Average Error: 0.1 → 0.1
Time: 13.7s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \left(x \cdot \log \left(\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\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(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \left(x \cdot \log \left(\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right)\right) + z\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 r68306 = x;
        double r68307 = y;
        double r68308 = log(r68307);
        double r68309 = r68306 * r68308;
        double r68310 = z;
        double r68311 = r68309 + r68310;
        double r68312 = t;
        double r68313 = r68311 + r68312;
        double r68314 = a;
        double r68315 = r68313 + r68314;
        double r68316 = b;
        double r68317 = 0.5;
        double r68318 = r68316 - r68317;
        double r68319 = c;
        double r68320 = log(r68319);
        double r68321 = r68318 * r68320;
        double r68322 = r68315 + r68321;
        double r68323 = i;
        double r68324 = r68307 * r68323;
        double r68325 = r68322 + r68324;
        return r68325;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68326 = x;
        double r68327 = 2.0;
        double r68328 = y;
        double r68329 = cbrt(r68328);
        double r68330 = log(r68329);
        double r68331 = r68327 * r68330;
        double r68332 = r68326 * r68331;
        double r68333 = r68329 * r68329;
        double r68334 = cbrt(r68333);
        double r68335 = log(r68334);
        double r68336 = r68326 * r68335;
        double r68337 = cbrt(r68329);
        double r68338 = log(r68337);
        double r68339 = r68326 * r68338;
        double r68340 = r68336 + r68339;
        double r68341 = r68332 + r68340;
        double r68342 = z;
        double r68343 = r68341 + r68342;
        double r68344 = t;
        double r68345 = r68343 + r68344;
        double r68346 = a;
        double r68347 = r68345 + r68346;
        double r68348 = b;
        double r68349 = 0.5;
        double r68350 = r68348 - r68349;
        double r68351 = c;
        double r68352 = log(r68351);
        double r68353 = r68350 * r68352;
        double r68354 = r68347 + r68353;
        double r68355 = i;
        double r68356 = r68328 * r68355;
        double r68357 = r68354 + r68356;
        return r68357;
}

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-lft-in0.1

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

  6. Simplified0.1

    \[\leadsto \left(\left(\left(\left(\left(\color{blue}{x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right)} + x \cdot \log \left(\sqrt[3]{y}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
  7. Using strategy rm

  8. Applied add-cube-cbrt0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(\sqrt[3]{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  9. Applied cbrt-prod0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \color{blue}{\left(\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \sqrt[3]{\sqrt[3]{y}}\right)}\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  10. Applied log-prod0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \color{blue}{\left(\log \left(\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) + \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right)}\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  11. Applied distribute-lft-in0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \color{blue}{\left(x \cdot \log \left(\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right)}\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  12. Final simplification0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + \left(x \cdot \log \left(\sqrt[3]{\sqrt[3]{y} \cdot \sqrt[3]{y}}\right) + x \cdot \log \left(\sqrt[3]{\sqrt[3]{y}}\right)\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

Reproduce

herbie shell --seed 2019353 
(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)))