Average Error: 0.1 → 0.1
Time: 13.2s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{\sqrt{y}} \cdot \sqrt[3]{\sqrt{y}}}\right)\right) + x \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{\sqrt{y}}}\right) \cdot 2 + \log \left(\sqrt[3]{\sqrt{y}}\right)\right)\right) + x \cdot \log \left(\sqrt{y}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\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(\left(x \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{\sqrt{y}} \cdot \sqrt[3]{\sqrt{y}}}\right)\right) + x \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{\sqrt{y}}}\right) \cdot 2 + \log \left(\sqrt[3]{\sqrt{y}}\right)\right)\right) + x \cdot \log \left(\sqrt{y}\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 r76392 = x;
        double r76393 = y;
        double r76394 = log(r76393);
        double r76395 = r76392 * r76394;
        double r76396 = z;
        double r76397 = r76395 + r76396;
        double r76398 = t;
        double r76399 = r76397 + r76398;
        double r76400 = a;
        double r76401 = r76399 + r76400;
        double r76402 = b;
        double r76403 = 0.5;
        double r76404 = r76402 - r76403;
        double r76405 = c;
        double r76406 = log(r76405);
        double r76407 = r76404 * r76406;
        double r76408 = r76401 + r76407;
        double r76409 = i;
        double r76410 = r76393 * r76409;
        double r76411 = r76408 + r76410;
        return r76411;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r76412 = x;
        double r76413 = 2.0;
        double r76414 = y;
        double r76415 = sqrt(r76414);
        double r76416 = cbrt(r76415);
        double r76417 = r76416 * r76416;
        double r76418 = cbrt(r76417);
        double r76419 = log(r76418);
        double r76420 = r76413 * r76419;
        double r76421 = r76412 * r76420;
        double r76422 = cbrt(r76416);
        double r76423 = log(r76422);
        double r76424 = r76423 * r76413;
        double r76425 = log(r76416);
        double r76426 = r76424 + r76425;
        double r76427 = r76412 * r76426;
        double r76428 = r76421 + r76427;
        double r76429 = log(r76415);
        double r76430 = r76412 * r76429;
        double r76431 = r76428 + r76430;
        double r76432 = z;
        double r76433 = r76431 + r76432;
        double r76434 = t;
        double r76435 = r76433 + r76434;
        double r76436 = a;
        double r76437 = r76435 + r76436;
        double r76438 = b;
        double r76439 = 0.5;
        double r76440 = r76438 - r76439;
        double r76441 = c;
        double r76442 = log(r76441);
        double r76443 = r76440 * r76442;
        double r76444 = r76437 + r76443;
        double r76445 = i;
        double r76446 = r76414 * r76445;
        double r76447 = r76444 + r76446;
        return r76447;
}

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-sqr-sqrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  7. Applied add-cube-cbrt0.1

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

  8. Applied log-prod0.1

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

  9. Applied distribute-lft-in0.1

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

  10. Simplified0.1

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

  12. Applied add-cube-cbrt0.1

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

  13. Applied cbrt-prod0.1

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

  14. Applied log-prod0.1

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

  15. Applied distribute-lft-in0.1

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

  16. Applied distribute-lft-in0.1

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

  17. Applied associate-+l+0.1

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

  18. Simplified0.1

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

  19. Final simplification0.1

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

Reproduce

herbie shell --seed 2020003 
(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)))