Average Error: 0.3 → 0.3
Time: 36.3s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(y + x\right) + \mathsf{fma}\left(a - 0.5, \log t, \log z - t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(y + x\right) + \mathsf{fma}\left(a - 0.5, \log t, \log z - t\right)
double f(double x, double y, double z, double t, double a) {
        double r15655223 = x;
        double r15655224 = y;
        double r15655225 = r15655223 + r15655224;
        double r15655226 = log(r15655225);
        double r15655227 = z;
        double r15655228 = log(r15655227);
        double r15655229 = r15655226 + r15655228;
        double r15655230 = t;
        double r15655231 = r15655229 - r15655230;
        double r15655232 = a;
        double r15655233 = 0.5;
        double r15655234 = r15655232 - r15655233;
        double r15655235 = log(r15655230);
        double r15655236 = r15655234 * r15655235;
        double r15655237 = r15655231 + r15655236;
        return r15655237;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r15655238 = y;
        double r15655239 = x;
        double r15655240 = r15655238 + r15655239;
        double r15655241 = log(r15655240);
        double r15655242 = a;
        double r15655243 = 0.5;
        double r15655244 = r15655242 - r15655243;
        double r15655245 = t;
        double r15655246 = log(r15655245);
        double r15655247 = z;
        double r15655248 = log(r15655247);
        double r15655249 = r15655248 - r15655245;
        double r15655250 = fma(r15655244, r15655246, r15655249);
        double r15655251 = r15655241 + r15655250;
        return r15655251;
}

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. Using strategy rm

  3. Applied associate--l+0.3

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

  4. Applied associate-+l+0.3

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

  5. Simplified0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"

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

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