Average Error: 0.1 → 0.1
Time: 13.5s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log \left(\sqrt[3]{c} \cdot \sqrt[3]{c}\right) \cdot \left(b - 0.5\right)\right) + \log \left({c}^{\frac{1}{3}}\right) \cdot \left(b - 0.5\right)\right) + y \cdot i\]
\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(\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({c}^{\frac{1}{3}}\right) \cdot \left(b - 0.5\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r99232 = x;
        double r99233 = y;
        double r99234 = log(r99233);
        double r99235 = r99232 * r99234;
        double r99236 = z;
        double r99237 = r99235 + r99236;
        double r99238 = t;
        double r99239 = r99237 + r99238;
        double r99240 = a;
        double r99241 = r99239 + r99240;
        double r99242 = b;
        double r99243 = 0.5;
        double r99244 = r99242 - r99243;
        double r99245 = c;
        double r99246 = log(r99245);
        double r99247 = r99244 * r99246;
        double r99248 = r99241 + r99247;
        double r99249 = i;
        double r99250 = r99233 * r99249;
        double r99251 = r99248 + r99250;
        return r99251;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r99252 = x;
        double r99253 = y;
        double r99254 = log(r99253);
        double r99255 = r99252 * r99254;
        double r99256 = z;
        double r99257 = r99255 + r99256;
        double r99258 = t;
        double r99259 = r99257 + r99258;
        double r99260 = a;
        double r99261 = r99259 + r99260;
        double r99262 = c;
        double r99263 = cbrt(r99262);
        double r99264 = r99263 * r99263;
        double r99265 = log(r99264);
        double r99266 = b;
        double r99267 = 0.5;
        double r99268 = r99266 - r99267;
        double r99269 = r99265 * r99268;
        double r99270 = r99261 + r99269;
        double r99271 = 0.3333333333333333;
        double r99272 = pow(r99262, r99271);
        double r99273 = log(r99272);
        double r99274 = r99273 * r99268;
        double r99275 = r99270 + r99274;
        double r99276 = i;
        double r99277 = r99253 * r99276;
        double r99278 = r99275 + r99277;
        return r99278;
}

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. Using strategy rm

  8. Applied pow1/30.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020089 
(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)))