Average Error: 0.3 → 0.3
Time: 31.0s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log z + \log t \cdot a\right) - \left(t + 0.5 \cdot \log t\right)\right) + \log \left(y + x\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log z + \log t \cdot a\right) - \left(t + 0.5 \cdot \log t\right)\right) + \log \left(y + x\right)
double f(double x, double y, double z, double t, double a) {
        double r15440982 = x;
        double r15440983 = y;
        double r15440984 = r15440982 + r15440983;
        double r15440985 = log(r15440984);
        double r15440986 = z;
        double r15440987 = log(r15440986);
        double r15440988 = r15440985 + r15440987;
        double r15440989 = t;
        double r15440990 = r15440988 - r15440989;
        double r15440991 = a;
        double r15440992 = 0.5;
        double r15440993 = r15440991 - r15440992;
        double r15440994 = log(r15440989);
        double r15440995 = r15440993 * r15440994;
        double r15440996 = r15440990 + r15440995;
        return r15440996;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r15440997 = z;
        double r15440998 = log(r15440997);
        double r15440999 = t;
        double r15441000 = log(r15440999);
        double r15441001 = a;
        double r15441002 = r15441000 * r15441001;
        double r15441003 = r15440998 + r15441002;
        double r15441004 = 0.5;
        double r15441005 = r15441004 * r15441000;
        double r15441006 = r15440999 + r15441005;
        double r15441007 = r15441003 - r15441006;
        double r15441008 = y;
        double r15441009 = x;
        double r15441010 = r15441008 + r15441009;
        double r15441011 = log(r15441010);
        double r15441012 = r15441007 + r15441011;
        return r15441012;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Taylor expanded around 0 0.3

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

  6. Final simplification0.3

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

Reproduce

herbie shell --seed 2019162 
(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))))