Average Error: 0.1 → 0.1
Time: 10.4s
Precision: 64
\[\left(\left(x \cdot \log y - y\right) - z\right) + \log t\]
↓
\[\log \left(\sqrt{\sqrt{y}}\right) \cdot x + \left(\log t + \left(x \cdot \left(\log \left(\sqrt{\sqrt{y}}\right) + \log \left(\sqrt{y}\right)\right) - \left(y + z\right)\right)\right)\]
\left(\left(x \cdot \log y - y\right) - z\right) + \log t
↓
\log \left(\sqrt{\sqrt{y}}\right) \cdot x + \left(\log t + \left(x \cdot \left(\log \left(\sqrt{\sqrt{y}}\right) + \log \left(\sqrt{y}\right)\right) - \left(y + z\right)\right)\right)
double f(double x, double y, double z, double t) {
        double r89237 = x;
        double r89238 = y;
        double r89239 = log(r89238);
        double r89240 = r89237 * r89239;
        double r89241 = r89240 - r89238;
        double r89242 = z;
        double r89243 = r89241 - r89242;
        double r89244 = t;
        double r89245 = log(r89244);
        double r89246 = r89243 + r89245;
        return r89246;
}
↓
double f(double x, double y, double z, double t) {
        double r89247 = y;
        double r89248 = sqrt(r89247);
        double r89249 = sqrt(r89248);
        double r89250 = log(r89249);
        double r89251 = x;
        double r89252 = r89250 * r89251;
        double r89253 = t;
        double r89254 = log(r89253);
        double r89255 = log(r89248);
        double r89256 = r89250 + r89255;
        double r89257 = r89251 * r89256;
        double r89258 = z;
        double r89259 = r89247 + r89258;
        double r89260 = r89257 - r89259;
        double r89261 = r89254 + r89260;
        double r89262 = r89252 + r89261;
        return r89262;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

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

  3. Applied add-sqr-sqrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-lft-in0.1

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

  6. Applied associate--l+0.1

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

  7. Applied associate--l+0.1

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

  8. Applied associate-+l+0.1

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

  10. Applied add-sqr-sqrt0.1

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

  11. Applied sqrt-prod0.1

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

  12. Applied log-prod0.1

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

  13. Applied distribute-rgt-in0.1

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

  14. Applied associate-+l+0.1

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

  15. Simplified0.1

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

  16. Final simplification0.1

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

Reproduce

herbie shell --seed 2020045 
(FPCore (x y z t)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, A"
  :precision binary64
  (+ (- (- (* x (log y)) y) z) (log t)))