Average Error: 0.0 → 0.0
Time: 11.6s
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 r862843 = x;
        double r862844 = y;
        double r862845 = z;
        double r862846 = r862844 - r862845;
        double r862847 = t;
        double r862848 = r862847 - r862843;
        double r862849 = r862846 * r862848;
        double r862850 = r862843 + r862849;
        return r862850;
}
↓
double f(double x, double y, double z, double t) {
        double r862851 = y;
        double r862852 = z;
        double r862853 = r862851 - r862852;
        double r862854 = t;
        double r862855 = x;
        double r862856 = r862854 - r862855;
        double r862857 = fma(r862853, r862856, r862855);
        return r862857;
}

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 2020046 +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))))