Average Error: 0.1 → 0.1
Time: 46.0s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\log \left(\sqrt{y}\right) \cdot x + \left(\log \left(\sqrt{y}\right) \cdot x + z\right)\right) + t\right) + a\right) + \left(\left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) \cdot \left(b - 0.5\right) + \log \left(\sqrt[3]{c}\right) \cdot \left(b - 0.5\right)\right)\right) + y \cdot i\]
\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(\log \left(\sqrt{y}\right) \cdot x + \left(\log \left(\sqrt{y}\right) \cdot x + z\right)\right) + t\right) + a\right) + \left(\left(2 \cdot \log \left(\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 r75288 = x;
        double r75289 = y;
        double r75290 = log(r75289);
        double r75291 = r75288 * r75290;
        double r75292 = z;
        double r75293 = r75291 + r75292;
        double r75294 = t;
        double r75295 = r75293 + r75294;
        double r75296 = a;
        double r75297 = r75295 + r75296;
        double r75298 = b;
        double r75299 = 0.5;
        double r75300 = r75298 - r75299;
        double r75301 = c;
        double r75302 = log(r75301);
        double r75303 = r75300 * r75302;
        double r75304 = r75297 + r75303;
        double r75305 = i;
        double r75306 = r75289 * r75305;
        double r75307 = r75304 + r75306;
        return r75307;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r75308 = y;
        double r75309 = sqrt(r75308);
        double r75310 = log(r75309);
        double r75311 = x;
        double r75312 = r75310 * r75311;
        double r75313 = z;
        double r75314 = r75312 + r75313;
        double r75315 = r75312 + r75314;
        double r75316 = t;
        double r75317 = r75315 + r75316;
        double r75318 = a;
        double r75319 = r75317 + r75318;
        double r75320 = 2.0;
        double r75321 = c;
        double r75322 = cbrt(r75321);
        double r75323 = log(r75322);
        double r75324 = r75320 * r75323;
        double r75325 = b;
        double r75326 = 0.5;
        double r75327 = r75325 - r75326;
        double r75328 = r75324 * r75327;
        double r75329 = r75323 * r75327;
        double r75330 = r75328 + r75329;
        double r75331 = r75319 + r75330;
        double r75332 = i;
        double r75333 = r75308 * r75332;
        double r75334 = r75331 + r75333;
        return r75334;
}

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-rgt-in0.1

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

  6. Applied associate-+l+0.1

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

  8. Applied add-cube-cbrt0.1

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

  9. Applied log-prod0.1

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

  10. Applied distribute-lft-in0.1

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

  11. Simplified0.1

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

  12. Simplified0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019303 
(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)))