Average Error: 0.1 → 0.1
Time: 18.2s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(\left(x + y\right) + z\right) - z \cdot \left(\log \left(\sqrt{t}\right) + \log \left(\left|\sqrt[3]{t}\right|\right)\right)\right) - z \cdot \log \left(\sqrt{\sqrt[3]{t}}\right)\right) + \left(a - 0.5\right) \cdot b\]
\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) - z \cdot \left(\log \left(\sqrt{t}\right) + \log \left(\left|\sqrt[3]{t}\right|\right)\right)\right) - z \cdot \log \left(\sqrt{\sqrt[3]{t}}\right)\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r316957 = x;
        double r316958 = y;
        double r316959 = r316957 + r316958;
        double r316960 = z;
        double r316961 = r316959 + r316960;
        double r316962 = t;
        double r316963 = log(r316962);
        double r316964 = r316960 * r316963;
        double r316965 = r316961 - r316964;
        double r316966 = a;
        double r316967 = 0.5;
        double r316968 = r316966 - r316967;
        double r316969 = b;
        double r316970 = r316968 * r316969;
        double r316971 = r316965 + r316970;
        return r316971;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r316972 = x;
        double r316973 = y;
        double r316974 = r316972 + r316973;
        double r316975 = z;
        double r316976 = r316974 + r316975;
        double r316977 = t;
        double r316978 = sqrt(r316977);
        double r316979 = log(r316978);
        double r316980 = cbrt(r316977);
        double r316981 = fabs(r316980);
        double r316982 = log(r316981);
        double r316983 = r316979 + r316982;
        double r316984 = r316975 * r316983;
        double r316985 = r316976 - r316984;
        double r316986 = sqrt(r316980);
        double r316987 = log(r316986);
        double r316988 = r316975 * r316987;
        double r316989 = r316985 - r316988;
        double r316990 = a;
        double r316991 = 0.5;
        double r316992 = r316990 - r316991;
        double r316993 = b;
        double r316994 = r316992 * r316993;
        double r316995 = r316989 + r316994;
        return r316995;
}

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
Target0.3
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-sqr-sqrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Applied associate--r+0.1

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

  7. Simplified0.1

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

  9. Applied add-cube-cbrt0.1

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

  10. Applied sqrt-prod0.1

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

  11. Applied log-prod0.1

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

  12. Applied distribute-lft-in0.1

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

  13. Applied associate--r+0.1

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

  14. Simplified0.1

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

  15. Final simplification0.1

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

Reproduce

herbie shell --seed 2019350 
(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)))