Average Error: 0.1 → 0.1
Time: 32.9s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(x \cdot \log \left({y}^{\frac{1}{3}}\right) + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\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(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(x \cdot \log \left({y}^{\frac{1}{3}}\right) + z\right)\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 r97054 = x;
        double r97055 = y;
        double r97056 = log(r97055);
        double r97057 = r97054 * r97056;
        double r97058 = z;
        double r97059 = r97057 + r97058;
        double r97060 = t;
        double r97061 = r97059 + r97060;
        double r97062 = a;
        double r97063 = r97061 + r97062;
        double r97064 = b;
        double r97065 = 0.5;
        double r97066 = r97064 - r97065;
        double r97067 = c;
        double r97068 = log(r97067);
        double r97069 = r97066 * r97068;
        double r97070 = r97063 + r97069;
        double r97071 = i;
        double r97072 = r97055 * r97071;
        double r97073 = r97070 + r97072;
        return r97073;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r97074 = y;
        double r97075 = cbrt(r97074);
        double r97076 = r97075 * r97075;
        double r97077 = log(r97076);
        double r97078 = x;
        double r97079 = r97077 * r97078;
        double r97080 = 0.3333333333333333;
        double r97081 = pow(r97074, r97080);
        double r97082 = log(r97081);
        double r97083 = r97078 * r97082;
        double r97084 = z;
        double r97085 = r97083 + r97084;
        double r97086 = r97079 + r97085;
        double r97087 = t;
        double r97088 = r97086 + r97087;
        double r97089 = a;
        double r97090 = r97088 + r97089;
        double r97091 = b;
        double r97092 = 0.5;
        double r97093 = r97091 - r97092;
        double r97094 = c;
        double r97095 = log(r97094);
        double r97096 = r97093 * r97095;
        double r97097 = r97090 + r97096;
        double r97098 = i;
        double r97099 = r97074 * r97098;
        double r97100 = r97097 + r97099;
        return r97100;
}

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. Applied associate-+l+0.1

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

  7. Simplified0.1

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

  9. Applied pow1/30.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019209 
(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)))