Average Error: 0.3 → 0.3
Time: 49.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(a - 0.5\right) \cdot \log \left({t}^{\frac{1}{3}}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(a - 0.5\right) \cdot \log \left({t}^{\frac{1}{3}}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right)\right) + \left(\left(\log \left(y + x\right) + \log z\right) - t\right)
double f(double x, double y, double z, double t, double a) {
        double r2949256 = x;
        double r2949257 = y;
        double r2949258 = r2949256 + r2949257;
        double r2949259 = log(r2949258);
        double r2949260 = z;
        double r2949261 = log(r2949260);
        double r2949262 = r2949259 + r2949261;
        double r2949263 = t;
        double r2949264 = r2949262 - r2949263;
        double r2949265 = a;
        double r2949266 = 0.5;
        double r2949267 = r2949265 - r2949266;
        double r2949268 = log(r2949263);
        double r2949269 = r2949267 * r2949268;
        double r2949270 = r2949264 + r2949269;
        return r2949270;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2949271 = a;
        double r2949272 = 0.5;
        double r2949273 = r2949271 - r2949272;
        double r2949274 = t;
        double r2949275 = 0.3333333333333333;
        double r2949276 = pow(r2949274, r2949275);
        double r2949277 = log(r2949276);
        double r2949278 = r2949273 * r2949277;
        double r2949279 = cbrt(r2949274);
        double r2949280 = r2949279 * r2949279;
        double r2949281 = log(r2949280);
        double r2949282 = r2949273 * r2949281;
        double r2949283 = r2949278 + r2949282;
        double r2949284 = y;
        double r2949285 = x;
        double r2949286 = r2949284 + r2949285;
        double r2949287 = log(r2949286);
        double r2949288 = z;
        double r2949289 = log(r2949288);
        double r2949290 = r2949287 + r2949289;
        double r2949291 = r2949290 - r2949274;
        double r2949292 = r2949283 + r2949291;
        return r2949292;
}

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. Using strategy rm

  7. Applied pow1/30.3

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

  8. Final simplification0.3

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

Reproduce

herbie shell --seed 2019119 +o rules:numerics
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))