Average Error: 0.1 → 0.1
Time: 13.3s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(\sqrt[3]{1} \cdot {y}^{\frac{1}{3}}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
↓
\left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(\sqrt[3]{1} \cdot {y}^{\frac{1}{3}}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r70457 = x;
        double r70458 = y;
        double r70459 = log(r70458);
        double r70460 = r70457 * r70459;
        double r70461 = z;
        double r70462 = r70460 + r70461;
        double r70463 = t;
        double r70464 = r70462 + r70463;
        double r70465 = a;
        double r70466 = r70464 + r70465;
        double r70467 = b;
        double r70468 = 0.5;
        double r70469 = r70467 - r70468;
        double r70470 = c;
        double r70471 = log(r70470);
        double r70472 = r70469 * r70471;
        double r70473 = r70466 + r70472;
        double r70474 = i;
        double r70475 = r70458 * r70474;
        double r70476 = r70473 + r70475;
        return r70476;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r70477 = x;
        double r70478 = 2.0;
        double r70479 = y;
        double r70480 = cbrt(r70479);
        double r70481 = log(r70480);
        double r70482 = r70478 * r70481;
        double r70483 = r70477 * r70482;
        double r70484 = 1.0;
        double r70485 = cbrt(r70484);
        double r70486 = 0.3333333333333333;
        double r70487 = pow(r70479, r70486);
        double r70488 = r70485 * r70487;
        double r70489 = log(r70488);
        double r70490 = r70477 * r70489;
        double r70491 = r70483 + r70490;
        double r70492 = z;
        double r70493 = r70491 + r70492;
        double r70494 = t;
        double r70495 = r70493 + r70494;
        double r70496 = a;
        double r70497 = r70495 + r70496;
        double r70498 = b;
        double r70499 = 0.5;
        double r70500 = r70498 - r70499;
        double r70501 = c;
        double r70502 = log(r70501);
        double r70503 = r70500 * r70502;
        double r70504 = r70497 + r70503;
        double r70505 = i;
        double r70506 = r70479 * r70505;
        double r70507 = r70504 + r70506;
        return r70507;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

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

  8. Applied *-un-lft-identity0.1

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

  9. Applied cbrt-prod0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019362 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))