Average Error: 0.0 → 0.0
Time: 19.1s
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 r997661 = x;
        double r997662 = y;
        double r997663 = z;
        double r997664 = r997662 - r997663;
        double r997665 = t;
        double r997666 = r997665 - r997661;
        double r997667 = r997664 * r997666;
        double r997668 = r997661 + r997667;
        return r997668;
}
↓
double f(double x, double y, double z, double t) {
        double r997669 = y;
        double r997670 = z;
        double r997671 = r997669 - r997670;
        double r997672 = t;
        double r997673 = x;
        double r997674 = r997672 - r997673;
        double r997675 = fma(r997671, r997674, r997673);
        return r997675;
}

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 2020045 +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))))