Average Error: 0.3 → 0.3
Time: 33.6s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right) + \left(\left(\left(\log \left(y + x\right) + \log z\right) - t\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right) + \left(\left(\left(\log \left(y + x\right) + \log z\right) - t\right) + \log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r2791237 = x;
        double r2791238 = y;
        double r2791239 = r2791237 + r2791238;
        double r2791240 = log(r2791239);
        double r2791241 = z;
        double r2791242 = log(r2791241);
        double r2791243 = r2791240 + r2791242;
        double r2791244 = t;
        double r2791245 = r2791243 - r2791244;
        double r2791246 = a;
        double r2791247 = 0.5;
        double r2791248 = r2791246 - r2791247;
        double r2791249 = log(r2791244);
        double r2791250 = r2791248 * r2791249;
        double r2791251 = r2791245 + r2791250;
        return r2791251;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2791252 = t;
        double r2791253 = sqrt(r2791252);
        double r2791254 = log(r2791253);
        double r2791255 = a;
        double r2791256 = 0.5;
        double r2791257 = r2791255 - r2791256;
        double r2791258 = r2791254 * r2791257;
        double r2791259 = y;
        double r2791260 = x;
        double r2791261 = r2791259 + r2791260;
        double r2791262 = log(r2791261);
        double r2791263 = z;
        double r2791264 = log(r2791263);
        double r2791265 = r2791262 + r2791264;
        double r2791266 = r2791265 - r2791252;
        double r2791267 = r2791266 + r2791258;
        double r2791268 = r2791258 + r2791267;
        return r2791268;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.3

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

  3. Applied add-sqr-sqrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied distribute-rgt-in0.3

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

  6. Applied associate-+r+0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019168 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))