Average Error: 0.1 → 0.1
Time: 16.1s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left({c}^{\frac{1}{3}}\right) + \log \left(\sqrt{\sqrt[3]{c}}\right)\right) + \log \left(\sqrt{\sqrt[3]{c}}\right) \cdot \left(b - 0.5\right)\right)\right) + y \cdot i\]
\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(b - 0.5\right) \cdot \left(2 \cdot \log \left({c}^{\frac{1}{3}}\right) + \log \left(\sqrt{\sqrt[3]{c}}\right)\right) + \log \left(\sqrt{\sqrt[3]{c}}\right) \cdot \left(b - 0.5\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 r80389 = x;
        double r80390 = y;
        double r80391 = log(r80390);
        double r80392 = r80389 * r80391;
        double r80393 = z;
        double r80394 = r80392 + r80393;
        double r80395 = t;
        double r80396 = r80394 + r80395;
        double r80397 = a;
        double r80398 = r80396 + r80397;
        double r80399 = b;
        double r80400 = 0.5;
        double r80401 = r80399 - r80400;
        double r80402 = c;
        double r80403 = log(r80402);
        double r80404 = r80401 * r80403;
        double r80405 = r80398 + r80404;
        double r80406 = i;
        double r80407 = r80390 * r80406;
        double r80408 = r80405 + r80407;
        return r80408;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r80409 = x;
        double r80410 = y;
        double r80411 = log(r80410);
        double r80412 = r80409 * r80411;
        double r80413 = z;
        double r80414 = r80412 + r80413;
        double r80415 = t;
        double r80416 = r80414 + r80415;
        double r80417 = a;
        double r80418 = r80416 + r80417;
        double r80419 = b;
        double r80420 = 0.5;
        double r80421 = r80419 - r80420;
        double r80422 = 2.0;
        double r80423 = c;
        double r80424 = 0.3333333333333333;
        double r80425 = pow(r80423, r80424);
        double r80426 = log(r80425);
        double r80427 = r80422 * r80426;
        double r80428 = cbrt(r80423);
        double r80429 = sqrt(r80428);
        double r80430 = log(r80429);
        double r80431 = r80427 + r80430;
        double r80432 = r80421 * r80431;
        double r80433 = r80430 * r80421;
        double r80434 = r80432 + r80433;
        double r80435 = r80418 + r80434;
        double r80436 = i;
        double r80437 = r80410 * r80436;
        double r80438 = r80435 + r80437;
        return r80438;
}

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

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

  8. Applied pow1/30.1

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

  10. Applied add-sqr-sqrt0.1

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

  11. Applied log-prod0.1

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

  12. Applied distribute-rgt-in0.1

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

  13. Applied associate-+r+0.1

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

  14. Simplified0.1

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

  15. Final simplification0.1

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

Reproduce

herbie shell --seed 2019322 
(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)))