Average Error: 0.3 → 0.3
Time: 31.4s
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 r19172550 = x;
        double r19172551 = y;
        double r19172552 = r19172550 + r19172551;
        double r19172553 = log(r19172552);
        double r19172554 = z;
        double r19172555 = log(r19172554);
        double r19172556 = r19172553 + r19172555;
        double r19172557 = t;
        double r19172558 = r19172556 - r19172557;
        double r19172559 = a;
        double r19172560 = 0.5;
        double r19172561 = r19172559 - r19172560;
        double r19172562 = log(r19172557);
        double r19172563 = r19172561 * r19172562;
        double r19172564 = r19172558 + r19172563;
        return r19172564;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r19172565 = y;
        double r19172566 = x;
        double r19172567 = r19172565 + r19172566;
        double r19172568 = log(r19172567);
        double r19172569 = a;
        double r19172570 = 0.5;
        double r19172571 = r19172569 - r19172570;
        double r19172572 = t;
        double r19172573 = 0.3333333333333333;
        double r19172574 = sqrt(r19172573);
        double r19172575 = pow(r19172572, r19172574);
        double r19172576 = pow(r19172575, r19172574);
        double r19172577 = log(r19172576);
        double r19172578 = r19172571 * r19172577;
        double r19172579 = cbrt(r19172572);
        double r19172580 = r19172579 * r19172579;
        double r19172581 = log(r19172580);
        double r19172582 = r19172581 * r19172571;
        double r19172583 = z;
        double r19172584 = log(r19172583);
        double r19172585 = r19172584 - r19172572;
        double r19172586 = r19172582 + r19172585;
        double r19172587 = r19172578 + r19172586;
        double r19172588 = r19172568 + r19172587;
        return r19172588;
}

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))))