Average Error: 0.0 → 0.0
Time: 3.1s
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 r835827 = x;
        double r835828 = y;
        double r835829 = z;
        double r835830 = r835828 - r835829;
        double r835831 = t;
        double r835832 = r835831 - r835827;
        double r835833 = r835830 * r835832;
        double r835834 = r835827 + r835833;
        return r835834;
}
↓
double f(double x, double y, double z, double t) {
        double r835835 = t;
        double r835836 = x;
        double r835837 = r835835 - r835836;
        double r835838 = y;
        double r835839 = z;
        double r835840 = r835838 - r835839;
        double r835841 = fma(r835837, r835840, r835836);
        return r835841;
}

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 2020027 +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))))