Average Error: 0.1 → 0.1
Time: 28.6s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(2 \cdot \log \left(\sqrt[3]{{c}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{c}}\right)\right) \cdot \left(b - 0.5\right) + \log \left(\sqrt[3]{c}\right) \cdot \left(b - 0.5\right)\right)\right) + y \cdot i\]
\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(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(2 \cdot \log \left(\sqrt[3]{{c}^{\frac{2}{3}}} \cdot \sqrt[3]{\sqrt[3]{c}}\right)\right) \cdot \left(b - 0.5\right) + \log \left(\sqrt[3]{c}\right) \cdot \left(b - 0.5\right)\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r64402 = x;
        double r64403 = y;
        double r64404 = log(r64403);
        double r64405 = r64402 * r64404;
        double r64406 = z;
        double r64407 = r64405 + r64406;
        double r64408 = t;
        double r64409 = r64407 + r64408;
        double r64410 = a;
        double r64411 = r64409 + r64410;
        double r64412 = b;
        double r64413 = 0.5;
        double r64414 = r64412 - r64413;
        double r64415 = c;
        double r64416 = log(r64415);
        double r64417 = r64414 * r64416;
        double r64418 = r64411 + r64417;
        double r64419 = i;
        double r64420 = r64403 * r64419;
        double r64421 = r64418 + r64420;
        return r64421;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r64422 = x;
        double r64423 = y;
        double r64424 = log(r64423);
        double r64425 = r64422 * r64424;
        double r64426 = z;
        double r64427 = r64425 + r64426;
        double r64428 = t;
        double r64429 = r64427 + r64428;
        double r64430 = a;
        double r64431 = r64429 + r64430;
        double r64432 = 2.0;
        double r64433 = c;
        double r64434 = 0.6666666666666666;
        double r64435 = pow(r64433, r64434);
        double r64436 = cbrt(r64435);
        double r64437 = cbrt(r64433);
        double r64438 = cbrt(r64437);
        double r64439 = r64436 * r64438;
        double r64440 = log(r64439);
        double r64441 = r64432 * r64440;
        double r64442 = b;
        double r64443 = 0.5;
        double r64444 = r64442 - r64443;
        double r64445 = r64441 * r64444;
        double r64446 = log(r64437);
        double r64447 = r64446 * r64444;
        double r64448 = r64445 + r64447;
        double r64449 = r64431 + r64448;
        double r64450 = i;
        double r64451 = r64423 * r64450;
        double r64452 = r64449 + r64451;
        return r64452;
}

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. Simplified0.1

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

  7. Simplified0.1

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

  9. Applied add-cube-cbrt0.1

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

  10. Applied cbrt-prod0.1

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019305 
(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)))