Average Error: 0.1 → 0.1
Time: 5.0s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(x + y\right) + \left(z \cdot \left(1 - \log \left(\sqrt{t}\right)\right) - z \cdot \log \left(\sqrt{t}\right)\right)\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(x + y\right) + \left(z \cdot \left(1 - \log \left(\sqrt{t}\right)\right) - z \cdot \log \left(\sqrt{t}\right)\right)\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r344969 = x;
        double r344970 = y;
        double r344971 = r344969 + r344970;
        double r344972 = z;
        double r344973 = r344971 + r344972;
        double r344974 = t;
        double r344975 = log(r344974);
        double r344976 = r344972 * r344975;
        double r344977 = r344973 - r344976;
        double r344978 = a;
        double r344979 = 0.5;
        double r344980 = r344978 - r344979;
        double r344981 = b;
        double r344982 = r344980 * r344981;
        double r344983 = r344977 + r344982;
        return r344983;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r344984 = x;
        double r344985 = y;
        double r344986 = r344984 + r344985;
        double r344987 = z;
        double r344988 = 1.0;
        double r344989 = t;
        double r344990 = sqrt(r344989);
        double r344991 = log(r344990);
        double r344992 = r344988 - r344991;
        double r344993 = r344987 * r344992;
        double r344994 = r344987 * r344991;
        double r344995 = r344993 - r344994;
        double r344996 = r344986 + r344995;
        double r344997 = a;
        double r344998 = 0.5;
        double r344999 = r344997 - r344998;
        double r345000 = b;
        double r345001 = r344999 * r345000;
        double r345002 = r344996 + r345001;
        return r345002;
}

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 associate--l+0.1

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

  5. Applied add-sqr-sqrt0.1

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

  6. Applied log-prod0.1

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

  7. Applied distribute-lft-in0.1

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

  8. Applied associate--r+0.1

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

  9. Simplified0.1

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

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

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

  12. Applied distribute-rgt-out--0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2020064 
(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)))