))