Average Error: 0.0 → 0.0
Time: 31.5s
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 r33077549 = x;
        double r33077550 = y;
        double r33077551 = z;
        double r33077552 = r33077550 - r33077551;
        double r33077553 = t;
        double r33077554 = r33077553 - r33077549;
        double r33077555 = r33077552 * r33077554;
        double r33077556 = r33077549 + r33077555;
        return r33077556;
}
↓
double f(double x, double y, double z, double t) {
        double r33077557 = t;
        double r33077558 = x;
        double r33077559 = r33077557 - r33077558;
        double r33077560 = y;
        double r33077561 = z;
        double r33077562 = r33077560 - r33077561;
        double r33077563 = fma(r33077559, r33077562, r33077558);
        return r33077563;
}

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 2019168 +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))))