Average Error: 0.3 → 0.3
Time: 12.2s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\log \left(\sqrt[3]{x + y}\right) + 2 \cdot \log \left(\sqrt{z}\right)\right)\right) - \left(t - \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right)\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right) + \left(\log \left(\sqrt[3]{x + y}\right) + 2 \cdot \log \left(\sqrt{z}\right)\right)\right) - \left(t - \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right)\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)
double f(double x, double y, double z, double t, double a) {
        double r81447 = x;
        double r81448 = y;
        double r81449 = r81447 + r81448;
        double r81450 = log(r81449);
        double r81451 = z;
        double r81452 = log(r81451);
        double r81453 = r81450 + r81452;
        double r81454 = t;
        double r81455 = r81453 - r81454;
        double r81456 = a;
        double r81457 = 0.5;
        double r81458 = r81456 - r81457;
        double r81459 = log(r81454);
        double r81460 = r81458 * r81459;
        double r81461 = r81455 + r81460;
        return r81461;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r81462 = x;
        double r81463 = y;
        double r81464 = r81462 + r81463;
        double r81465 = cbrt(r81464);
        double r81466 = r81465 * r81465;
        double r81467 = log(r81466);
        double r81468 = log(r81465);
        double r81469 = 2.0;
        double r81470 = z;
        double r81471 = sqrt(r81470);
        double r81472 = log(r81471);
        double r81473 = r81469 * r81472;
        double r81474 = r81468 + r81473;
        double r81475 = r81467 + r81474;
        double r81476 = t;
        double r81477 = sqrt(r81476);
        double r81478 = log(r81477);
        double r81479 = a;
        double r81480 = 0.5;
        double r81481 = r81479 - r81480;
        double r81482 = r81478 * r81481;
        double r81483 = r81476 - r81482;
        double r81484 = r81475 - r81483;
        double r81485 = r81484 + r81482;
        return r81485;
}

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

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

  4. Applied log-prod0.3

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

  5. Applied associate-+r+0.3

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

  7. Applied add-sqr-sqrt0.3

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

  8. Applied log-prod0.3

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

  9. Applied distribute-rgt-in0.3

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

  10. Applied associate-+r+0.3

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

  11. Simplified0.3

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

  13. Applied add-cube-cbrt0.3

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

  14. Applied log-prod0.3

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

  15. Applied associate-+l+0.3

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

  16. Final simplification0.3

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

Reproduce

herbie shell --seed 2020046 
(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))))