Average Error: 0.1 → 0.1
Time: 26.8s
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 r16671310 = x;
        double r16671311 = y;
        double r16671312 = 0.5;
        double r16671313 = r16671311 + r16671312;
        double r16671314 = log(r16671311);
        double r16671315 = r16671313 * r16671314;
        double r16671316 = r16671310 - r16671315;
        double r16671317 = r16671316 + r16671311;
        double r16671318 = z;
        double r16671319 = r16671317 - r16671318;
        return r16671319;
}
↓
double f(double x, double y, double z) {
        double r16671320 = x;
        double r16671321 = y;
        double r16671322 = log(r16671321);
        double r16671323 = 0.5;
        double r16671324 = r16671321 + r16671323;
        double r16671325 = z;
        double r16671326 = r16671325 - r16671321;
        double r16671327 = fma(r16671322, r16671324, r16671326);
        double r16671328 = r16671320 - r16671327;
        return r16671328;
}

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 2019164 +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))