Average Error: 0.0 → 0.0
Time: 5.2s
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 r962887 = x;
        double r962888 = y;
        double r962889 = z;
        double r962890 = r962888 - r962889;
        double r962891 = t;
        double r962892 = r962891 - r962887;
        double r962893 = r962890 * r962892;
        double r962894 = r962887 + r962893;
        return r962894;
}
↓
double f(double x, double y, double z, double t) {
        double r962895 = t;
        double r962896 = x;
        double r962897 = r962895 - r962896;
        double r962898 = y;
        double r962899 = z;
        double r962900 = r962898 - r962899;
        double r962901 = fma(r962897, r962900, r962896);
        return r962901;
}

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 2019353 +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))))