Average Error: 0.0 → 0.0
Time: 4.1s
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 r888261 = x;
        double r888262 = y;
        double r888263 = z;
        double r888264 = r888262 - r888263;
        double r888265 = t;
        double r888266 = r888265 - r888261;
        double r888267 = r888264 * r888266;
        double r888268 = r888261 + r888267;
        return r888268;
}
↓
double f(double x, double y, double z, double t) {
        double r888269 = t;
        double r888270 = x;
        double r888271 = r888269 - r888270;
        double r888272 = y;
        double r888273 = z;
        double r888274 = r888272 - r888273;
        double r888275 = fma(r888271, r888274, r888270);
        return r888275;
}

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 2019354 +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))))