Average Error: 0.1 → 0.1
Time: 12.1s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(1 \cdot {y}^{\frac{1}{3}}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\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) + x \cdot \log \left(1 \cdot {y}^{\frac{1}{3}}\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 r81335 = x;
        double r81336 = y;
        double r81337 = log(r81336);
        double r81338 = r81335 * r81337;
        double r81339 = z;
        double r81340 = r81338 + r81339;
        double r81341 = t;
        double r81342 = r81340 + r81341;
        double r81343 = a;
        double r81344 = r81342 + r81343;
        double r81345 = b;
        double r81346 = 0.5;
        double r81347 = r81345 - r81346;
        double r81348 = c;
        double r81349 = log(r81348);
        double r81350 = r81347 * r81349;
        double r81351 = r81344 + r81350;
        double r81352 = i;
        double r81353 = r81336 * r81352;
        double r81354 = r81351 + r81353;
        return r81354;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r81355 = x;
        double r81356 = 2.0;
        double r81357 = y;
        double r81358 = cbrt(r81357);
        double r81359 = log(r81358);
        double r81360 = r81356 * r81359;
        double r81361 = r81355 * r81360;
        double r81362 = 1.0;
        double r81363 = 0.3333333333333333;
        double r81364 = pow(r81357, r81363);
        double r81365 = r81362 * r81364;
        double r81366 = log(r81365);
        double r81367 = r81355 * r81366;
        double r81368 = r81361 + r81367;
        double r81369 = z;
        double r81370 = r81368 + r81369;
        double r81371 = t;
        double r81372 = r81370 + r81371;
        double r81373 = a;
        double r81374 = r81372 + r81373;
        double r81375 = b;
        double r81376 = 0.5;
        double r81377 = r81375 - r81376;
        double r81378 = c;
        double r81379 = log(r81378);
        double r81380 = r81377 * r81379;
        double r81381 = r81374 + r81380;
        double r81382 = i;
        double r81383 = r81357 * r81382;
        double r81384 = r81381 + r81383;
        return r81384;
}

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 *-un-lft-identity0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(\sqrt[3]{\color{blue}{1 \cdot y}}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  9. Applied cbrt-prod0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \color{blue}{\left(\sqrt[3]{1} \cdot \sqrt[3]{y}\right)}\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  10. Simplified0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(\color{blue}{1} \cdot \sqrt[3]{y}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  11. Simplified0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(1 \cdot \color{blue}{{y}^{\frac{1}{3}}}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  12. Final simplification0.1

    \[\leadsto \left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) + x \cdot \log \left(1 \cdot {y}^{\frac{1}{3}}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

Reproduce

herbie shell --seed 2020060 
(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)))