Average Error: 0.3 → 0.3
Time: 15.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\log \left(\sqrt[3]{x + y}\right) + \log z\right)\right) - t\right) + \left(\left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\log \left(\sqrt[3]{x + y}\right) + \log z\right)\right) - t\right) + \left(\left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt{t}\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r59419 = x;
        double r59420 = y;
        double r59421 = r59419 + r59420;
        double r59422 = log(r59421);
        double r59423 = z;
        double r59424 = log(r59423);
        double r59425 = r59422 + r59424;
        double r59426 = t;
        double r59427 = r59425 - r59426;
        double r59428 = a;
        double r59429 = 0.5;
        double r59430 = r59428 - r59429;
        double r59431 = log(r59426);
        double r59432 = r59430 * r59431;
        double r59433 = r59427 + r59432;
        return r59433;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r59434 = x;
        double r59435 = y;
        double r59436 = r59434 + r59435;
        double r59437 = cbrt(r59436);
        double r59438 = r59437 * r59437;
        double r59439 = log(r59438);
        double r59440 = log(r59437);
        double r59441 = z;
        double r59442 = log(r59441);
        double r59443 = r59440 + r59442;
        double r59444 = r59439 + r59443;
        double r59445 = t;
        double r59446 = r59444 - r59445;
        double r59447 = a;
        double r59448 = 0.5;
        double r59449 = r59447 - r59448;
        double r59450 = sqrt(r59445);
        double r59451 = log(r59450);
        double r59452 = r59449 * r59451;
        double r59453 = r59452 + r59452;
        double r59454 = r59446 + r59453;
        return r59454;
}

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-sqr-sqrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied distribute-lft-in0.3

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

  7. Applied add-cube-cbrt0.3

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

  8. Applied log-prod0.3

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

  9. Applied associate-+l+0.3

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

  10. Final simplification0.3

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

Reproduce

herbie shell --seed 2020035 
(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))))