Average Error: 0.2 → 0.2
Time: 32.2s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(x + y\right) + \left(\left(\log \left(\sqrt{z}\right) + \left(\log \left(\sqrt{z}\right) - t\right)\right) + \left(a - 0.5\right) \cdot \log t\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(x + y\right) + \left(\left(\log \left(\sqrt{z}\right) + \left(\log \left(\sqrt{z}\right) - t\right)\right) + \left(a - 0.5\right) \cdot \log t\right)
double f(double x, double y, double z, double t, double a) {
        double r65261 = x;
        double r65262 = y;
        double r65263 = r65261 + r65262;
        double r65264 = log(r65263);
        double r65265 = z;
        double r65266 = log(r65265);
        double r65267 = r65264 + r65266;
        double r65268 = t;
        double r65269 = r65267 - r65268;
        double r65270 = a;
        double r65271 = 0.5;
        double r65272 = r65270 - r65271;
        double r65273 = log(r65268);
        double r65274 = r65272 * r65273;
        double r65275 = r65269 + r65274;
        return r65275;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r65276 = x;
        double r65277 = y;
        double r65278 = r65276 + r65277;
        double r65279 = log(r65278);
        double r65280 = z;
        double r65281 = sqrt(r65280);
        double r65282 = log(r65281);
        double r65283 = t;
        double r65284 = r65282 - r65283;
        double r65285 = r65282 + r65284;
        double r65286 = a;
        double r65287 = 0.5;
        double r65288 = r65286 - r65287;
        double r65289 = log(r65283);
        double r65290 = r65288 * r65289;
        double r65291 = r65285 + r65290;
        double r65292 = r65279 + r65291;
        return r65292;
}

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 0.2

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

  3. Applied associate--l+0.2

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

  4. Applied associate-+l+0.2

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

  6. Applied add-sqr-sqrt0.2

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

  7. Applied log-prod0.2

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

  8. Applied associate--l+0.2

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

  9. Final simplification0.2

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

Reproduce

herbie shell --seed 2019235 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))