Average Error: 0.0 → 0.0
Time: 14.3s
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 r853499 = x;
        double r853500 = y;
        double r853501 = z;
        double r853502 = r853500 - r853501;
        double r853503 = t;
        double r853504 = r853503 - r853499;
        double r853505 = r853502 * r853504;
        double r853506 = r853499 + r853505;
        return r853506;
}
↓
double f(double x, double y, double z, double t) {
        double r853507 = y;
        double r853508 = z;
        double r853509 = r853507 - r853508;
        double r853510 = t;
        double r853511 = x;
        double r853512 = r853510 - r853511;
        double r853513 = fma(r853509, r853512, r853511);
        return r853513;
}

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 2020045 +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))))