Average Error: 0.1 → 0.1
Time: 16.7s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(2 \cdot \log \left(\left(\sqrt[3]{\sqrt[3]{c}} \cdot \sqrt[3]{\sqrt[3]{c}}\right) \cdot \sqrt[3]{\sqrt[3]{c}}\right)\right) \cdot \left(b - 0.5\right) + \left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right)\right) + \log \left(\sqrt[3]{c}\right) \cdot \left(b - 0.5\right)\right) + y \cdot i\]
\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(2 \cdot \log \left(\left(\sqrt[3]{\sqrt[3]{c}} \cdot \sqrt[3]{\sqrt[3]{c}}\right) \cdot \sqrt[3]{\sqrt[3]{c}}\right)\right) \cdot \left(b - 0.5\right) + \left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right)\right) + \log \left(\sqrt[3]{c}\right) \cdot \left(b - 0.5\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r62485 = x;
        double r62486 = y;
        double r62487 = log(r62486);
        double r62488 = r62485 * r62487;
        double r62489 = z;
        double r62490 = r62488 + r62489;
        double r62491 = t;
        double r62492 = r62490 + r62491;
        double r62493 = a;
        double r62494 = r62492 + r62493;
        double r62495 = b;
        double r62496 = 0.5;
        double r62497 = r62495 - r62496;
        double r62498 = c;
        double r62499 = log(r62498);
        double r62500 = r62497 * r62499;
        double r62501 = r62494 + r62500;
        double r62502 = i;
        double r62503 = r62486 * r62502;
        double r62504 = r62501 + r62503;
        return r62504;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r62505 = 2.0;
        double r62506 = c;
        double r62507 = cbrt(r62506);
        double r62508 = cbrt(r62507);
        double r62509 = r62508 * r62508;
        double r62510 = r62509 * r62508;
        double r62511 = log(r62510);
        double r62512 = r62505 * r62511;
        double r62513 = b;
        double r62514 = 0.5;
        double r62515 = r62513 - r62514;
        double r62516 = r62512 * r62515;
        double r62517 = x;
        double r62518 = y;
        double r62519 = log(r62518);
        double r62520 = r62517 * r62519;
        double r62521 = z;
        double r62522 = r62520 + r62521;
        double r62523 = t;
        double r62524 = r62522 + r62523;
        double r62525 = a;
        double r62526 = r62524 + r62525;
        double r62527 = r62516 + r62526;
        double r62528 = log(r62507);
        double r62529 = r62528 * r62515;
        double r62530 = r62527 + r62529;
        double r62531 = i;
        double r62532 = r62518 * r62531;
        double r62533 = r62530 + r62532;
        return r62533;
}

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-rgt-in0.1

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

  6. Applied associate-+r+0.1

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

  7. Simplified0.1

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

  9. Applied add-cube-cbrt0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 
(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)))