Average Error: 0.1 → 0.1
Time: 35.1s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[y \cdot i + \left(\left(\left(\left(\left(\log y \cdot x + t\right) + z\right) + \left(\left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right)\right) + a\right) + \log \left({\left({c}^{\left(\sqrt[3]{\frac{1}{3}} \cdot \sqrt[3]{\frac{1}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{1}{3}}\right)}\right) \cdot \left(b - 0.5\right)\right)\]
\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
↓
y \cdot i + \left(\left(\left(\left(\left(\log y \cdot x + t\right) + z\right) + \left(\left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right)\right) + a\right) + \log \left({\left({c}^{\left(\sqrt[3]{\frac{1}{3}} \cdot \sqrt[3]{\frac{1}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{1}{3}}\right)}\right) \cdot \left(b - 0.5\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3700584 = x;
        double r3700585 = y;
        double r3700586 = log(r3700585);
        double r3700587 = r3700584 * r3700586;
        double r3700588 = z;
        double r3700589 = r3700587 + r3700588;
        double r3700590 = t;
        double r3700591 = r3700589 + r3700590;
        double r3700592 = a;
        double r3700593 = r3700591 + r3700592;
        double r3700594 = b;
        double r3700595 = 0.5;
        double r3700596 = r3700594 - r3700595;
        double r3700597 = c;
        double r3700598 = log(r3700597);
        double r3700599 = r3700596 * r3700598;
        double r3700600 = r3700593 + r3700599;
        double r3700601 = i;
        double r3700602 = r3700585 * r3700601;
        double r3700603 = r3700600 + r3700602;
        return r3700603;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3700604 = y;
        double r3700605 = i;
        double r3700606 = r3700604 * r3700605;
        double r3700607 = log(r3700604);
        double r3700608 = x;
        double r3700609 = r3700607 * r3700608;
        double r3700610 = t;
        double r3700611 = r3700609 + r3700610;
        double r3700612 = z;
        double r3700613 = r3700611 + r3700612;
        double r3700614 = b;
        double r3700615 = 0.5;
        double r3700616 = r3700614 - r3700615;
        double r3700617 = c;
        double r3700618 = cbrt(r3700617);
        double r3700619 = log(r3700618);
        double r3700620 = r3700616 * r3700619;
        double r3700621 = r3700620 + r3700620;
        double r3700622 = r3700613 + r3700621;
        double r3700623 = a;
        double r3700624 = r3700622 + r3700623;
        double r3700625 = 0.3333333333333333;
        double r3700626 = cbrt(r3700625);
        double r3700627 = r3700626 * r3700626;
        double r3700628 = pow(r3700617, r3700627);
        double r3700629 = pow(r3700628, r3700626);
        double r3700630 = log(r3700629);
        double r3700631 = r3700630 * r3700616;
        double r3700632 = r3700624 + r3700631;
        double r3700633 = r3700606 + r3700632;
        return r3700633;
}

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

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

  9. Applied pow1/30.1

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

  11. Applied add-cube-cbrt0.2

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

  12. Applied pow-unpow0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019169 
(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)))