Average Error: 0.1 → 0.1
Time: 1.7m
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[i \cdot y + \left(\left(\left(\left(z + \left(\left(\log \left(\sqrt[3]{y}\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right) + \log \left(\sqrt[3]{y}\right) \cdot x\right)\right) + t\right) + a\right) + \log c \cdot \left(b - 0.5\right)\right)\]
\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
↓
i \cdot y + \left(\left(\left(\left(z + \left(\left(\log \left(\sqrt[3]{y}\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right) + \log \left(\sqrt[3]{y}\right) \cdot x\right)\right) + t\right) + a\right) + \log c \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 r3653678 = x;
        double r3653679 = y;
        double r3653680 = log(r3653679);
        double r3653681 = r3653678 * r3653680;
        double r3653682 = z;
        double r3653683 = r3653681 + r3653682;
        double r3653684 = t;
        double r3653685 = r3653683 + r3653684;
        double r3653686 = a;
        double r3653687 = r3653685 + r3653686;
        double r3653688 = b;
        double r3653689 = 0.5;
        double r3653690 = r3653688 - r3653689;
        double r3653691 = c;
        double r3653692 = log(r3653691);
        double r3653693 = r3653690 * r3653692;
        double r3653694 = r3653687 + r3653693;
        double r3653695 = i;
        double r3653696 = r3653679 * r3653695;
        double r3653697 = r3653694 + r3653696;
        return r3653697;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3653698 = i;
        double r3653699 = y;
        double r3653700 = r3653698 * r3653699;
        double r3653701 = z;
        double r3653702 = cbrt(r3653699);
        double r3653703 = log(r3653702);
        double r3653704 = x;
        double r3653705 = r3653703 * r3653704;
        double r3653706 = r3653705 + r3653705;
        double r3653707 = r3653706 + r3653705;
        double r3653708 = r3653701 + r3653707;
        double r3653709 = t;
        double r3653710 = r3653708 + r3653709;
        double r3653711 = a;
        double r3653712 = r3653710 + r3653711;
        double r3653713 = c;
        double r3653714 = log(r3653713);
        double r3653715 = b;
        double r3653716 = 0.5;
        double r3653717 = r3653715 - r3653716;
        double r3653718 = r3653714 * r3653717;
        double r3653719 = r3653712 + r3653718;
        double r3653720 = r3653700 + r3653719;
        return r3653720;
}

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

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019200 
(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)))