Average Error: 0.1 → 0.1
Time: 10.5s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right) + \log \left(\sqrt[3]{\sqrt[3]{c} \cdot \sqrt[3]{c}}\right)\right) + \log \left(\sqrt[3]{\sqrt[3]{c}}\right) \cdot \left(b - 0.5\right)\right)\right) + y \cdot i\]
\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) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right) + \log \left(\sqrt[3]{\sqrt[3]{c} \cdot \sqrt[3]{c}}\right)\right) + \log \left(\sqrt[3]{\sqrt[3]{c}}\right) \cdot \left(b - 0.5\right)\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r73591 = x;
        double r73592 = y;
        double r73593 = log(r73592);
        double r73594 = r73591 * r73593;
        double r73595 = z;
        double r73596 = r73594 + r73595;
        double r73597 = t;
        double r73598 = r73596 + r73597;
        double r73599 = a;
        double r73600 = r73598 + r73599;
        double r73601 = b;
        double r73602 = 0.5;
        double r73603 = r73601 - r73602;
        double r73604 = c;
        double r73605 = log(r73604);
        double r73606 = r73603 * r73605;
        double r73607 = r73600 + r73606;
        double r73608 = i;
        double r73609 = r73592 * r73608;
        double r73610 = r73607 + r73609;
        return r73610;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r73611 = x;
        double r73612 = y;
        double r73613 = log(r73612);
        double r73614 = r73611 * r73613;
        double r73615 = z;
        double r73616 = r73614 + r73615;
        double r73617 = t;
        double r73618 = r73616 + r73617;
        double r73619 = a;
        double r73620 = r73618 + r73619;
        double r73621 = b;
        double r73622 = 0.5;
        double r73623 = r73621 - r73622;
        double r73624 = 2.0;
        double r73625 = c;
        double r73626 = cbrt(r73625);
        double r73627 = log(r73626);
        double r73628 = r73624 * r73627;
        double r73629 = r73626 * r73626;
        double r73630 = cbrt(r73629);
        double r73631 = log(r73630);
        double r73632 = r73628 + r73631;
        double r73633 = r73623 * r73632;
        double r73634 = cbrt(r73626);
        double r73635 = log(r73634);
        double r73636 = r73635 * r73623;
        double r73637 = r73633 + r73636;
        double r73638 = r73620 + r73637;
        double r73639 = i;
        double r73640 = r73612 * r73639;
        double r73641 = r73638 + r73640;
        return r73641;
}

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

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

  8. Applied add-cube-cbrt0.1

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

  9. Applied cbrt-prod0.1

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

  10. Applied log-prod0.1

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

  11. Applied distribute-rgt-in0.1

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

  12. Applied associate-+r+0.1

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

  13. Simplified0.1

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

  14. Final simplification0.1

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

Reproduce

herbie shell --seed 2020062 
(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)))