Average Error: 0.1 → 0.1
Time: 36.5s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(x \cdot \log y + \left(z + t\right)\right) + \left(\left(\left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right) + a\right)\right) + \left(b - 0.5\right) \cdot \log \left({c}^{\frac{1}{3}}\right)\right) + y \cdot i\]
\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(x \cdot \log y + \left(z + t\right)\right) + \left(\left(\left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right) + \left(b - 0.5\right) \cdot \log \left(\sqrt[3]{c}\right)\right) + a\right)\right) + \left(b - 0.5\right) \cdot \log \left({c}^{\frac{1}{3}}\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4202063 = x;
        double r4202064 = y;
        double r4202065 = log(r4202064);
        double r4202066 = r4202063 * r4202065;
        double r4202067 = z;
        double r4202068 = r4202066 + r4202067;
        double r4202069 = t;
        double r4202070 = r4202068 + r4202069;
        double r4202071 = a;
        double r4202072 = r4202070 + r4202071;
        double r4202073 = b;
        double r4202074 = 0.5;
        double r4202075 = r4202073 - r4202074;
        double r4202076 = c;
        double r4202077 = log(r4202076);
        double r4202078 = r4202075 * r4202077;
        double r4202079 = r4202072 + r4202078;
        double r4202080 = i;
        double r4202081 = r4202064 * r4202080;
        double r4202082 = r4202079 + r4202081;
        return r4202082;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4202083 = x;
        double r4202084 = y;
        double r4202085 = log(r4202084);
        double r4202086 = r4202083 * r4202085;
        double r4202087 = z;
        double r4202088 = t;
        double r4202089 = r4202087 + r4202088;
        double r4202090 = r4202086 + r4202089;
        double r4202091 = b;
        double r4202092 = 0.5;
        double r4202093 = r4202091 - r4202092;
        double r4202094 = c;
        double r4202095 = cbrt(r4202094);
        double r4202096 = log(r4202095);
        double r4202097 = r4202093 * r4202096;
        double r4202098 = r4202097 + r4202097;
        double r4202099 = a;
        double r4202100 = r4202098 + r4202099;
        double r4202101 = r4202090 + r4202100;
        double r4202102 = 0.3333333333333333;
        double r4202103 = pow(r4202094, r4202102);
        double r4202104 = log(r4202103);
        double r4202105 = r4202093 * r4202104;
        double r4202106 = r4202101 + r4202105;
        double r4202107 = i;
        double r4202108 = r4202084 * r4202107;
        double r4202109 = r4202106 + r4202108;
        return r4202109;
}

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-lft-in0.1

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

  6. Applied associate-+r+0.1

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

  7. Simplified0.1

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

  9. Applied pow1/30.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(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)))