Average Error: 0.0 → 0.0
Time: 4.4s
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 r833534 = x;
        double r833535 = y;
        double r833536 = z;
        double r833537 = r833535 - r833536;
        double r833538 = t;
        double r833539 = r833538 - r833534;
        double r833540 = r833537 * r833539;
        double r833541 = r833534 + r833540;
        return r833541;
}
↓
double f(double x, double y, double z, double t) {
        double r833542 = t;
        double r833543 = x;
        double r833544 = r833542 - r833543;
        double r833545 = y;
        double r833546 = z;
        double r833547 = r833545 - r833546;
        double r833548 = fma(r833544, r833547, r833543);
        return r833548;
}

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 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))))