Average Error: 0.0 → 0.0
Time: 12.5s
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 r34496591 = x;
        double r34496592 = y;
        double r34496593 = z;
        double r34496594 = r34496592 - r34496593;
        double r34496595 = t;
        double r34496596 = r34496595 - r34496591;
        double r34496597 = r34496594 * r34496596;
        double r34496598 = r34496591 + r34496597;
        return r34496598;
}
↓
double f(double x, double y, double z, double t) {
        double r34496599 = t;
        double r34496600 = x;
        double r34496601 = r34496599 - r34496600;
        double r34496602 = y;
        double r34496603 = z;
        double r34496604 = r34496602 - r34496603;
        double r34496605 = fma(r34496601, r34496604, r34496600);
        return r34496605;
}

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 2019162 +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))))