Average Error: 0.2 → 0.3
Time: 13.8s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{1} \cdot {t}^{\frac{1}{3}}\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{1} \cdot {t}^{\frac{1}{3}}\right)
double f(double x, double y, double z, double t, double a) {
        double r72169 = x;
        double r72170 = y;
        double r72171 = r72169 + r72170;
        double r72172 = log(r72171);
        double r72173 = z;
        double r72174 = log(r72173);
        double r72175 = r72172 + r72174;
        double r72176 = t;
        double r72177 = r72175 - r72176;
        double r72178 = a;
        double r72179 = 0.5;
        double r72180 = r72178 - r72179;
        double r72181 = log(r72176);
        double r72182 = r72180 * r72181;
        double r72183 = r72177 + r72182;
        return r72183;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r72184 = x;
        double r72185 = y;
        double r72186 = r72184 + r72185;
        double r72187 = log(r72186);
        double r72188 = z;
        double r72189 = log(r72188);
        double r72190 = r72187 + r72189;
        double r72191 = t;
        double r72192 = r72190 - r72191;
        double r72193 = cbrt(r72191);
        double r72194 = r72193 * r72193;
        double r72195 = log(r72194);
        double r72196 = a;
        double r72197 = 0.5;
        double r72198 = r72196 - r72197;
        double r72199 = r72195 * r72198;
        double r72200 = r72192 + r72199;
        double r72201 = 1.0;
        double r72202 = cbrt(r72201);
        double r72203 = 0.3333333333333333;
        double r72204 = pow(r72191, r72203);
        double r72205 = r72202 * r72204;
        double r72206 = log(r72205);
        double r72207 = r72198 * r72206;
        double r72208 = r72200 + r72207;
        return r72208;
}

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

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 add-cube-cbrt0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}\]

  4. Applied log-prod0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right)}\]

  5. Applied distribute-lft-in0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{\left(\left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)}\]

  6. Applied associate-+r+0.3

    \[\leadsto \color{blue}{\left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)}\]

  7. Simplified0.3

    \[\leadsto \color{blue}{\left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right)} + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\]
  8. Using strategy rm

  9. Applied *-un-lft-identity0.3

    \[\leadsto \left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{\color{blue}{1 \cdot t}}\right)\]

  10. Applied cbrt-prod0.3

    \[\leadsto \left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{t}\right)}\]

  11. Simplified0.3

    \[\leadsto \left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{1} \cdot \color{blue}{{t}^{\frac{1}{3}}}\right)\]

  12. Final simplification0.3

    \[\leadsto \left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{1} \cdot {t}^{\frac{1}{3}}\right)\]

Reproduce

herbie shell --seed 2020083 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))