Average Error: 0.1 → 0.1
Time: 11.4s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(x \cdot \left(2 \cdot \log \left({y}^{\frac{1}{3}}\right)\right) + x \cdot \log \left(\sqrt[3]{y}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\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({y}^{\frac{1}{3}}\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
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r77398 = x;
        double r77399 = y;
        double r77400 = log(r77399);
        double r77401 = r77398 * r77400;
        double r77402 = z;
        double r77403 = r77401 + r77402;
        double r77404 = t;
        double r77405 = r77403 + r77404;
        double r77406 = a;
        double r77407 = r77405 + r77406;
        double r77408 = b;
        double r77409 = 0.5;
        double r77410 = r77408 - r77409;
        double r77411 = c;
        double r77412 = log(r77411);
        double r77413 = r77410 * r77412;
        double r77414 = r77407 + r77413;
        double r77415 = i;
        double r77416 = r77399 * r77415;
        double r77417 = r77414 + r77416;
        return r77417;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r77418 = x;
        double r77419 = 2.0;
        double r77420 = y;
        double r77421 = 0.3333333333333333;
        double r77422 = pow(r77420, r77421);
        double r77423 = log(r77422);
        double r77424 = r77419 * r77423;
        double r77425 = r77418 * r77424;
        double r77426 = cbrt(r77420);
        double r77427 = log(r77426);
        double r77428 = r77418 * r77427;
        double r77429 = r77425 + r77428;
        double r77430 = z;
        double r77431 = r77429 + r77430;
        double r77432 = t;
        double r77433 = r77431 + r77432;
        double r77434 = a;
        double r77435 = r77433 + r77434;
        double r77436 = b;
        double r77437 = 0.5;
        double r77438 = r77436 - r77437;
        double r77439 = c;
        double r77440 = log(r77439);
        double r77441 = r77438 * r77440;
        double r77442 = r77435 + r77441;
        double r77443 = i;
        double r77444 = r77420 * r77443;
        double r77445 = r77442 + r77444;
        return r77445;
}

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 pow1/30.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020081 
(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)))