Average Error: 0.0 → 0.0
Time: 5.3s
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 r780751 = x;
        double r780752 = y;
        double r780753 = z;
        double r780754 = r780752 - r780753;
        double r780755 = t;
        double r780756 = r780755 - r780751;
        double r780757 = r780754 * r780756;
        double r780758 = r780751 + r780757;
        return r780758;
}
↓
double f(double x, double y, double z, double t) {
        double r780759 = t;
        double r780760 = x;
        double r780761 = r780759 - r780760;
        double r780762 = y;
        double r780763 = z;
        double r780764 = r780762 - r780763;
        double r780765 = fma(r780761, r780764, r780760);
        return r780765;
}

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))))