Average Error: 0.1 → 0.1
Time: 40.9s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + \log \left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}}\right) \cdot x\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\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 + \log \left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}}\right) \cdot x\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 r74525 = x;
        double r74526 = y;
        double r74527 = log(r74526);
        double r74528 = r74525 * r74527;
        double r74529 = z;
        double r74530 = r74528 + r74529;
        double r74531 = t;
        double r74532 = r74530 + r74531;
        double r74533 = a;
        double r74534 = r74532 + r74533;
        double r74535 = b;
        double r74536 = 0.5;
        double r74537 = r74535 - r74536;
        double r74538 = c;
        double r74539 = log(r74538);
        double r74540 = r74537 * r74539;
        double r74541 = r74534 + r74540;
        double r74542 = i;
        double r74543 = r74526 * r74542;
        double r74544 = r74541 + r74543;
        return r74544;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r74545 = 2.0;
        double r74546 = y;
        double r74547 = cbrt(r74546);
        double r74548 = log(r74547);
        double r74549 = r74545 * r74548;
        double r74550 = x;
        double r74551 = r74549 * r74550;
        double r74552 = 1.0;
        double r74553 = r74552 / r74546;
        double r74554 = -0.3333333333333333;
        double r74555 = pow(r74553, r74554);
        double r74556 = log(r74555);
        double r74557 = r74556 * r74550;
        double r74558 = r74551 + r74557;
        double r74559 = z;
        double r74560 = r74558 + r74559;
        double r74561 = t;
        double r74562 = r74560 + r74561;
        double r74563 = a;
        double r74564 = r74562 + r74563;
        double r74565 = b;
        double r74566 = 0.5;
        double r74567 = r74565 - r74566;
        double r74568 = c;
        double r74569 = log(r74568);
        double r74570 = r74567 * r74569;
        double r74571 = r74564 + r74570;
        double r74572 = i;
        double r74573 = r74546 * r74572;
        double r74574 = r74571 + r74573;
        return r74574;
}

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. Simplified0.1

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

  8. Taylor expanded around inf 0.1

    \[\leadsto \left(\left(\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + \log \color{blue}{\left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}}\right)} \cdot x\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

  9. Final simplification0.1

    \[\leadsto \left(\left(\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + \log \left({\left(\frac{1}{y}\right)}^{\frac{-1}{3}}\right) \cdot x\right) + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]

Reproduce

herbie shell --seed 2019322 
(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)))