Average Error: 0.1 → 0.1
Time: 31.0s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(a + \left(y \cdot i + \left(\left(x \cdot \log y + z\right) + t\right)\right)\right) + 2 \cdot \left(\log \left(\sqrt[3]{c}\right) \cdot \left(b - 0.5\right) + \left(b - 0.5\right) \cdot \log \left({\left(\frac{\sqrt{1}}{\sqrt{c}}\right)}^{\frac{-1}{3}}\right)\right)\]
\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(a + \left(y \cdot i + \left(\left(x \cdot \log y + z\right) + t\right)\right)\right) + 2 \cdot \left(\log \left(\sqrt[3]{c}\right) \cdot \left(b - 0.5\right) + \left(b - 0.5\right) \cdot \log \left({\left(\frac{\sqrt{1}}{\sqrt{c}}\right)}^{\frac{-1}{3}}\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r84605 = x;
        double r84606 = y;
        double r84607 = log(r84606);
        double r84608 = r84605 * r84607;
        double r84609 = z;
        double r84610 = r84608 + r84609;
        double r84611 = t;
        double r84612 = r84610 + r84611;
        double r84613 = a;
        double r84614 = r84612 + r84613;
        double r84615 = b;
        double r84616 = 0.5;
        double r84617 = r84615 - r84616;
        double r84618 = c;
        double r84619 = log(r84618);
        double r84620 = r84617 * r84619;
        double r84621 = r84614 + r84620;
        double r84622 = i;
        double r84623 = r84606 * r84622;
        double r84624 = r84621 + r84623;
        return r84624;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r84625 = a;
        double r84626 = y;
        double r84627 = i;
        double r84628 = r84626 * r84627;
        double r84629 = x;
        double r84630 = log(r84626);
        double r84631 = r84629 * r84630;
        double r84632 = z;
        double r84633 = r84631 + r84632;
        double r84634 = t;
        double r84635 = r84633 + r84634;
        double r84636 = r84628 + r84635;
        double r84637 = r84625 + r84636;
        double r84638 = 2.0;
        double r84639 = c;
        double r84640 = cbrt(r84639);
        double r84641 = log(r84640);
        double r84642 = b;
        double r84643 = 0.5;
        double r84644 = r84642 - r84643;
        double r84645 = r84641 * r84644;
        double r84646 = 1.0;
        double r84647 = sqrt(r84646);
        double r84648 = sqrt(r84639);
        double r84649 = r84647 / r84648;
        double r84650 = -0.3333333333333333;
        double r84651 = pow(r84649, r84650);
        double r84652 = log(r84651);
        double r84653 = r84644 * r84652;
        double r84654 = r84645 + r84653;
        double r84655 = r84638 * r84654;
        double r84656 = r84637 + r84655;
        return r84656;
}

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. Taylor expanded around inf 0.1

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

  9. Applied add-sqr-sqrt0.1

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

  10. Applied add-sqr-sqrt0.1

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

  11. Applied times-frac0.1

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

  12. Applied unpow-prod-down0.1

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

  13. Applied log-prod0.1

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

  14. Applied distribute-lft-in0.1

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

  15. Applied associate-+r+0.1

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

  16. Simplified0.1

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

  17. Final simplification0.1

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

Reproduce

herbie shell --seed 2019297 
(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)))