Average Error: 0.0 → 0.0
Time: 12.3s
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 r701250 = x;
        double r701251 = y;
        double r701252 = z;
        double r701253 = r701251 - r701252;
        double r701254 = t;
        double r701255 = r701254 - r701250;
        double r701256 = r701253 * r701255;
        double r701257 = r701250 + r701256;
        return r701257;
}
↓
double f(double x, double y, double z, double t) {
        double r701258 = y;
        double r701259 = z;
        double r701260 = r701258 - r701259;
        double r701261 = t;
        double r701262 = x;
        double r701263 = r701261 - r701262;
        double r701264 = fma(r701260, r701263, r701262);
        return r701264;
}

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 2020047 +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))))