Average Error: 0.1 → 0.2
Time: 14.9s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(2 \cdot \log \left(\sqrt[3]{{\left({c}^{\left(\sqrt[3]{\frac{2}{3}} \cdot \sqrt[3]{\frac{2}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{2}{3}}\right)}} \cdot \sqrt[3]{\sqrt[3]{c}}\right)\right) \cdot \left(b - 0.5\right) + \left(b - 0.5\right) \cdot \log \left({c}^{\frac{1}{3}}\right)\right)\right) + y \cdot i\]
\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(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(2 \cdot \log \left(\sqrt[3]{{\left({c}^{\left(\sqrt[3]{\frac{2}{3}} \cdot \sqrt[3]{\frac{2}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{2}{3}}\right)}} \cdot \sqrt[3]{\sqrt[3]{c}}\right)\right) \cdot \left(b - 0.5\right) + \left(b - 0.5\right) \cdot \log \left({c}^{\frac{1}{3}}\right)\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r92400 = x;
        double r92401 = y;
        double r92402 = log(r92401);
        double r92403 = r92400 * r92402;
        double r92404 = z;
        double r92405 = r92403 + r92404;
        double r92406 = t;
        double r92407 = r92405 + r92406;
        double r92408 = a;
        double r92409 = r92407 + r92408;
        double r92410 = b;
        double r92411 = 0.5;
        double r92412 = r92410 - r92411;
        double r92413 = c;
        double r92414 = log(r92413);
        double r92415 = r92412 * r92414;
        double r92416 = r92409 + r92415;
        double r92417 = i;
        double r92418 = r92401 * r92417;
        double r92419 = r92416 + r92418;
        return r92419;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r92420 = x;
        double r92421 = y;
        double r92422 = log(r92421);
        double r92423 = r92420 * r92422;
        double r92424 = z;
        double r92425 = r92423 + r92424;
        double r92426 = t;
        double r92427 = r92425 + r92426;
        double r92428 = a;
        double r92429 = r92427 + r92428;
        double r92430 = 2.0;
        double r92431 = c;
        double r92432 = 0.6666666666666666;
        double r92433 = cbrt(r92432);
        double r92434 = r92433 * r92433;
        double r92435 = pow(r92431, r92434);
        double r92436 = pow(r92435, r92433);
        double r92437 = cbrt(r92436);
        double r92438 = cbrt(r92431);
        double r92439 = cbrt(r92438);
        double r92440 = r92437 * r92439;
        double r92441 = log(r92440);
        double r92442 = r92430 * r92441;
        double r92443 = b;
        double r92444 = 0.5;
        double r92445 = r92443 - r92444;
        double r92446 = r92442 * r92445;
        double r92447 = 0.3333333333333333;
        double r92448 = pow(r92431, r92447);
        double r92449 = log(r92448);
        double r92450 = r92445 * r92449;
        double r92451 = r92446 + r92450;
        double r92452 = r92429 + r92451;
        double r92453 = i;
        double r92454 = r92421 * r92453;
        double r92455 = r92452 + r92454;
        return r92455;
}

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

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

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

  8. Applied pow1/30.1

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

  10. Applied add-cube-cbrt0.1

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

  11. Applied cbrt-prod0.1

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

  12. Simplified0.1

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

  14. Applied add-cube-cbrt0.2

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

  15. Applied pow-unpow0.2

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

  16. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 
(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)))