Average Error: 0.3 → 0.3
Time: 1.2m
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(y + x\right) + \left(\left(a - 0.5\right) \cdot \log \left({\left({t}^{\left(\sqrt{\frac{1}{3}}\right)}\right)}^{\left(\sqrt{\frac{1}{3}}\right)}\right) + \left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \left(\log z - t\right)\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\log \left(y + x\right) + \left(\left(a - 0.5\right) \cdot \log \left({\left({t}^{\left(\sqrt{\frac{1}{3}}\right)}\right)}^{\left(\sqrt{\frac{1}{3}}\right)}\right) + \left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \left(\log z - t\right)\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r15966291 = x;
        double r15966292 = y;
        double r15966293 = r15966291 + r15966292;
        double r15966294 = log(r15966293);
        double r15966295 = z;
        double r15966296 = log(r15966295);
        double r15966297 = r15966294 + r15966296;
        double r15966298 = t;
        double r15966299 = r15966297 - r15966298;
        double r15966300 = a;
        double r15966301 = 0.5;
        double r15966302 = r15966300 - r15966301;
        double r15966303 = log(r15966298);
        double r15966304 = r15966302 * r15966303;
        double r15966305 = r15966299 + r15966304;
        return r15966305;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r15966306 = y;
        double r15966307 = x;
        double r15966308 = r15966306 + r15966307;
        double r15966309 = log(r15966308);
        double r15966310 = a;
        double r15966311 = 0.5;
        double r15966312 = r15966310 - r15966311;
        double r15966313 = t;
        double r15966314 = 0.3333333333333333;
        double r15966315 = sqrt(r15966314);
        double r15966316 = pow(r15966313, r15966315);
        double r15966317 = pow(r15966316, r15966315);
        double r15966318 = log(r15966317);
        double r15966319 = r15966312 * r15966318;
        double r15966320 = cbrt(r15966313);
        double r15966321 = r15966320 * r15966320;
        double r15966322 = log(r15966321);
        double r15966323 = r15966322 * r15966312;
        double r15966324 = z;
        double r15966325 = log(r15966324);
        double r15966326 = r15966325 - r15966313;
        double r15966327 = r15966323 + r15966326;
        double r15966328 = r15966319 + r15966327;
        double r15966329 = r15966309 + r15966328;
        return r15966329;
}

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

Target

Original0.3
Target0.3
Herbie0.3
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

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 associate--l+0.3

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

  4. Applied associate-+l+0.3

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

  6. Applied add-cube-cbrt0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log \color{blue}{\left(\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}\right)}\right)\]

  7. Applied log-prod0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \color{blue}{\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right)}\right)\]

  8. Applied distribute-rgt-in0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\log z - t\right) + \color{blue}{\left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right)}\right)\]

  9. Applied associate-+r+0.3

    \[\leadsto \log \left(x + y\right) + \color{blue}{\left(\left(\left(\log z - t\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right)}\]
  10. Using strategy rm

  11. Applied pow1/30.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\left(\log z - t\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \log \color{blue}{\left({t}^{\frac{1}{3}}\right)} \cdot \left(a - 0.5\right)\right)\]
  12. Using strategy rm

  13. Applied add-sqr-sqrt0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\left(\log z - t\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \log \left({t}^{\color{blue}{\left(\sqrt{\frac{1}{3}} \cdot \sqrt{\frac{1}{3}}\right)}}\right) \cdot \left(a - 0.5\right)\right)\]

  14. Applied pow-unpow0.3

    \[\leadsto \log \left(x + y\right) + \left(\left(\left(\log z - t\right) + \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\right) + \log \color{blue}{\left({\left({t}^{\left(\sqrt{\frac{1}{3}}\right)}\right)}^{\left(\sqrt{\frac{1}{3}}\right)}\right)} \cdot \left(a - 0.5\right)\right)\]

  15. Final simplification0.3

    \[\leadsto \log \left(y + x\right) + \left(\left(a - 0.5\right) \cdot \log \left({\left({t}^{\left(\sqrt{\frac{1}{3}}\right)}\right)}^{\left(\sqrt{\frac{1}{3}}\right)}\right) + \left(\log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \left(a - 0.5\right) + \left(\log z - t\right)\right)\right)\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"

  :herbie-target
  (+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))

  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))