Average Error: 0.1 → 0.1
Time: 10.9s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\log \left(\sqrt[3]{y}\right) \cdot x + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\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(x \cdot \log \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) + \left(\log \left(\sqrt[3]{y}\right) \cdot x + z\right)\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 r101419 = x;
        double r101420 = y;
        double r101421 = log(r101420);
        double r101422 = r101419 * r101421;
        double r101423 = z;
        double r101424 = r101422 + r101423;
        double r101425 = t;
        double r101426 = r101424 + r101425;
        double r101427 = a;
        double r101428 = r101426 + r101427;
        double r101429 = b;
        double r101430 = 0.5;
        double r101431 = r101429 - r101430;
        double r101432 = c;
        double r101433 = log(r101432);
        double r101434 = r101431 * r101433;
        double r101435 = r101428 + r101434;
        double r101436 = i;
        double r101437 = r101420 * r101436;
        double r101438 = r101435 + r101437;
        return r101438;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r101439 = x;
        double r101440 = y;
        double r101441 = cbrt(r101440);
        double r101442 = r101441 * r101441;
        double r101443 = log(r101442);
        double r101444 = r101439 * r101443;
        double r101445 = log(r101441);
        double r101446 = r101445 * r101439;
        double r101447 = z;
        double r101448 = r101446 + r101447;
        double r101449 = r101444 + r101448;
        double r101450 = t;
        double r101451 = r101449 + r101450;
        double r101452 = a;
        double r101453 = r101451 + r101452;
        double r101454 = b;
        double r101455 = 0.5;
        double r101456 = r101454 - r101455;
        double r101457 = c;
        double r101458 = log(r101457);
        double r101459 = r101456 * r101458;
        double r101460 = r101453 + r101459;
        double r101461 = i;
        double r101462 = r101440 * r101461;
        double r101463 = r101460 + r101462;
        return r101463;
}

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. Applied associate-+l+0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019347 
(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)))