Average Error: 0.1 → 0.1
Time: 22.9s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[x - \mathsf{fma}\left(\log y, y + 0.5, z - y\right)\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
x - \mathsf{fma}\left(\log y, y + 0.5, z - y\right)
double f(double x, double y, double z) {
        double r16818436 = x;
        double r16818437 = y;
        double r16818438 = 0.5;
        double r16818439 = r16818437 + r16818438;
        double r16818440 = log(r16818437);
        double r16818441 = r16818439 * r16818440;
        double r16818442 = r16818436 - r16818441;
        double r16818443 = r16818442 + r16818437;
        double r16818444 = z;
        double r16818445 = r16818443 - r16818444;
        return r16818445;
}
↓
double f(double x, double y, double z) {
        double r16818446 = x;
        double r16818447 = y;
        double r16818448 = log(r16818447);
        double r16818449 = 0.5;
        double r16818450 = r16818447 + r16818449;
        double r16818451 = z;
        double r16818452 = r16818451 - r16818447;
        double r16818453 = fma(r16818448, r16818450, r16818452);
        double r16818454 = r16818446 - r16818453;
        return r16818454;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Target

Original0.1
Target0.1
Herbie0.1
\[\left(\left(y + x\right) - z\right) - \left(y + 0.5\right) \cdot \log y\]

Derivation

  1. Initial program 0.1

    \[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]

  2. Simplified0.1

    \[\leadsto \color{blue}{x - \mathsf{fma}\left(\log y, 0.5 + y, z - y\right)}\]

  3. Final simplification0.1

    \[\leadsto x - \mathsf{fma}\left(\log y, y + 0.5, z - y\right)\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"

  :herbie-target
  (- (- (+ y x) z) (* (+ y 0.5) (log y)))

  (- (+ (- x (* (+ y 0.5) (log y))) y) z))