Average Error: 0.0 → 0.0
Time: 22.1s
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 r894904 = x;
        double r894905 = y;
        double r894906 = z;
        double r894907 = r894905 - r894906;
        double r894908 = t;
        double r894909 = r894908 - r894904;
        double r894910 = r894907 * r894909;
        double r894911 = r894904 + r894910;
        return r894911;
}
↓
double f(double x, double y, double z, double t) {
        double r894912 = y;
        double r894913 = z;
        double r894914 = r894912 - r894913;
        double r894915 = t;
        double r894916 = x;
        double r894917 = r894915 - r894916;
        double r894918 = fma(r894914, r894917, r894916);
        return r894918;
}

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 2019350 +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))))