Average Error: 0.1 → 0.1
Time: 33.5s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(t + \left(\left(\left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right) + z\right)\right)\right)\right) + i \cdot y\]
\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(b - 0.5\right) \cdot \log c + \left(a + \left(t + \left(\left(\left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right) + z\right)\right)\right)\right) + i \cdot y
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3285658 = x;
        double r3285659 = y;
        double r3285660 = log(r3285659);
        double r3285661 = r3285658 * r3285660;
        double r3285662 = z;
        double r3285663 = r3285661 + r3285662;
        double r3285664 = t;
        double r3285665 = r3285663 + r3285664;
        double r3285666 = a;
        double r3285667 = r3285665 + r3285666;
        double r3285668 = b;
        double r3285669 = 0.5;
        double r3285670 = r3285668 - r3285669;
        double r3285671 = c;
        double r3285672 = log(r3285671);
        double r3285673 = r3285670 * r3285672;
        double r3285674 = r3285667 + r3285673;
        double r3285675 = i;
        double r3285676 = r3285659 * r3285675;
        double r3285677 = r3285674 + r3285676;
        return r3285677;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3285678 = b;
        double r3285679 = 0.5;
        double r3285680 = r3285678 - r3285679;
        double r3285681 = c;
        double r3285682 = log(r3285681);
        double r3285683 = r3285680 * r3285682;
        double r3285684 = a;
        double r3285685 = t;
        double r3285686 = y;
        double r3285687 = cbrt(r3285686);
        double r3285688 = log(r3285687);
        double r3285689 = r3285688 + r3285688;
        double r3285690 = x;
        double r3285691 = r3285689 * r3285690;
        double r3285692 = r3285688 * r3285690;
        double r3285693 = r3285691 + r3285692;
        double r3285694 = z;
        double r3285695 = r3285693 + r3285694;
        double r3285696 = r3285685 + r3285695;
        double r3285697 = r3285684 + r3285696;
        double r3285698 = r3285683 + r3285697;
        double r3285699 = i;
        double r3285700 = r3285699 * r3285686;
        double r3285701 = r3285698 + r3285700;
        return r3285701;
}

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. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019165 
(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)))