Average Error: 0.0 → 0.0
Time: 9.9s
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 r22460387 = x;
        double r22460388 = y;
        double r22460389 = z;
        double r22460390 = r22460388 - r22460389;
        double r22460391 = t;
        double r22460392 = r22460391 - r22460387;
        double r22460393 = r22460390 * r22460392;
        double r22460394 = r22460387 + r22460393;
        return r22460394;
}
↓
double f(double x, double y, double z, double t) {
        double r22460395 = t;
        double r22460396 = x;
        double r22460397 = r22460395 - r22460396;
        double r22460398 = y;
        double r22460399 = z;
        double r22460400 = r22460398 - r22460399;
        double r22460401 = fma(r22460397, r22460400, r22460396);
        return r22460401;
}

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 2019163 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

  (+ x (* (- y z) (- t x))))