Average Error: 0.1 → 0.1
Time: 5.6s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(x + y\right) + \left(z - \left(z \cdot \log \left(\sqrt{t}\right) + z \cdot \log \left(\sqrt{t}\right)\right)\right)\right) + \left(a - 0.5\right) \cdot b\]
\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 - \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
double f(double x, double y, double z, double t, double a, double b) {
        double r372989 = x;
        double r372990 = y;
        double r372991 = r372989 + r372990;
        double r372992 = z;
        double r372993 = r372991 + r372992;
        double r372994 = t;
        double r372995 = log(r372994);
        double r372996 = r372992 * r372995;
        double r372997 = r372993 - r372996;
        double r372998 = a;
        double r372999 = 0.5;
        double r373000 = r372998 - r372999;
        double r373001 = b;
        double r373002 = r373000 * r373001;
        double r373003 = r372997 + r373002;
        return r373003;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r373004 = x;
        double r373005 = y;
        double r373006 = r373004 + r373005;
        double r373007 = z;
        double r373008 = t;
        double r373009 = sqrt(r373008);
        double r373010 = log(r373009);
        double r373011 = r373007 * r373010;
        double r373012 = r373011 + r373011;
        double r373013 = r373007 - r373012;
        double r373014 = r373006 + r373013;
        double r373015 = a;
        double r373016 = 0.5;
        double r373017 = r373015 - r373016;
        double r373018 = b;
        double r373019 = r373017 * r373018;
        double r373020 = r373014 + r373019;
        return r373020;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020060 
(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)))