Average Error: 0.3 → 0.3
Time: 34.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)
double f(double x, double y, double z, double t, double a) {
        double r255160 = x;
        double r255161 = y;
        double r255162 = r255160 + r255161;
        double r255163 = log(r255162);
        double r255164 = z;
        double r255165 = log(r255164);
        double r255166 = r255163 + r255165;
        double r255167 = t;
        double r255168 = r255166 - r255167;
        double r255169 = a;
        double r255170 = 0.5;
        double r255171 = r255169 - r255170;
        double r255172 = log(r255167);
        double r255173 = r255171 * r255172;
        double r255174 = r255168 + r255173;
        return r255174;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r255175 = x;
        double r255176 = y;
        double r255177 = r255175 + r255176;
        double r255178 = log(r255177);
        double r255179 = z;
        double r255180 = log(r255179);
        double r255181 = t;
        double r255182 = r255180 - r255181;
        double r255183 = a;
        double r255184 = 0.5;
        double r255185 = r255183 - r255184;
        double r255186 = log(r255181);
        double r255187 = r255185 * r255186;
        double r255188 = r255182 + r255187;
        double r255189 = r255178 + r255188;
        return r255189;
}

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. Final simplification0.3

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

Reproduce

herbie shell --seed 2019303 
(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))))