Average Error: 0.0 → 0.0
Time: 2.1s
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 r768300 = x;
        double r768301 = y;
        double r768302 = z;
        double r768303 = r768301 - r768302;
        double r768304 = t;
        double r768305 = r768304 - r768300;
        double r768306 = r768303 * r768305;
        double r768307 = r768300 + r768306;
        return r768307;
}
↓
double f(double x, double y, double z, double t) {
        double r768308 = t;
        double r768309 = x;
        double r768310 = r768308 - r768309;
        double r768311 = y;
        double r768312 = z;
        double r768313 = r768311 - r768312;
        double r768314 = fma(r768310, r768313, r768309);
        return r768314;
}

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 2020064 +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))))