Average Error: 0.1 → 0.1
Time: 38.2s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(a + \left(\log y \cdot x + z\right)\right) + t\right) + \left(\log \left(\sqrt[3]{c}\right) + \log \left(\sqrt[3]{c}\right)\right) \cdot \left(b - 0.5\right)\right) + \left(b - 0.5\right) \cdot \log \left({c}^{\frac{1}{3}}\right)\right) + i \cdot y\]
\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(a + \left(\log y \cdot x + z\right)\right) + t\right) + \left(\log \left(\sqrt[3]{c}\right) + \log \left(\sqrt[3]{c}\right)\right) \cdot \left(b - 0.5\right)\right) + \left(b - 0.5\right) \cdot \log \left({c}^{\frac{1}{3}}\right)\right) + i \cdot y
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3962929 = x;
        double r3962930 = y;
        double r3962931 = log(r3962930);
        double r3962932 = r3962929 * r3962931;
        double r3962933 = z;
        double r3962934 = r3962932 + r3962933;
        double r3962935 = t;
        double r3962936 = r3962934 + r3962935;
        double r3962937 = a;
        double r3962938 = r3962936 + r3962937;
        double r3962939 = b;
        double r3962940 = 0.5;
        double r3962941 = r3962939 - r3962940;
        double r3962942 = c;
        double r3962943 = log(r3962942);
        double r3962944 = r3962941 * r3962943;
        double r3962945 = r3962938 + r3962944;
        double r3962946 = i;
        double r3962947 = r3962930 * r3962946;
        double r3962948 = r3962945 + r3962947;
        return r3962948;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3962949 = a;
        double r3962950 = y;
        double r3962951 = log(r3962950);
        double r3962952 = x;
        double r3962953 = r3962951 * r3962952;
        double r3962954 = z;
        double r3962955 = r3962953 + r3962954;
        double r3962956 = r3962949 + r3962955;
        double r3962957 = t;
        double r3962958 = r3962956 + r3962957;
        double r3962959 = c;
        double r3962960 = cbrt(r3962959);
        double r3962961 = log(r3962960);
        double r3962962 = r3962961 + r3962961;
        double r3962963 = b;
        double r3962964 = 0.5;
        double r3962965 = r3962963 - r3962964;
        double r3962966 = r3962962 * r3962965;
        double r3962967 = r3962958 + r3962966;
        double r3962968 = 0.3333333333333333;
        double r3962969 = pow(r3962959, r3962968);
        double r3962970 = log(r3962969);
        double r3962971 = r3962965 * r3962970;
        double r3962972 = r3962967 + r3962971;
        double r3962973 = i;
        double r3962974 = r3962973 * r3962950;
        double r3962975 = r3962972 + r3962974;
        return r3962975;
}

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

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

  4. Applied log-prod0.1

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

  5. Applied distribute-rgt-in0.1

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

  6. Applied associate-+r+0.1

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

  7. Simplified0.1

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

  9. Applied pow1/30.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019162 
(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)))