Average Error: 0.0 → 0.0
Time: 1.3s
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 r786705 = x;
        double r786706 = y;
        double r786707 = z;
        double r786708 = r786706 - r786707;
        double r786709 = t;
        double r786710 = r786709 - r786705;
        double r786711 = r786708 * r786710;
        double r786712 = r786705 + r786711;
        return r786712;
}
↓
double f(double x, double y, double z, double t) {
        double r786713 = t;
        double r786714 = x;
        double r786715 = r786713 - r786714;
        double r786716 = y;
        double r786717 = z;
        double r786718 = r786716 - r786717;
        double r786719 = fma(r786715, r786718, r786714);
        return r786719;
}

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 2020062 +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))))