Average Error: 0.3 → 0.3
Time: 17.3s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \left(\sqrt[3]{t} \cdot \left(\sqrt[3]{1} \cdot {t}^{\frac{1}{3}}\right)\right) \cdot \left(a - 0.5\right)\right) + \log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \left(\sqrt[3]{t} \cdot \left(\sqrt[3]{1} \cdot {t}^{\frac{1}{3}}\right)\right) \cdot \left(a - 0.5\right)\right) + \log \left(\sqrt[3]{t}\right) \cdot \left(a - 0.5\right)
double f(double x, double y, double z, double t, double a) {
        double r378566 = x;
        double r378567 = y;
        double r378568 = r378566 + r378567;
        double r378569 = log(r378568);
        double r378570 = z;
        double r378571 = log(r378570);
        double r378572 = r378569 + r378571;
        double r378573 = t;
        double r378574 = r378572 - r378573;
        double r378575 = a;
        double r378576 = 0.5;
        double r378577 = r378575 - r378576;
        double r378578 = log(r378573);
        double r378579 = r378577 * r378578;
        double r378580 = r378574 + r378579;
        return r378580;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r378581 = x;
        double r378582 = y;
        double r378583 = r378581 + r378582;
        double r378584 = log(r378583);
        double r378585 = z;
        double r378586 = log(r378585);
        double r378587 = r378584 + r378586;
        double r378588 = t;
        double r378589 = r378587 - r378588;
        double r378590 = cbrt(r378588);
        double r378591 = 1.0;
        double r378592 = cbrt(r378591);
        double r378593 = 0.3333333333333333;
        double r378594 = pow(r378588, r378593);
        double r378595 = r378592 * r378594;
        double r378596 = r378590 * r378595;
        double r378597 = log(r378596);
        double r378598 = a;
        double r378599 = 0.5;
        double r378600 = r378598 - r378599;
        double r378601 = r378597 * r378600;
        double r378602 = r378589 + r378601;
        double r378603 = log(r378590);
        double r378604 = r378603 * r378600;
        double r378605 = r378602 + r378604;
        return r378605;
}

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 add-cube-cbrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied distribute-rgt-in0.3

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

  6. Applied associate-+r+0.3

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

  8. Applied *-un-lft-identity0.3

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

  9. Applied cbrt-prod0.3

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

  10. Simplified0.3

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

  11. Final simplification0.3

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

Reproduce

herbie shell --seed 2019322 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

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

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