Average Error: 0.1 → 0.1
Time: 8.7s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(\left(x + y\right) + z\right) - \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot z\right) - z \cdot \log \left({\left({\left({t}^{\frac{1}{3}}\right)}^{\left(\sqrt[3]{\frac{2}{3}} \cdot \sqrt[3]{\frac{2}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{2}{3}}\right)} \cdot {\left(\sqrt[3]{t}\right)}^{\frac{1}{3}}\right)\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(\left(x + y\right) + z\right) - \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot z\right) - z \cdot \log \left({\left({\left({t}^{\frac{1}{3}}\right)}^{\left(\sqrt[3]{\frac{2}{3}} \cdot \sqrt[3]{\frac{2}{3}}\right)}\right)}^{\left(\sqrt[3]{\frac{2}{3}}\right)} \cdot {\left(\sqrt[3]{t}\right)}^{\frac{1}{3}}\right)\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r480820 = x;
        double r480821 = y;
        double r480822 = r480820 + r480821;
        double r480823 = z;
        double r480824 = r480822 + r480823;
        double r480825 = t;
        double r480826 = log(r480825);
        double r480827 = r480823 * r480826;
        double r480828 = r480824 - r480827;
        double r480829 = a;
        double r480830 = 0.5;
        double r480831 = r480829 - r480830;
        double r480832 = b;
        double r480833 = r480831 * r480832;
        double r480834 = r480828 + r480833;
        return r480834;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r480835 = x;
        double r480836 = y;
        double r480837 = r480835 + r480836;
        double r480838 = z;
        double r480839 = r480837 + r480838;
        double r480840 = t;
        double r480841 = cbrt(r480840);
        double r480842 = r480841 * r480841;
        double r480843 = log(r480842);
        double r480844 = r480843 * r480838;
        double r480845 = r480839 - r480844;
        double r480846 = 0.3333333333333333;
        double r480847 = pow(r480840, r480846);
        double r480848 = 0.6666666666666666;
        double r480849 = cbrt(r480848);
        double r480850 = r480849 * r480849;
        double r480851 = pow(r480847, r480850);
        double r480852 = pow(r480851, r480849);
        double r480853 = pow(r480841, r480846);
        double r480854 = r480852 * r480853;
        double r480855 = log(r480854);
        double r480856 = r480838 * r480855;
        double r480857 = r480845 - r480856;
        double r480858 = a;
        double r480859 = 0.5;
        double r480860 = r480858 - r480859;
        double r480861 = b;
        double r480862 = r480860 * r480861;
        double r480863 = r480857 + r480862;
        return r480863;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.4
Herbie0.1
\[\left(\left(x + y\right) + \frac{\left(1 - {\left(\log t\right)}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b\]

Derivation

  1. Initial program 0.1

    \[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Applied associate--r+0.1

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

  7. Simplified0.1

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

  9. Applied pow1/30.1

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

  11. Applied add-cube-cbrt0.1

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

  12. Simplified0.1

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

  13. Simplified0.1

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

  15. Applied add-cube-cbrt0.1

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

  16. Applied pow-unpow0.1

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

  17. Final simplification0.1

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

Reproduce

herbie shell --seed 2020100 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1 (pow (log t) 2)) z) (+ 1 (log t)))) (* (- a 0.5) b))

  (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))