Average Error: 0.1 → 0.1
Time: 36.6s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\log c \cdot \left(b - 0.5\right) + \left(\left(\left(\log \left({y}^{\frac{1}{3}}\right) \cdot x + x \cdot \left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{\sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)\right)\right)\right) + z\right) + \left(t + a\right)\right)\right) + y \cdot i\]
\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(\log c \cdot \left(b - 0.5\right) + \left(\left(\left(\log \left({y}^{\frac{1}{3}}\right) \cdot x + x \cdot \left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{\sqrt[3]{y}} \cdot \left(\sqrt[3]{\sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)\right)\right)\right) + z\right) + \left(t + a\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 r4263571 = x;
        double r4263572 = y;
        double r4263573 = log(r4263572);
        double r4263574 = r4263571 * r4263573;
        double r4263575 = z;
        double r4263576 = r4263574 + r4263575;
        double r4263577 = t;
        double r4263578 = r4263576 + r4263577;
        double r4263579 = a;
        double r4263580 = r4263578 + r4263579;
        double r4263581 = b;
        double r4263582 = 0.5;
        double r4263583 = r4263581 - r4263582;
        double r4263584 = c;
        double r4263585 = log(r4263584);
        double r4263586 = r4263583 * r4263585;
        double r4263587 = r4263580 + r4263586;
        double r4263588 = i;
        double r4263589 = r4263572 * r4263588;
        double r4263590 = r4263587 + r4263589;
        return r4263590;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4263591 = c;
        double r4263592 = log(r4263591);
        double r4263593 = b;
        double r4263594 = 0.5;
        double r4263595 = r4263593 - r4263594;
        double r4263596 = r4263592 * r4263595;
        double r4263597 = y;
        double r4263598 = 0.3333333333333333;
        double r4263599 = pow(r4263597, r4263598);
        double r4263600 = log(r4263599);
        double r4263601 = x;
        double r4263602 = r4263600 * r4263601;
        double r4263603 = cbrt(r4263597);
        double r4263604 = log(r4263603);
        double r4263605 = cbrt(r4263603);
        double r4263606 = r4263605 * r4263605;
        double r4263607 = r4263605 * r4263606;
        double r4263608 = log(r4263607);
        double r4263609 = r4263604 + r4263608;
        double r4263610 = r4263601 * r4263609;
        double r4263611 = r4263602 + r4263610;
        double r4263612 = z;
        double r4263613 = r4263611 + r4263612;
        double r4263614 = t;
        double r4263615 = a;
        double r4263616 = r4263614 + r4263615;
        double r4263617 = r4263613 + r4263616;
        double r4263618 = r4263596 + r4263617;
        double r4263619 = i;
        double r4263620 = r4263597 * r4263619;
        double r4263621 = r4263618 + r4263620;
        return r4263621;
}

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 associate-+l+0.1

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

  5. Applied add-cube-cbrt0.1

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

  6. Applied log-prod0.1

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

  7. Applied distribute-lft-in0.1

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

  8. Simplified0.1

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

  10. Applied pow1/30.1

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

  12. Applied add-cube-cbrt0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019163 
(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)))