Average Error: 0.1 → 0.1
Time: 10.0s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\log \left({y}^{\frac{1}{3}}\right) \cdot x + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
↓
\left(\left(\left(\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\log \left({y}^{\frac{1}{3}}\right) \cdot x + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r90497 = x;
        double r90498 = y;
        double r90499 = log(r90498);
        double r90500 = r90497 * r90499;
        double r90501 = z;
        double r90502 = r90500 + r90501;
        double r90503 = t;
        double r90504 = r90502 + r90503;
        double r90505 = a;
        double r90506 = r90504 + r90505;
        double r90507 = b;
        double r90508 = 0.5;
        double r90509 = r90507 - r90508;
        double r90510 = c;
        double r90511 = log(r90510);
        double r90512 = r90509 * r90511;
        double r90513 = r90506 + r90512;
        double r90514 = i;
        double r90515 = r90498 * r90514;
        double r90516 = r90513 + r90515;
        return r90516;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r90517 = x;
        double r90518 = y;
        double r90519 = cbrt(r90518);
        double r90520 = r90519 * r90519;
        double r90521 = log(r90520);
        double r90522 = r90517 * r90521;
        double r90523 = 0.3333333333333333;
        double r90524 = pow(r90518, r90523);
        double r90525 = log(r90524);
        double r90526 = r90525 * r90517;
        double r90527 = z;
        double r90528 = r90526 + r90527;
        double r90529 = r90522 + r90528;
        double r90530 = t;
        double r90531 = r90529 + r90530;
        double r90532 = a;
        double r90533 = r90531 + r90532;
        double r90534 = b;
        double r90535 = 0.5;
        double r90536 = r90534 - r90535;
        double r90537 = c;
        double r90538 = log(r90537);
        double r90539 = r90536 * r90538;
        double r90540 = r90533 + r90539;
        double r90541 = i;
        double r90542 = r90518 * r90541;
        double r90543 = r90540 + r90542;
        return r90543;
}

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

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Applied associate-+l+0.1

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

  7. Simplified0.1

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

  9. Applied pow1/30.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020065 
(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)))