Average Error: 0.1 → 0.1
Time: 11.7s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left({c}^{\frac{1}{3}}\right)\right)\right) + y \cdot i\]
\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(\left(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(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\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 r78565 = x;
        double r78566 = y;
        double r78567 = log(r78566);
        double r78568 = r78565 * r78567;
        double r78569 = z;
        double r78570 = r78568 + r78569;
        double r78571 = t;
        double r78572 = r78570 + r78571;
        double r78573 = a;
        double r78574 = r78572 + r78573;
        double r78575 = b;
        double r78576 = 0.5;
        double r78577 = r78575 - r78576;
        double r78578 = c;
        double r78579 = log(r78578);
        double r78580 = r78577 * r78579;
        double r78581 = r78574 + r78580;
        double r78582 = i;
        double r78583 = r78566 * r78582;
        double r78584 = r78581 + r78583;
        return r78584;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r78585 = x;
        double r78586 = 2.0;
        double r78587 = y;
        double r78588 = cbrt(r78587);
        double r78589 = log(r78588);
        double r78590 = r78586 * r78589;
        double r78591 = r78585 * r78590;
        double r78592 = r78585 * r78589;
        double r78593 = r78591 + r78592;
        double r78594 = z;
        double r78595 = r78593 + r78594;
        double r78596 = t;
        double r78597 = r78595 + r78596;
        double r78598 = a;
        double r78599 = r78597 + r78598;
        double r78600 = b;
        double r78601 = 0.5;
        double r78602 = r78600 - r78601;
        double r78603 = c;
        double r78604 = cbrt(r78603);
        double r78605 = log(r78604);
        double r78606 = r78586 * r78605;
        double r78607 = r78602 * r78606;
        double r78608 = 0.3333333333333333;
        double r78609 = pow(r78603, r78608);
        double r78610 = log(r78609);
        double r78611 = r78602 * r78610;
        double r78612 = r78607 + r78611;
        double r78613 = r78599 + r78612;
        double r78614 = i;
        double r78615 = r78587 * r78614;
        double r78616 = r78613 + r78615;
        return r78616;
}

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

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

  10. Applied add-cube-cbrt0.1

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

  11. Applied log-prod0.1

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

  12. Applied distribute-lft-in0.1

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

  13. Simplified0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2020018 
(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)))