Average Error: 0.1 → 0.1
Time: 38.9s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log \left(\sqrt[3]{-c} \cdot \sqrt[3]{-1}\right) \cdot \left(3 \cdot b - 1.5\right)\right) + y \cdot i\]
\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(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log \left(\sqrt[3]{-c} \cdot \sqrt[3]{-1}\right) \cdot \left(3 \cdot b - 1.5\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r63304 = x;
        double r63305 = y;
        double r63306 = log(r63305);
        double r63307 = r63304 * r63306;
        double r63308 = z;
        double r63309 = r63307 + r63308;
        double r63310 = t;
        double r63311 = r63309 + r63310;
        double r63312 = a;
        double r63313 = r63311 + r63312;
        double r63314 = b;
        double r63315 = 0.5;
        double r63316 = r63314 - r63315;
        double r63317 = c;
        double r63318 = log(r63317);
        double r63319 = r63316 * r63318;
        double r63320 = r63313 + r63319;
        double r63321 = i;
        double r63322 = r63305 * r63321;
        double r63323 = r63320 + r63322;
        return r63323;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r63324 = x;
        double r63325 = y;
        double r63326 = log(r63325);
        double r63327 = r63324 * r63326;
        double r63328 = z;
        double r63329 = r63327 + r63328;
        double r63330 = t;
        double r63331 = r63329 + r63330;
        double r63332 = a;
        double r63333 = r63331 + r63332;
        double r63334 = c;
        double r63335 = -r63334;
        double r63336 = cbrt(r63335);
        double r63337 = -1.0;
        double r63338 = cbrt(r63337);
        double r63339 = r63336 * r63338;
        double r63340 = log(r63339);
        double r63341 = 3.0;
        double r63342 = b;
        double r63343 = r63341 * r63342;
        double r63344 = 1.5;
        double r63345 = r63343 - r63344;
        double r63346 = r63340 * r63345;
        double r63347 = r63333 + r63346;
        double r63348 = i;
        double r63349 = r63325 * r63348;
        double r63350 = r63347 + r63349;
        return r63350;
}

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. Taylor expanded around -inf 64.0

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\left(3 \cdot \left(b \cdot \log \left({\left(-1 \cdot c\right)}^{\frac{1}{3}} \cdot \sqrt[3]{-1}\right)\right) - 1.5 \cdot \log \left({\left(-1 \cdot c\right)}^{\frac{1}{3}} \cdot \sqrt[3]{-1}\right)\right)}\right) + y \cdot i\]

  9. Simplified0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \color{blue}{\log \left(\sqrt[3]{-c} \cdot \sqrt[3]{-1}\right) \cdot \left(3 \cdot b - 1.5\right)}\right) + y \cdot i\]

  10. Final simplification0.1

    \[\leadsto \left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \log \left(\sqrt[3]{-c} \cdot \sqrt[3]{-1}\right) \cdot \left(3 \cdot b - 1.5\right)\right) + y \cdot i\]

Reproduce

herbie shell --seed 2019304 
(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)))