Average Error: 0.0 → 0.0
Time: 24.7s
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 r743349 = x;
        double r743350 = y;
        double r743351 = z;
        double r743352 = r743350 - r743351;
        double r743353 = t;
        double r743354 = r743353 - r743349;
        double r743355 = r743352 * r743354;
        double r743356 = r743349 + r743355;
        return r743356;
}
↓
double f(double x, double y, double z, double t) {
        double r743357 = y;
        double r743358 = z;
        double r743359 = r743357 - r743358;
        double r743360 = t;
        double r743361 = x;
        double r743362 = r743360 - r743361;
        double r743363 = fma(r743359, r743362, r743361);
        return r743363;
}

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 2020047 +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))))