Average Error: 0.1 → 0.1
Time: 37.8s
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 r60448 = x;
        double r60449 = y;
        double r60450 = log(r60449);
        double r60451 = r60448 * r60450;
        double r60452 = z;
        double r60453 = r60451 + r60452;
        double r60454 = t;
        double r60455 = r60453 + r60454;
        double r60456 = a;
        double r60457 = r60455 + r60456;
        double r60458 = b;
        double r60459 = 0.5;
        double r60460 = r60458 - r60459;
        double r60461 = c;
        double r60462 = log(r60461);
        double r60463 = r60460 * r60462;
        double r60464 = r60457 + r60463;
        double r60465 = i;
        double r60466 = r60449 * r60465;
        double r60467 = r60464 + r60466;
        return r60467;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r60468 = x;
        double r60469 = y;
        double r60470 = log(r60469);
        double r60471 = r60468 * r60470;
        double r60472 = z;
        double r60473 = r60471 + r60472;
        double r60474 = t;
        double r60475 = r60473 + r60474;
        double r60476 = a;
        double r60477 = r60475 + r60476;
        double r60478 = 2.0;
        double r60479 = c;
        double r60480 = 0.6666666666666666;
        double r60481 = pow(r60479, r60480);
        double r60482 = cbrt(r60481);
        double r60483 = cbrt(r60479);
        double r60484 = cbrt(r60483);
        double r60485 = r60482 * r60484;
        double r60486 = log(r60485);
        double r60487 = r60478 * r60486;
        double r60488 = b;
        double r60489 = 0.5;
        double r60490 = r60488 - r60489;
        double r60491 = r60487 * r60490;
        double r60492 = log(r60483);
        double r60493 = r60492 * r60490;
        double r60494 = r60491 + r60493;
        double r60495 = r60477 + r60494;
        double r60496 = i;
        double r60497 = r60469 * r60496;
        double r60498 = r60495 + r60497;
        return r60498;
}

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 2019199 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, B"
  (+ (+ (+ (+ (+ (* x (log y)) z) t) a) (* (- b 0.5) (log c))) (* y i)))