Average Error: 0.2 → 0.2
Time: 26.9s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(x + y\right) + \left(\left(\log \left(\sqrt{z}\right) + \left(\log \left(\sqrt{z}\right) - t\right)\right) + \left(a - 0.5\right) \cdot \log t\right)\]
\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 \left(\sqrt{z}\right) + \left(\log \left(\sqrt{z}\right) - t\right)\right) + \left(a - 0.5\right) \cdot \log t\right)
double f(double x, double y, double z, double t, double a) {
        double r1572139 = x;
        double r1572140 = y;
        double r1572141 = r1572139 + r1572140;
        double r1572142 = log(r1572141);
        double r1572143 = z;
        double r1572144 = log(r1572143);
        double r1572145 = r1572142 + r1572144;
        double r1572146 = t;
        double r1572147 = r1572145 - r1572146;
        double r1572148 = a;
        double r1572149 = 0.5;
        double r1572150 = r1572148 - r1572149;
        double r1572151 = log(r1572146);
        double r1572152 = r1572150 * r1572151;
        double r1572153 = r1572147 + r1572152;
        return r1572153;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1572154 = x;
        double r1572155 = y;
        double r1572156 = r1572154 + r1572155;
        double r1572157 = log(r1572156);
        double r1572158 = z;
        double r1572159 = sqrt(r1572158);
        double r1572160 = log(r1572159);
        double r1572161 = t;
        double r1572162 = r1572160 - r1572161;
        double r1572163 = r1572160 + r1572162;
        double r1572164 = a;
        double r1572165 = 0.5;
        double r1572166 = r1572164 - r1572165;
        double r1572167 = log(r1572161);
        double r1572168 = r1572166 * r1572167;
        double r1572169 = r1572163 + r1572168;
        double r1572170 = r1572157 + r1572169;
        return r1572170;
}

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

Original0.2
Target0.2
Herbie0.2
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

Derivation

  1. Initial program 0.2

    \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
  2. Using strategy rm

  3. Applied associate--l+0.2

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

  4. Applied associate-+l+0.2

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

  6. Applied add-sqr-sqrt0.2

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

  7. Applied log-prod0.2

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

  8. Applied associate--l+0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019235 
(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))))