Average Error: 0.1 → 0.1
Time: 40.7s
Precision: 64
\[\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z\]
↓
\[x - \left(\mathsf{fma}\left(\log y, y + 0.5, z\right) - y\right)\]
\left(\left(x - \left(y + 0.5\right) \cdot \log y\right) + y\right) - z
↓
x - \left(\mathsf{fma}\left(\log y, y + 0.5, z\right) - y\right)
double f(double x, double y, double z) {
        double r379983 = x;
        double r379984 = y;
        double r379985 = 0.5;
        double r379986 = r379984 + r379985;
        double r379987 = log(r379984);
        double r379988 = r379986 * r379987;
        double r379989 = r379983 - r379988;
        double r379990 = r379989 + r379984;
        double r379991 = z;
        double r379992 = r379990 - r379991;
        return r379992;
}
↓
double f(double x, double y, double z) {
        double r379993 = x;
        double r379994 = y;
        double r379995 = log(r379994);
        double r379996 = 0.5;
        double r379997 = r379994 + r379996;
        double r379998 = z;
        double r379999 = fma(r379995, r379997, r379998);
        double r380000 = r379999 - r379994;
        double r380001 = r379993 - r380000;
        return r380001;
}

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

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

  3. Final simplification0.1

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y z)
  :name "Numeric.SpecFunctions:stirlingError from math-functions-0.1.5.2"
  :precision binary64

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

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