Average Error: 0.0 → 0.0
Time: 3.9s
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 r917673 = x;
        double r917674 = y;
        double r917675 = z;
        double r917676 = r917674 - r917675;
        double r917677 = t;
        double r917678 = r917677 - r917673;
        double r917679 = r917676 * r917678;
        double r917680 = r917673 + r917679;
        return r917680;
}
↓
double f(double x, double y, double z, double t) {
        double r917681 = t;
        double r917682 = x;
        double r917683 = r917681 - r917682;
        double r917684 = y;
        double r917685 = z;
        double r917686 = r917684 - r917685;
        double r917687 = fma(r917683, r917686, r917682);
        return r917687;
}

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 2020021 +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))))