Average Error: 0.0 → 0.0
Time: 10.7s
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 r36079609 = x;
        double r36079610 = y;
        double r36079611 = z;
        double r36079612 = r36079610 - r36079611;
        double r36079613 = t;
        double r36079614 = r36079613 - r36079609;
        double r36079615 = r36079612 * r36079614;
        double r36079616 = r36079609 + r36079615;
        return r36079616;
}
↓
double f(double x, double y, double z, double t) {
        double r36079617 = t;
        double r36079618 = x;
        double r36079619 = r36079617 - r36079618;
        double r36079620 = y;
        double r36079621 = z;
        double r36079622 = r36079620 - r36079621;
        double r36079623 = fma(r36079619, r36079622, r36079618);
        return r36079623;
}

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 2019163 +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))))