Average Error: 0.1 → 0.1
Time: 11.4s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(\left(b - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) + \left(b - 0.5\right) \cdot \log \left(e^{\log \left({c}^{\frac{1}{3}}\right)}\right)\right)\right) + y \cdot i\]
\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)\right) + \left(b - 0.5\right) \cdot \log \left(e^{\log \left({c}^{\frac{1}{3}}\right)}\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 r91592 = x;
        double r91593 = y;
        double r91594 = log(r91593);
        double r91595 = r91592 * r91594;
        double r91596 = z;
        double r91597 = r91595 + r91596;
        double r91598 = t;
        double r91599 = r91597 + r91598;
        double r91600 = a;
        double r91601 = r91599 + r91600;
        double r91602 = b;
        double r91603 = 0.5;
        double r91604 = r91602 - r91603;
        double r91605 = c;
        double r91606 = log(r91605);
        double r91607 = r91604 * r91606;
        double r91608 = r91601 + r91607;
        double r91609 = i;
        double r91610 = r91593 * r91609;
        double r91611 = r91608 + r91610;
        return r91611;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r91612 = x;
        double r91613 = y;
        double r91614 = log(r91613);
        double r91615 = r91612 * r91614;
        double r91616 = z;
        double r91617 = r91615 + r91616;
        double r91618 = t;
        double r91619 = r91617 + r91618;
        double r91620 = a;
        double r91621 = r91619 + r91620;
        double r91622 = b;
        double r91623 = 0.5;
        double r91624 = r91622 - r91623;
        double r91625 = 2.0;
        double r91626 = c;
        double r91627 = cbrt(r91626);
        double r91628 = log(r91627);
        double r91629 = r91625 * r91628;
        double r91630 = r91624 * r91629;
        double r91631 = 0.3333333333333333;
        double r91632 = pow(r91626, r91631);
        double r91633 = log(r91632);
        double r91634 = exp(r91633);
        double r91635 = log(r91634);
        double r91636 = r91624 * r91635;
        double r91637 = r91630 + r91636;
        double r91638 = r91621 + r91637;
        double r91639 = i;
        double r91640 = r91613 * r91639;
        double r91641 = r91638 + r91640;
        return r91641;
}

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-exp-log0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020027 
(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)))