Average Error: 0.0 → 0.0
Time: 32.6s
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 r488482 = x;
        double r488483 = y;
        double r488484 = z;
        double r488485 = r488483 - r488484;
        double r488486 = t;
        double r488487 = r488486 - r488482;
        double r488488 = r488485 * r488487;
        double r488489 = r488482 + r488488;
        return r488489;
}
↓
double f(double x, double y, double z, double t) {
        double r488490 = y;
        double r488491 = z;
        double r488492 = r488490 - r488491;
        double r488493 = t;
        double r488494 = x;
        double r488495 = r488493 - r488494;
        double r488496 = fma(r488492, r488495, r488494);
        return r488496;
}

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 2019326 +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))))