Average Error: 0.0 → 0.0
Time: 12.2s
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 r52642450 = x;
        double r52642451 = y;
        double r52642452 = z;
        double r52642453 = r52642451 - r52642452;
        double r52642454 = t;
        double r52642455 = r52642454 - r52642450;
        double r52642456 = r52642453 * r52642455;
        double r52642457 = r52642450 + r52642456;
        return r52642457;
}
↓
double f(double x, double y, double z, double t) {
        double r52642458 = y;
        double r52642459 = z;
        double r52642460 = r52642458 - r52642459;
        double r52642461 = t;
        double r52642462 = x;
        double r52642463 = r52642461 - r52642462;
        double r52642464 = fma(r52642460, r52642463, r52642462);
        return r52642464;
}

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 2019174 +o rules:numerics
(FPCore (x y z t)
  :name "Data.Metrics.Snapshot:quantile from metrics-0.3.0.2"

  :herbie-target
  (+ x (+ (* t (- y z)) (* (- x) (- y z))))

  (+ x (* (- y z) (- t x))))