Average Error: 0.0 → 0.0
Time: 34.3s
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 r666131 = x;
        double r666132 = y;
        double r666133 = z;
        double r666134 = r666132 - r666133;
        double r666135 = t;
        double r666136 = r666135 - r666131;
        double r666137 = r666134 * r666136;
        double r666138 = r666131 + r666137;
        return r666138;
}
↓
double f(double x, double y, double z, double t) {
        double r666139 = y;
        double r666140 = z;
        double r666141 = r666139 - r666140;
        double r666142 = t;
        double r666143 = x;
        double r666144 = r666142 - r666143;
        double r666145 = fma(r666141, r666144, r666143);
        return r666145;
}

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 2019303 +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))))