Average Error: 0.0 → 0.0
Time: 10.5s
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 r96888046 = x;
        double r96888047 = y;
        double r96888048 = z;
        double r96888049 = r96888047 - r96888048;
        double r96888050 = t;
        double r96888051 = r96888050 - r96888046;
        double r96888052 = r96888049 * r96888051;
        double r96888053 = r96888046 + r96888052;
        return r96888053;
}
↓
double f(double x, double y, double z, double t) {
        double r96888054 = y;
        double r96888055 = z;
        double r96888056 = r96888054 - r96888055;
        double r96888057 = t;
        double r96888058 = x;
        double r96888059 = r96888057 - r96888058;
        double r96888060 = fma(r96888056, r96888059, r96888058);
        return r96888060;
}

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 2019173 +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))))