Average Error: 0.0 → 0.0
Time: 15.4s
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 r777415 = x;
        double r777416 = y;
        double r777417 = z;
        double r777418 = r777416 - r777417;
        double r777419 = t;
        double r777420 = r777419 - r777415;
        double r777421 = r777418 * r777420;
        double r777422 = r777415 + r777421;
        return r777422;
}
↓
double f(double x, double y, double z, double t) {
        double r777423 = y;
        double r777424 = z;
        double r777425 = r777423 - r777424;
        double r777426 = t;
        double r777427 = x;
        double r777428 = r777426 - r777427;
        double r777429 = fma(r777425, r777428, r777427);
        return r777429;
}

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))))