Average Error: 0.0 → 0.0
Time: 11.1s
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 r34034673 = x;
        double r34034674 = y;
        double r34034675 = z;
        double r34034676 = r34034674 - r34034675;
        double r34034677 = t;
        double r34034678 = r34034677 - r34034673;
        double r34034679 = r34034676 * r34034678;
        double r34034680 = r34034673 + r34034679;
        return r34034680;
}
↓
double f(double x, double y, double z, double t) {
        double r34034681 = t;
        double r34034682 = x;
        double r34034683 = r34034681 - r34034682;
        double r34034684 = y;
        double r34034685 = z;
        double r34034686 = r34034684 - r34034685;
        double r34034687 = fma(r34034683, r34034686, r34034682);
        return r34034687;
}

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 2019158 +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))))