Average Error: 0.1 → 0.1
Time: 17.5s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + x \cdot \log \left(\sqrt[3]{y}\right)\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\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(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + 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
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68489 = x;
        double r68490 = y;
        double r68491 = log(r68490);
        double r68492 = r68489 * r68491;
        double r68493 = z;
        double r68494 = r68492 + r68493;
        double r68495 = t;
        double r68496 = r68494 + r68495;
        double r68497 = a;
        double r68498 = r68496 + r68497;
        double r68499 = b;
        double r68500 = 0.5;
        double r68501 = r68499 - r68500;
        double r68502 = c;
        double r68503 = log(r68502);
        double r68504 = r68501 * r68503;
        double r68505 = r68498 + r68504;
        double r68506 = i;
        double r68507 = r68490 * r68506;
        double r68508 = r68505 + r68507;
        return r68508;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68509 = 2.0;
        double r68510 = y;
        double r68511 = cbrt(r68510);
        double r68512 = log(r68511);
        double r68513 = r68509 * r68512;
        double r68514 = x;
        double r68515 = r68513 * r68514;
        double r68516 = r68514 * r68512;
        double r68517 = r68515 + r68516;
        double r68518 = z;
        double r68519 = r68517 + r68518;
        double r68520 = t;
        double r68521 = r68519 + r68520;
        double r68522 = a;
        double r68523 = r68521 + r68522;
        double r68524 = b;
        double r68525 = 0.5;
        double r68526 = r68524 - r68525;
        double r68527 = c;
        double r68528 = log(r68527);
        double r68529 = r68526 * r68528;
        double r68530 = r68523 + r68529;
        double r68531 = i;
        double r68532 = r68510 * r68531;
        double r68533 = r68530 + r68532;
        return r68533;
}

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. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 
(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)))