Average Error: 0.1 → 0.1
Time: 40.8s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot x + \left(\log \left(\sqrt[3]{y}\right) \cdot x + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\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(\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
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r13352218 = x;
        double r13352219 = y;
        double r13352220 = log(r13352219);
        double r13352221 = r13352218 * r13352220;
        double r13352222 = z;
        double r13352223 = r13352221 + r13352222;
        double r13352224 = t;
        double r13352225 = r13352223 + r13352224;
        double r13352226 = a;
        double r13352227 = r13352225 + r13352226;
        double r13352228 = b;
        double r13352229 = 0.5;
        double r13352230 = r13352228 - r13352229;
        double r13352231 = c;
        double r13352232 = log(r13352231);
        double r13352233 = r13352230 * r13352232;
        double r13352234 = r13352227 + r13352233;
        double r13352235 = i;
        double r13352236 = r13352219 * r13352235;
        double r13352237 = r13352234 + r13352236;
        return r13352237;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r13352238 = y;
        double r13352239 = cbrt(r13352238);
        double r13352240 = r13352239 * r13352239;
        double r13352241 = log(r13352240);
        double r13352242 = x;
        double r13352243 = r13352241 * r13352242;
        double r13352244 = log(r13352239);
        double r13352245 = r13352244 * r13352242;
        double r13352246 = z;
        double r13352247 = r13352245 + r13352246;
        double r13352248 = r13352243 + r13352247;
        double r13352249 = t;
        double r13352250 = r13352248 + r13352249;
        double r13352251 = a;
        double r13352252 = r13352250 + r13352251;
        double r13352253 = b;
        double r13352254 = 0.5;
        double r13352255 = r13352253 - r13352254;
        double r13352256 = c;
        double r13352257 = log(r13352256);
        double r13352258 = r13352255 * r13352257;
        double r13352259 = r13352252 + r13352258;
        double r13352260 = i;
        double r13352261 = r13352238 * r13352260;
        double r13352262 = r13352259 + r13352261;
        return r13352262;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019173 
(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)))