Average Error: 0.3 → 0.3
Time: 12.3s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\mathsf{fma}\left(\log t, a - 0.5, \left(\log \left(x + y\right) + \log z\right) - t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\mathsf{fma}\left(\log t, a - 0.5, \left(\log \left(x + y\right) + \log z\right) - t\right)
double f(double x, double y, double z, double t, double a) {
        double r370708 = x;
        double r370709 = y;
        double r370710 = r370708 + r370709;
        double r370711 = log(r370710);
        double r370712 = z;
        double r370713 = log(r370712);
        double r370714 = r370711 + r370713;
        double r370715 = t;
        double r370716 = r370714 - r370715;
        double r370717 = a;
        double r370718 = 0.5;
        double r370719 = r370717 - r370718;
        double r370720 = log(r370715);
        double r370721 = r370719 * r370720;
        double r370722 = r370716 + r370721;
        return r370722;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r370723 = t;
        double r370724 = log(r370723);
        double r370725 = a;
        double r370726 = 0.5;
        double r370727 = r370725 - r370726;
        double r370728 = x;
        double r370729 = y;
        double r370730 = r370728 + r370729;
        double r370731 = log(r370730);
        double r370732 = z;
        double r370733 = log(r370732);
        double r370734 = r370731 + r370733;
        double r370735 = r370734 - r370723;
        double r370736 = fma(r370724, r370727, r370735);
        return r370736;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original0.3
Target0.3
Herbie0.3
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

Derivation

  1. Initial program 0.3

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

  2. Simplified0.3

    \[\leadsto \color{blue}{\mathsf{fma}\left(\log t, a - 0.5, \left(\log \left(x + y\right) + \log z\right) - t\right)}\]
  3. Using strategy rm

  4. Applied *-un-lft-identity0.3

    \[\leadsto \color{blue}{1 \cdot \mathsf{fma}\left(\log t, a - 0.5, \left(\log \left(x + y\right) + \log z\right) - t\right)}\]

  5. Final simplification0.3

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

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

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

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