Average Error: 0.1 → 0.1
Time: 47.6s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(z + \left(\left(\log \left(\sqrt[3]{y}\right) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right) + \log \left({y}^{\frac{1}{3}}\right) \cdot x\right)\right) + t\right) + a\right) + \log c \cdot \left(b - 0.5\right)\right) + y \cdot i\]
\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) \cdot x + \log \left(\sqrt[3]{y}\right) \cdot x\right) + \log \left({y}^{\frac{1}{3}}\right) \cdot x\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 r4308940 = x;
        double r4308941 = y;
        double r4308942 = log(r4308941);
        double r4308943 = r4308940 * r4308942;
        double r4308944 = z;
        double r4308945 = r4308943 + r4308944;
        double r4308946 = t;
        double r4308947 = r4308945 + r4308946;
        double r4308948 = a;
        double r4308949 = r4308947 + r4308948;
        double r4308950 = b;
        double r4308951 = 0.5;
        double r4308952 = r4308950 - r4308951;
        double r4308953 = c;
        double r4308954 = log(r4308953);
        double r4308955 = r4308952 * r4308954;
        double r4308956 = r4308949 + r4308955;
        double r4308957 = i;
        double r4308958 = r4308941 * r4308957;
        double r4308959 = r4308956 + r4308958;
        return r4308959;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4308960 = z;
        double r4308961 = y;
        double r4308962 = cbrt(r4308961);
        double r4308963 = log(r4308962);
        double r4308964 = x;
        double r4308965 = r4308963 * r4308964;
        double r4308966 = r4308965 + r4308965;
        double r4308967 = 0.3333333333333333;
        double r4308968 = pow(r4308961, r4308967);
        double r4308969 = log(r4308968);
        double r4308970 = r4308969 * r4308964;
        double r4308971 = r4308966 + r4308970;
        double r4308972 = r4308960 + r4308971;
        double r4308973 = t;
        double r4308974 = r4308972 + r4308973;
        double r4308975 = a;
        double r4308976 = r4308974 + r4308975;
        double r4308977 = c;
        double r4308978 = log(r4308977);
        double r4308979 = b;
        double r4308980 = 0.5;
        double r4308981 = r4308979 - r4308980;
        double r4308982 = r4308978 * r4308981;
        double r4308983 = r4308976 + r4308982;
        double r4308984 = i;
        double r4308985 = r4308961 * r4308984;
        double r4308986 = r4308983 + r4308985;
        return r4308986;
}

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

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

  8. Applied pow1/30.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 
(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)))