Average Error: 0.1 → 0.1
Time: 47.7s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[\left(\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) \cdot \left(b - 0.5\right)\right) + \left(b - 0.5\right) \cdot \log \left({\left(\frac{1}{c}\right)}^{\frac{-1}{3}}\right)\right) + y \cdot i\]
\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(x \cdot \log y + z\right) + t\right) + a\right) + \left(2 \cdot \log \left(\sqrt[3]{c}\right)\right) \cdot \left(b - 0.5\right)\right) + \left(b - 0.5\right) \cdot \log \left({\left(\frac{1}{c}\right)}^{\frac{-1}{3}}\right)\right) + y \cdot i
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r53698 = x;
        double r53699 = y;
        double r53700 = log(r53699);
        double r53701 = r53698 * r53700;
        double r53702 = z;
        double r53703 = r53701 + r53702;
        double r53704 = t;
        double r53705 = r53703 + r53704;
        double r53706 = a;
        double r53707 = r53705 + r53706;
        double r53708 = b;
        double r53709 = 0.5;
        double r53710 = r53708 - r53709;
        double r53711 = c;
        double r53712 = log(r53711);
        double r53713 = r53710 * r53712;
        double r53714 = r53707 + r53713;
        double r53715 = i;
        double r53716 = r53699 * r53715;
        double r53717 = r53714 + r53716;
        return r53717;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r53718 = x;
        double r53719 = y;
        double r53720 = log(r53719);
        double r53721 = r53718 * r53720;
        double r53722 = z;
        double r53723 = r53721 + r53722;
        double r53724 = t;
        double r53725 = r53723 + r53724;
        double r53726 = a;
        double r53727 = r53725 + r53726;
        double r53728 = 2.0;
        double r53729 = c;
        double r53730 = cbrt(r53729);
        double r53731 = log(r53730);
        double r53732 = r53728 * r53731;
        double r53733 = b;
        double r53734 = 0.5;
        double r53735 = r53733 - r53734;
        double r53736 = r53732 * r53735;
        double r53737 = r53727 + r53736;
        double r53738 = 1.0;
        double r53739 = r53738 / r53729;
        double r53740 = -0.3333333333333333;
        double r53741 = pow(r53739, r53740);
        double r53742 = log(r53741);
        double r53743 = r53735 * r53742;
        double r53744 = r53737 + r53743;
        double r53745 = i;
        double r53746 = r53719 * r53745;
        double r53747 = r53744 + r53746;
        return r53747;
}

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. Applied associate-+r+0.1

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

  7. Simplified0.1

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

  8. Taylor expanded around inf 0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019326 
(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)))