Average Error: 0.1 → 0.1
Time: 36.2s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(a + \left(\log y \cdot x + z\right)\right) + t\right) + \left(\log \left(\sqrt[3]{c}\right) + \log \left(\sqrt[3]{c}\right)\right) \cdot \left(b - 0.5\right)\right) + \left(b - 0.5\right) \cdot \log \left({c}^{\frac{1}{3}}\right)\right) + i \cdot y\]
\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(a + \left(\log y \cdot x + z\right)\right) + t\right) + \left(\log \left(\sqrt[3]{c}\right) + \log \left(\sqrt[3]{c}\right)\right) \cdot \left(b - 0.5\right)\right) + \left(b - 0.5\right) \cdot \log \left({c}^{\frac{1}{3}}\right)\right) + i \cdot y
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4132400 = x;
        double r4132401 = y;
        double r4132402 = log(r4132401);
        double r4132403 = r4132400 * r4132402;
        double r4132404 = z;
        double r4132405 = r4132403 + r4132404;
        double r4132406 = t;
        double r4132407 = r4132405 + r4132406;
        double r4132408 = a;
        double r4132409 = r4132407 + r4132408;
        double r4132410 = b;
        double r4132411 = 0.5;
        double r4132412 = r4132410 - r4132411;
        double r4132413 = c;
        double r4132414 = log(r4132413);
        double r4132415 = r4132412 * r4132414;
        double r4132416 = r4132409 + r4132415;
        double r4132417 = i;
        double r4132418 = r4132401 * r4132417;
        double r4132419 = r4132416 + r4132418;
        return r4132419;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4132420 = a;
        double r4132421 = y;
        double r4132422 = log(r4132421);
        double r4132423 = x;
        double r4132424 = r4132422 * r4132423;
        double r4132425 = z;
        double r4132426 = r4132424 + r4132425;
        double r4132427 = r4132420 + r4132426;
        double r4132428 = t;
        double r4132429 = r4132427 + r4132428;
        double r4132430 = c;
        double r4132431 = cbrt(r4132430);
        double r4132432 = log(r4132431);
        double r4132433 = r4132432 + r4132432;
        double r4132434 = b;
        double r4132435 = 0.5;
        double r4132436 = r4132434 - r4132435;
        double r4132437 = r4132433 * r4132436;
        double r4132438 = r4132429 + r4132437;
        double r4132439 = 0.3333333333333333;
        double r4132440 = pow(r4132430, r4132439);
        double r4132441 = log(r4132440);
        double r4132442 = r4132436 * r4132441;
        double r4132443 = r4132438 + r4132442;
        double r4132444 = i;
        double r4132445 = r4132444 * r4132421;
        double r4132446 = r4132443 + r4132445;
        return r4132446;
}

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-rgt-in0.1

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

  6. Applied associate-+r+0.1

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

  7. Simplified0.1

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

  9. Applied pow1/30.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))