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 r749485 = x;
        double r749486 = y;
        double r749487 = z;
        double r749488 = r749486 - r749487;
        double r749489 = t;
        double r749490 = r749489 - r749485;
        double r749491 = r749488 * r749490;
        double r749492 = r749485 + r749491;
        return r749492;
}
↓
double f(double x, double y, double z, double t) {
        double r749493 = t;
        double r749494 = x;
        double r749495 = r749493 - r749494;
        double r749496 = y;
        double r749497 = z;
        double r749498 = r749496 - r749497;
        double r749499 = fma(r749495, r749498, r749494);
        return r749499;
}

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 2020083 +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))))