Average Error: 0.1 → 0.1
Time: 12.3s
Precision: 64
\[\left(\left(\left(\left(x \cdot \log y + z\right) + t\right) + a\right) + \left(b - 0.5\right) \cdot \log c\right) + y \cdot i\]
↓
\[y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(t + \left(z + \left(x \cdot \log \left({y}^{\frac{1}{3}}\right) + x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right)\right)\right)\right)\right)\right)\]
\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
↓
y \cdot i + \left(\left(b - 0.5\right) \cdot \log c + \left(a + \left(t + \left(z + \left(x \cdot \log \left({y}^{\frac{1}{3}}\right) + x \cdot \left(2 \cdot \log \left(\sqrt[3]{y}\right)\right)\right)\right)\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r52804 = x;
        double r52805 = y;
        double r52806 = log(r52805);
        double r52807 = r52804 * r52806;
        double r52808 = z;
        double r52809 = r52807 + r52808;
        double r52810 = t;
        double r52811 = r52809 + r52810;
        double r52812 = a;
        double r52813 = r52811 + r52812;
        double r52814 = b;
        double r52815 = 0.5;
        double r52816 = r52814 - r52815;
        double r52817 = c;
        double r52818 = log(r52817);
        double r52819 = r52816 * r52818;
        double r52820 = r52813 + r52819;
        double r52821 = i;
        double r52822 = r52805 * r52821;
        double r52823 = r52820 + r52822;
        return r52823;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r52824 = y;
        double r52825 = i;
        double r52826 = r52824 * r52825;
        double r52827 = b;
        double r52828 = 0.5;
        double r52829 = r52827 - r52828;
        double r52830 = c;
        double r52831 = log(r52830);
        double r52832 = r52829 * r52831;
        double r52833 = a;
        double r52834 = t;
        double r52835 = z;
        double r52836 = x;
        double r52837 = 0.3333333333333333;
        double r52838 = pow(r52824, r52837);
        double r52839 = log(r52838);
        double r52840 = r52836 * r52839;
        double r52841 = 2.0;
        double r52842 = cbrt(r52824);
        double r52843 = log(r52842);
        double r52844 = r52841 * r52843;
        double r52845 = r52836 * r52844;
        double r52846 = r52840 + r52845;
        double r52847 = r52835 + r52846;
        double r52848 = r52834 + r52847;
        double r52849 = r52833 + r52848;
        double r52850 = r52832 + r52849;
        double r52851 = r52826 + r52850;
        return r52851;
}

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

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Simplified0.1

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

  8. Applied pow10.1

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

  9. Applied pow10.1

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

  10. Applied pow-prod-down0.1

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

  11. Simplified0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2020034 
(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)))