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 r4174 = x;
        double r4175 = y;
        double r4176 = z;
        double r4177 = r4175 - r4176;
        double r4178 = t;
        double r4179 = r4178 - r4174;
        double r4180 = r4177 * r4179;
        double r4181 = r4174 + r4180;
        return r4181;
}
↓
double f(double x, double y, double z, double t) {
        double r4182 = t;
        double r4183 = x;
        double r4184 = r4182 - r4183;
        double r4185 = y;
        double r4186 = z;
        double r4187 = r4185 - r4186;
        double r4188 = fma(r4184, r4187, r4183);
        return r4188;
}

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 2020025 +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))))