Average Error: 0.1 → 0.1
Time: 13.7s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log \left({y}^{\frac{2}{3}}\right) + \left(\log \left(\sqrt[3]{y}\right) \cdot x + z\right)\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
\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({y}^{\frac{2}{3}}\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 r91556 = x;
        double r91557 = y;
        double r91558 = log(r91557);
        double r91559 = r91556 * r91558;
        double r91560 = z;
        double r91561 = r91559 + r91560;
        double r91562 = t;
        double r91563 = r91561 + r91562;
        double r91564 = a;
        double r91565 = r91563 + r91564;
        double r91566 = b;
        double r91567 = 0.5;
        double r91568 = r91566 - r91567;
        double r91569 = c;
        double r91570 = log(r91569);
        double r91571 = r91568 * r91570;
        double r91572 = r91565 + r91571;
        double r91573 = i;
        double r91574 = r91557 * r91573;
        double r91575 = r91572 + r91574;
        return r91575;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r91576 = x;
        double r91577 = y;
        double r91578 = 0.6666666666666666;
        double r91579 = pow(r91577, r91578);
        double r91580 = log(r91579);
        double r91581 = r91576 * r91580;
        double r91582 = cbrt(r91577);
        double r91583 = log(r91582);
        double r91584 = r91583 * r91576;
        double r91585 = z;
        double r91586 = r91584 + r91585;
        double r91587 = r91581 + r91586;
        double r91588 = t;
        double r91589 = r91587 + r91588;
        double r91590 = a;
        double r91591 = r91589 + r91590;
        double r91592 = b;
        double r91593 = 0.5;
        double r91594 = r91592 - r91593;
        double r91595 = c;
        double r91596 = log(r91595);
        double r91597 = r91594 * r91596;
        double r91598 = r91591 + r91597;
        double r91599 = i;
        double r91600 = r91577 * r91599;
        double r91601 = r91598 + r91600;
        return r91601;
}

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. Using strategy rm

  9. Applied pow1/30.1

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

  10. Applied pow1/30.1

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

  11. Applied pow-prod-up0.1

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

  12. Simplified0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2020036 
(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)))