Average Error: 0.1 → 0.1
Time: 27.2s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(2 \cdot \log \left(\left(\sqrt[3]{{\left({c}^{\frac{2}{3}}\right)}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{{c}^{\frac{2}{3}}}}\right) \cdot \sqrt[3]{\sqrt[3]{c}}\right)\right) \cdot \left(b - 0.5\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right) + y \cdot i\]
\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(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(2 \cdot \log \left(\left(\sqrt[3]{{\left({c}^{\frac{2}{3}}\right)}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{{c}^{\frac{2}{3}}}}\right) \cdot \sqrt[3]{\sqrt[3]{c}}\right)\right) \cdot \left(b - 0.5\right)\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r91507 = x;
        double r91508 = y;
        double r91509 = log(r91508);
        double r91510 = r91507 * r91509;
        double r91511 = z;
        double r91512 = r91510 + r91511;
        double r91513 = t;
        double r91514 = r91512 + r91513;
        double r91515 = a;
        double r91516 = r91514 + r91515;
        double r91517 = b;
        double r91518 = 0.5;
        double r91519 = r91517 - r91518;
        double r91520 = c;
        double r91521 = log(r91520);
        double r91522 = r91519 * r91521;
        double r91523 = r91516 + r91522;
        double r91524 = i;
        double r91525 = r91508 * r91524;
        double r91526 = r91523 + r91525;
        return r91526;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r91527 = x;
        double r91528 = y;
        double r91529 = log(r91528);
        double r91530 = r91527 * r91529;
        double r91531 = z;
        double r91532 = r91530 + r91531;
        double r91533 = t;
        double r91534 = r91532 + r91533;
        double r91535 = a;
        double r91536 = r91534 + r91535;
        double r91537 = 2.0;
        double r91538 = c;
        double r91539 = 0.6666666666666666;
        double r91540 = pow(r91538, r91539);
        double r91541 = pow(r91540, r91539);
        double r91542 = cbrt(r91541);
        double r91543 = cbrt(r91540);
        double r91544 = cbrt(r91543);
        double r91545 = r91542 * r91544;
        double r91546 = cbrt(r91538);
        double r91547 = cbrt(r91546);
        double r91548 = r91545 * r91547;
        double r91549 = log(r91548);
        double r91550 = r91537 * r91549;
        double r91551 = b;
        double r91552 = 0.5;
        double r91553 = r91551 - r91552;
        double r91554 = r91550 * r91553;
        double r91555 = r91536 + r91554;
        double r91556 = log(r91546);
        double r91557 = r91553 * r91556;
        double r91558 = r91555 + r91557;
        double r91559 = i;
        double r91560 = r91528 * r91559;
        double r91561 = r91558 + r91560;
        return r91561;
}

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. Applied associate-+r+0.1

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

  7. Simplified0.1

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

  9. Applied add-cube-cbrt0.1

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

  10. Applied cbrt-prod0.1

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

  11. Simplified0.1

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

  13. Applied add-cube-cbrt0.1

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

  14. Applied cbrt-prod0.1

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

  15. Simplified0.1

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

  16. Final simplification0.1

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

Reproduce

herbie shell --seed 2019350 
(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)))