Average Error: 0.1 → 0.1
Time: 15.6s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(\left(2 \cdot \log \left(\sqrt[3]{y}\right)\right) \cdot x + x \cdot \log \left(\sqrt[3]{y}\right)\right) + z\right) + t\right) + a\right) + \left(\left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) \cdot \left(b - 0.5\right) + \left(b - 0.5\right) \cdot \log \left({\left(\frac{1}{c}\right)}^{\frac{-1}{3}}\right)\right)\right) + y \cdot i\]
\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(\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(\left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) \cdot \left(b - 0.5\right) + \left(b - 0.5\right) \cdot \log \left({\left(\frac{1}{c}\right)}^{\frac{-1}{3}}\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 r76624 = x;
        double r76625 = y;
        double r76626 = log(r76625);
        double r76627 = r76624 * r76626;
        double r76628 = z;
        double r76629 = r76627 + r76628;
        double r76630 = t;
        double r76631 = r76629 + r76630;
        double r76632 = a;
        double r76633 = r76631 + r76632;
        double r76634 = b;
        double r76635 = 0.5;
        double r76636 = r76634 - r76635;
        double r76637 = c;
        double r76638 = log(r76637);
        double r76639 = r76636 * r76638;
        double r76640 = r76633 + r76639;
        double r76641 = i;
        double r76642 = r76625 * r76641;
        double r76643 = r76640 + r76642;
        return r76643;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r76644 = 2.0;
        double r76645 = y;
        double r76646 = cbrt(r76645);
        double r76647 = log(r76646);
        double r76648 = r76644 * r76647;
        double r76649 = x;
        double r76650 = r76648 * r76649;
        double r76651 = r76649 * r76647;
        double r76652 = r76650 + r76651;
        double r76653 = z;
        double r76654 = r76652 + r76653;
        double r76655 = t;
        double r76656 = r76654 + r76655;
        double r76657 = a;
        double r76658 = r76656 + r76657;
        double r76659 = c;
        double r76660 = cbrt(r76659);
        double r76661 = log(r76660);
        double r76662 = r76644 * r76661;
        double r76663 = b;
        double r76664 = 0.5;
        double r76665 = r76663 - r76664;
        double r76666 = r76662 * r76665;
        double r76667 = 1.0;
        double r76668 = r76667 / r76659;
        double r76669 = -0.3333333333333333;
        double r76670 = pow(r76668, r76669);
        double r76671 = log(r76670);
        double r76672 = r76665 * r76671;
        double r76673 = r76666 + r76672;
        double r76674 = r76658 + r76673;
        double r76675 = i;
        double r76676 = r76645 * r76675;
        double r76677 = r76674 + r76676;
        return r76677;
}

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

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

  7. Taylor expanded around inf 0.1

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

  9. Applied add-cube-cbrt0.1

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

  10. Applied log-prod0.1

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

  11. Applied distribute-lft-in0.1

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

  12. Simplified0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2020046 
(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)))