Average Error: 0.3 → 0.3
Time: 24.0s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\log \left(x + y\right) + \log z\right) - \left(t - \left(a - \frac{1}{2}\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right) + \log \left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right)\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\log \left(x + y\right) + \log z\right) - \left(t - \left(a - \frac{1}{2}\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right) + \log \left({\left(\frac{1}{t}\right)}^{\frac{-1}{3}}\right)\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r73272 = x;
        double r73273 = y;
        double r73274 = r73272 + r73273;
        double r73275 = log(r73274);
        double r73276 = z;
        double r73277 = log(r73276);
        double r73278 = r73275 + r73277;
        double r73279 = t;
        double r73280 = r73278 - r73279;
        double r73281 = a;
        double r73282 = 0.5;
        double r73283 = r73281 - r73282;
        double r73284 = log(r73279);
        double r73285 = r73283 * r73284;
        double r73286 = r73280 + r73285;
        return r73286;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r73287 = x;
        double r73288 = y;
        double r73289 = r73287 + r73288;
        double r73290 = log(r73289);
        double r73291 = z;
        double r73292 = log(r73291);
        double r73293 = r73290 + r73292;
        double r73294 = t;
        double r73295 = a;
        double r73296 = 1.0;
        double r73297 = 2.0;
        double r73298 = r73296 / r73297;
        double r73299 = r73295 - r73298;
        double r73300 = 2.0;
        double r73301 = cbrt(r73294);
        double r73302 = log(r73301);
        double r73303 = r73300 * r73302;
        double r73304 = 1.0;
        double r73305 = r73304 / r73294;
        double r73306 = -0.3333333333333333;
        double r73307 = pow(r73305, r73306);
        double r73308 = log(r73307);
        double r73309 = r73303 + r73308;
        double r73310 = r73299 * r73309;
        double r73311 = r73294 - r73310;
        double r73312 = r73293 - r73311;
        return r73312;
}

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-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. Simplified0.3

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

  7. Simplified0.3

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

  8. Taylor expanded around inf 0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019304 
(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))))