Average Error: 0.3 → 0.3
Time: 45.0s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right)\right) + \log \left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right) \cdot \left(a - 0.5\right)\]
\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) + \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right)\right) + \log \left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right) \cdot \left(a - 0.5\right)
double f(double x, double y, double z, double t, double a) {
        double r59168 = x;
        double r59169 = y;
        double r59170 = r59168 + r59169;
        double r59171 = log(r59170);
        double r59172 = z;
        double r59173 = log(r59172);
        double r59174 = r59171 + r59173;
        double r59175 = t;
        double r59176 = r59174 - r59175;
        double r59177 = a;
        double r59178 = 0.5;
        double r59179 = r59177 - r59178;
        double r59180 = log(r59175);
        double r59181 = r59179 * r59180;
        double r59182 = r59176 + r59181;
        return r59182;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r59183 = x;
        double r59184 = y;
        double r59185 = r59183 + r59184;
        double r59186 = log(r59185);
        double r59187 = z;
        double r59188 = log(r59187);
        double r59189 = r59186 + r59188;
        double r59190 = t;
        double r59191 = r59189 - r59190;
        double r59192 = 2.0;
        double r59193 = cbrt(r59190);
        double r59194 = log(r59193);
        double r59195 = r59192 * r59194;
        double r59196 = a;
        double r59197 = 0.5;
        double r59198 = r59196 - r59197;
        double r59199 = r59195 * r59198;
        double r59200 = r59191 + r59199;
        double r59201 = 1.0;
        double r59202 = r59201 / r59190;
        double r59203 = -0.3333333333333333;
        double r59204 = pow(r59202, r59203);
        double r59205 = log(r59204);
        double r59206 = r59205 * r59198;
        double r59207 = r59200 + r59206;
        return r59207;
}

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 0.3

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

  3. Applied 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-rgt-in0.3

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

  6. Applied associate-+r+0.3

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

  7. Simplified0.3

    \[\leadsto \color{blue}{\left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right)\right)} + \log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\]

  8. Taylor expanded around inf 0.3

    \[\leadsto \left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right)\right) + \log \color{blue}{\left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right)} \cdot \left(a - 0.5\right)\]

  9. Final simplification0.3

    \[\leadsto \left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot \left(a - 0.5\right)\right) + \log \left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right) \cdot \left(a - 0.5\right)\]

Reproduce

herbie shell --seed 2019322 
(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))))