Average Error: 0.0 → 0.0
Time: 13.7s
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 r541016 = x;
        double r541017 = y;
        double r541018 = z;
        double r541019 = r541017 - r541018;
        double r541020 = t;
        double r541021 = r541020 - r541016;
        double r541022 = r541019 * r541021;
        double r541023 = r541016 + r541022;
        return r541023;
}
↓
double f(double x, double y, double z, double t) {
        double r541024 = y;
        double r541025 = z;
        double r541026 = r541024 - r541025;
        double r541027 = t;
        double r541028 = x;
        double r541029 = r541027 - r541028;
        double r541030 = fma(r541026, r541029, r541028);
        return r541030;
}

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 2019198 +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))))