Average Error: 0.0 → 0.0
Time: 35.2s
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 r489531 = x;
        double r489532 = y;
        double r489533 = z;
        double r489534 = r489532 - r489533;
        double r489535 = t;
        double r489536 = r489535 - r489531;
        double r489537 = r489534 * r489536;
        double r489538 = r489531 + r489537;
        return r489538;
}
↓
double f(double x, double y, double z, double t) {
        double r489539 = y;
        double r489540 = z;
        double r489541 = r489539 - r489540;
        double r489542 = t;
        double r489543 = x;
        double r489544 = r489542 - r489543;
        double r489545 = fma(r489541, r489544, r489543);
        return r489545;
}

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 2019347 +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))))