Average Error: 0.3 → 0.3
Time: 16.3s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + \log \left(x + y\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \log \left({t}^{\frac{1}{3}}\right) \cdot \left(a - 0.5\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{z}\right) + \log \left(x + y\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \log \left({t}^{\frac{1}{3}}\right) \cdot \left(a - 0.5\right)
double f(double x, double y, double z, double t, double a) {
        double r65313 = x;
        double r65314 = y;
        double r65315 = r65313 + r65314;
        double r65316 = log(r65315);
        double r65317 = z;
        double r65318 = log(r65317);
        double r65319 = r65316 + r65318;
        double r65320 = t;
        double r65321 = r65319 - r65320;
        double r65322 = a;
        double r65323 = 0.5;
        double r65324 = r65322 - r65323;
        double r65325 = log(r65320);
        double r65326 = r65324 * r65325;
        double r65327 = r65321 + r65326;
        return r65327;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r65328 = 2.0;
        double r65329 = z;
        double r65330 = cbrt(r65329);
        double r65331 = log(r65330);
        double r65332 = r65328 * r65331;
        double r65333 = x;
        double r65334 = y;
        double r65335 = r65333 + r65334;
        double r65336 = log(r65335);
        double r65337 = r65332 + r65336;
        double r65338 = r65337 + r65331;
        double r65339 = t;
        double r65340 = r65338 - r65339;
        double r65341 = cbrt(r65339);
        double r65342 = r65341 * r65341;
        double r65343 = log(r65342);
        double r65344 = a;
        double r65345 = 0.5;
        double r65346 = r65344 - r65345;
        double r65347 = r65343 * r65346;
        double r65348 = r65340 + r65347;
        double r65349 = 0.3333333333333333;
        double r65350 = pow(r65339, r65349);
        double r65351 = log(r65350);
        double r65352 = r65351 * r65346;
        double r65353 = r65348 + r65352;
        return r65353;
}

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. Using strategy rm

  8. Applied add-cube-cbrt0.3

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

  9. Applied log-prod0.3

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

  10. Applied associate-+r+0.3

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

  11. Simplified0.3

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

  13. Applied pow1/30.3

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

  14. Final simplification0.3

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

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))))