Average Error: 0.0 → 0.0
Time: 1.4s
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 r735185 = x;
        double r735186 = y;
        double r735187 = z;
        double r735188 = r735186 - r735187;
        double r735189 = t;
        double r735190 = r735189 - r735185;
        double r735191 = r735188 * r735190;
        double r735192 = r735185 + r735191;
        return r735192;
}
↓
double f(double x, double y, double z, double t) {
        double r735193 = t;
        double r735194 = x;
        double r735195 = r735193 - r735194;
        double r735196 = y;
        double r735197 = z;
        double r735198 = r735196 - r735197;
        double r735199 = fma(r735195, r735198, r735194);
        return r735199;
}

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 2020001 +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))))