Average Error: 0.0 → 0.0
Time: 32.5s
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 r463671 = x;
        double r463672 = y;
        double r463673 = z;
        double r463674 = r463672 - r463673;
        double r463675 = t;
        double r463676 = r463675 - r463671;
        double r463677 = r463674 * r463676;
        double r463678 = r463671 + r463677;
        return r463678;
}
↓
double f(double x, double y, double z, double t) {
        double r463679 = y;
        double r463680 = z;
        double r463681 = r463679 - r463680;
        double r463682 = t;
        double r463683 = x;
        double r463684 = r463682 - r463683;
        double r463685 = fma(r463681, r463684, r463683);
        return r463685;
}

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 2019303 +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))))