Average Error: 0.0 → 0.0
Time: 1.3s
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 r971324 = x;
        double r971325 = y;
        double r971326 = z;
        double r971327 = r971325 - r971326;
        double r971328 = t;
        double r971329 = r971328 - r971324;
        double r971330 = r971327 * r971329;
        double r971331 = r971324 + r971330;
        return r971331;
}
↓
double f(double x, double y, double z, double t) {
        double r971332 = t;
        double r971333 = x;
        double r971334 = r971332 - r971333;
        double r971335 = y;
        double r971336 = z;
        double r971337 = r971335 - r971336;
        double r971338 = fma(r971334, r971337, r971333);
        return r971338;
}

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 2019362 +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))))