Average Error: 0.1 → 0.1
Time: 14.2s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\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(\left(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
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r72920 = x;
        double r72921 = y;
        double r72922 = log(r72921);
        double r72923 = r72920 * r72922;
        double r72924 = z;
        double r72925 = r72923 + r72924;
        double r72926 = t;
        double r72927 = r72925 + r72926;
        double r72928 = a;
        double r72929 = r72927 + r72928;
        double r72930 = b;
        double r72931 = 0.5;
        double r72932 = r72930 - r72931;
        double r72933 = c;
        double r72934 = log(r72933);
        double r72935 = r72932 * r72934;
        double r72936 = r72929 + r72935;
        double r72937 = i;
        double r72938 = r72921 * r72937;
        double r72939 = r72936 + r72938;
        return r72939;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r72940 = x;
        double r72941 = 2.0;
        double r72942 = y;
        double r72943 = cbrt(r72942);
        double r72944 = log(r72943);
        double r72945 = r72941 * r72944;
        double r72946 = r72940 * r72945;
        double r72947 = r72940 * r72944;
        double r72948 = r72946 + r72947;
        double r72949 = z;
        double r72950 = r72948 + r72949;
        double r72951 = t;
        double r72952 = r72950 + r72951;
        double r72953 = a;
        double r72954 = r72952 + r72953;
        double r72955 = b;
        double r72956 = 0.5;
        double r72957 = r72955 - r72956;
        double r72958 = c;
        double r72959 = log(r72958);
        double r72960 = r72957 * r72959;
        double r72961 = r72954 + r72960;
        double r72962 = i;
        double r72963 = r72942 * r72962;
        double r72964 = r72961 + r72963;
        return r72964;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020001 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  :precision binary64
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))