Average Error: 0.0 → 0.0
Time: 3.6s
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 r924008 = x;
        double r924009 = y;
        double r924010 = z;
        double r924011 = r924009 - r924010;
        double r924012 = t;
        double r924013 = r924012 - r924008;
        double r924014 = r924011 * r924013;
        double r924015 = r924008 + r924014;
        return r924015;
}
↓
double f(double x, double y, double z, double t) {
        double r924016 = t;
        double r924017 = x;
        double r924018 = r924016 - r924017;
        double r924019 = y;
        double r924020 = z;
        double r924021 = r924019 - r924020;
        double r924022 = fma(r924018, r924021, r924017);
        return r924022;
}

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 2020057 +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))))