Average Error: 0.3 → 0.3
Time: 12.1s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\log \left(\sqrt{x + y}\right) + \left(\log \left(\sqrt{x + y}\right) + \left(\log z - t\right)\right)\right) + \left(a - 0.5\right) \cdot \log t\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\log \left(\sqrt{x + y}\right) + \left(\log \left(\sqrt{x + y}\right) + \left(\log z - t\right)\right)\right) + \left(a - 0.5\right) \cdot \log t
double f(double x, double y, double z, double t, double a) {
        double r357209 = x;
        double r357210 = y;
        double r357211 = r357209 + r357210;
        double r357212 = log(r357211);
        double r357213 = z;
        double r357214 = log(r357213);
        double r357215 = r357212 + r357214;
        double r357216 = t;
        double r357217 = r357215 - r357216;
        double r357218 = a;
        double r357219 = 0.5;
        double r357220 = r357218 - r357219;
        double r357221 = log(r357216);
        double r357222 = r357220 * r357221;
        double r357223 = r357217 + r357222;
        return r357223;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r357224 = x;
        double r357225 = y;
        double r357226 = r357224 + r357225;
        double r357227 = sqrt(r357226);
        double r357228 = log(r357227);
        double r357229 = z;
        double r357230 = log(r357229);
        double r357231 = t;
        double r357232 = r357230 - r357231;
        double r357233 = r357228 + r357232;
        double r357234 = r357228 + r357233;
        double r357235 = a;
        double r357236 = 0.5;
        double r357237 = r357235 - r357236;
        double r357238 = log(r357231);
        double r357239 = r357237 * r357238;
        double r357240 = r357234 + r357239;
        return r357240;
}

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. Using strategy rm

  5. Applied add-sqr-sqrt0.3

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

  6. Applied log-prod0.3

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

  7. Applied associate-+l+0.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2020027 +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))))