Average Error: 0.1 → 0.1
Time: 34.1s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(\left(\log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot x + x \cdot \left(\log \left(\sqrt[3]{{y}^{\frac{2}{3}}}\right) + \log y \cdot \frac{2}{3}\right)\right) + z\right)\right)\right)\right) + y \cdot i\]
\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(a + \left(t + \left(\left(\log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot x + x \cdot \left(\log \left(\sqrt[3]{{y}^{\frac{2}{3}}}\right) + \log y \cdot \frac{2}{3}\right)\right) + z\right)\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 r75933 = x;
        double r75934 = y;
        double r75935 = log(r75934);
        double r75936 = r75933 * r75935;
        double r75937 = z;
        double r75938 = r75936 + r75937;
        double r75939 = t;
        double r75940 = r75938 + r75939;
        double r75941 = a;
        double r75942 = r75940 + r75941;
        double r75943 = b;
        double r75944 = 0.5;
        double r75945 = r75943 - r75944;
        double r75946 = c;
        double r75947 = log(r75946);
        double r75948 = r75945 * r75947;
        double r75949 = r75942 + r75948;
        double r75950 = i;
        double r75951 = r75934 * r75950;
        double r75952 = r75949 + r75951;
        return r75952;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r75953 = c;
        double r75954 = log(r75953);
        double r75955 = b;
        double r75956 = 0.5;
        double r75957 = r75955 - r75956;
        double r75958 = r75954 * r75957;
        double r75959 = a;
        double r75960 = t;
        double r75961 = y;
        double r75962 = cbrt(r75961);
        double r75963 = cbrt(r75962);
        double r75964 = log(r75963);
        double r75965 = x;
        double r75966 = r75964 * r75965;
        double r75967 = 0.6666666666666666;
        double r75968 = pow(r75961, r75967);
        double r75969 = cbrt(r75968);
        double r75970 = log(r75969);
        double r75971 = log(r75961);
        double r75972 = r75971 * r75967;
        double r75973 = r75970 + r75972;
        double r75974 = r75965 * r75973;
        double r75975 = r75966 + r75974;
        double r75976 = z;
        double r75977 = r75975 + r75976;
        double r75978 = r75960 + r75977;
        double r75979 = r75959 + r75978;
        double r75980 = r75958 + r75979;
        double r75981 = i;
        double r75982 = r75961 * r75981;
        double r75983 = r75980 + r75982;
        return r75983;
}

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

    \[\leadsto \left(\left(\left(\left(\left(\color{blue}{x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right)} + x \cdot \log \left(\sqrt[3]{y}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
  7. Using strategy rm

  8. Applied add-cube-cbrt0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(\sqrt[3]{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  9. Applied cbrt-prod0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \color{blue}{\left(\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)}\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  10. Applied log-prod0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \color{blue}{\left(\log \left(\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) + \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right)}\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  11. Applied distribute-rgt-in0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \color{blue}{\left(\log \left(\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot x + \log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot x\right)}\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  12. Applied associate-+r+0.1

    \[\leadsto \left(\left(\left(\left(\color{blue}{\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \log \left(\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) \cdot x\right) + \log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot x\right)} + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  13. Simplified0.1

    \[\leadsto \left(\left(\left(\left(\left(\color{blue}{x \cdot \left(\frac{2}{3} \cdot \log y + \log \left(\sqrt[3]{{y}^{\frac{2}{3}}}\right)\right)} + \log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot x\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  14. Final simplification0.1

    \[\leadsto \left(\log c \cdot \left(b - 0.5\right) + \left(a + \left(t + \left(\left(\log \left(\sqrt[3]{\sqrt[3]{y}}\right) \cdot x + x \cdot \left(\log \left(\sqrt[3]{{y}^{\frac{2}{3}}}\right) + \log y \cdot \frac{2}{3}\right)\right) + z\right)\right)\right)\right) + y \cdot i\]

Reproduce

herbie shell --seed 2019194 
(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)))