Average Error: 0.1 → 0.1
Time: 38.7s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(z + \left(\left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right) \cdot x + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right)\right) + t\right) + a\right) + \log c \cdot \left(b - 0.5\right)\right) + y \cdot i\]
\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(\left(\left(\left(z + \left(\left(\log \left(\sqrt[3]{y}\right) + \log \left(\sqrt[3]{y}\right)\right) \cdot x + x \cdot \log \left({y}^{\frac{1}{3}}\right)\right)\right) + t\right) + a\right) + \log c \cdot \left(b - 0.5\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3311001 = x;
        double r3311002 = y;
        double r3311003 = log(r3311002);
        double r3311004 = r3311001 * r3311003;
        double r3311005 = z;
        double r3311006 = r3311004 + r3311005;
        double r3311007 = t;
        double r3311008 = r3311006 + r3311007;
        double r3311009 = a;
        double r3311010 = r3311008 + r3311009;
        double r3311011 = b;
        double r3311012 = 0.5;
        double r3311013 = r3311011 - r3311012;
        double r3311014 = c;
        double r3311015 = log(r3311014);
        double r3311016 = r3311013 * r3311015;
        double r3311017 = r3311010 + r3311016;
        double r3311018 = i;
        double r3311019 = r3311002 * r3311018;
        double r3311020 = r3311017 + r3311019;
        return r3311020;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3311021 = z;
        double r3311022 = y;
        double r3311023 = cbrt(r3311022);
        double r3311024 = log(r3311023);
        double r3311025 = r3311024 + r3311024;
        double r3311026 = x;
        double r3311027 = r3311025 * r3311026;
        double r3311028 = 0.3333333333333333;
        double r3311029 = pow(r3311022, r3311028);
        double r3311030 = log(r3311029);
        double r3311031 = r3311026 * r3311030;
        double r3311032 = r3311027 + r3311031;
        double r3311033 = r3311021 + r3311032;
        double r3311034 = t;
        double r3311035 = r3311033 + r3311034;
        double r3311036 = a;
        double r3311037 = r3311035 + r3311036;
        double r3311038 = c;
        double r3311039 = log(r3311038);
        double r3311040 = b;
        double r3311041 = 0.5;
        double r3311042 = r3311040 - r3311041;
        double r3311043 = r3311039 * r3311042;
        double r3311044 = r3311037 + r3311043;
        double r3311045 = i;
        double r3311046 = r3311022 * r3311045;
        double r3311047 = r3311044 + r3311046;
        return r3311047;
}

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-rgt-in0.1

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

  6. Simplified0.1

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

  8. Applied pow1/30.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 
(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)))