Average Error: 0.0 → 0.0
Time: 960.0ms
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 r794759 = x;
        double r794760 = y;
        double r794761 = z;
        double r794762 = r794760 - r794761;
        double r794763 = t;
        double r794764 = r794763 - r794759;
        double r794765 = r794762 * r794764;
        double r794766 = r794759 + r794765;
        return r794766;
}
↓
double f(double x, double y, double z, double t) {
        double r794767 = t;
        double r794768 = x;
        double r794769 = r794767 - r794768;
        double r794770 = y;
        double r794771 = z;
        double r794772 = r794770 - r794771;
        double r794773 = fma(r794769, r794772, r794768);
        return r794773;
}

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 2020020 +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))))