Average Error: 0.1 → 0.1
Time: 6.7s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(\left(x + y\right) + z\right) - \log \left(\left(\sqrt[3]{\sqrt{t}} \cdot \sqrt{\sqrt[3]{t}}\right) \cdot \left(\sqrt[3]{\sqrt{t}} \cdot \sqrt{\sqrt[3]{t}}\right)\right) \cdot z\right) - \log \left(1 \cdot \left({\left({t}^{\frac{1}{3}}\right)}^{\frac{2}{3}} \cdot {\left(\sqrt[3]{t}\right)}^{\frac{1}{3}}\right)\right) \cdot z\right) + \left(a - 0.5\right) \cdot b\]
\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(\left(\sqrt[3]{\sqrt{t}} \cdot \sqrt{\sqrt[3]{t}}\right) \cdot \left(\sqrt[3]{\sqrt{t}} \cdot \sqrt{\sqrt[3]{t}}\right)\right) \cdot z\right) - \log \left(1 \cdot \left({\left({t}^{\frac{1}{3}}\right)}^{\frac{2}{3}} \cdot {\left(\sqrt[3]{t}\right)}^{\frac{1}{3}}\right)\right) \cdot z\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r418043 = x;
        double r418044 = y;
        double r418045 = r418043 + r418044;
        double r418046 = z;
        double r418047 = r418045 + r418046;
        double r418048 = t;
        double r418049 = log(r418048);
        double r418050 = r418046 * r418049;
        double r418051 = r418047 - r418050;
        double r418052 = a;
        double r418053 = 0.5;
        double r418054 = r418052 - r418053;
        double r418055 = b;
        double r418056 = r418054 * r418055;
        double r418057 = r418051 + r418056;
        return r418057;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r418058 = x;
        double r418059 = y;
        double r418060 = r418058 + r418059;
        double r418061 = z;
        double r418062 = r418060 + r418061;
        double r418063 = t;
        double r418064 = sqrt(r418063);
        double r418065 = cbrt(r418064);
        double r418066 = cbrt(r418063);
        double r418067 = sqrt(r418066);
        double r418068 = r418065 * r418067;
        double r418069 = r418068 * r418068;
        double r418070 = log(r418069);
        double r418071 = r418070 * r418061;
        double r418072 = r418062 - r418071;
        double r418073 = 1.0;
        double r418074 = 0.3333333333333333;
        double r418075 = pow(r418063, r418074);
        double r418076 = 0.6666666666666666;
        double r418077 = pow(r418075, r418076);
        double r418078 = pow(r418066, r418074);
        double r418079 = r418077 * r418078;
        double r418080 = r418073 * r418079;
        double r418081 = log(r418080);
        double r418082 = r418081 * r418061;
        double r418083 = r418072 - r418082;
        double r418084 = a;
        double r418085 = 0.5;
        double r418086 = r418084 - r418085;
        double r418087 = b;
        double r418088 = r418086 * r418087;
        double r418089 = r418083 + r418088;
        return r418089;
}

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-rgt-in0.1

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

  6. Applied associate--r+0.1

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

  8. Applied *-un-lft-identity0.1

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

  9. Applied cbrt-prod0.1

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

  10. Simplified0.1

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

  11. Simplified0.1

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

  13. Applied add-sqr-sqrt0.1

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

  14. Applied add-sqr-sqrt0.1

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

  15. Applied cbrt-prod0.1

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

  16. Applied unswap-sqr0.1

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

  18. Applied add-cube-cbrt0.1

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

  19. Simplified0.1

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

  20. Simplified0.1

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

  21. Final simplification0.1

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

Reproduce

herbie shell --seed 2020036 
(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)))