Average Error: 0.0 → 0.0
Time: 3.2s
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 r36958853 = x;
        double r36958854 = y;
        double r36958855 = z;
        double r36958856 = r36958854 - r36958855;
        double r36958857 = t;
        double r36958858 = r36958857 - r36958853;
        double r36958859 = r36958856 * r36958858;
        double r36958860 = r36958853 + r36958859;
        return r36958860;
}
↓
double f(double x, double y, double z, double t) {
        double r36958861 = t;
        double r36958862 = x;
        double r36958863 = r36958861 - r36958862;
        double r36958864 = y;
        double r36958865 = z;
        double r36958866 = r36958864 - r36958865;
        double r36958867 = fma(r36958863, r36958866, r36958862);
        return r36958867;
}

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 2019171 +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))))