Average Error: 0.3 → 0.3
Time: 33.6s
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 r2075559 = x;
        double r2075560 = y;
        double r2075561 = r2075559 + r2075560;
        double r2075562 = log(r2075561);
        double r2075563 = z;
        double r2075564 = log(r2075563);
        double r2075565 = r2075562 + r2075564;
        double r2075566 = t;
        double r2075567 = r2075565 - r2075566;
        double r2075568 = a;
        double r2075569 = 0.5;
        double r2075570 = r2075568 - r2075569;
        double r2075571 = log(r2075566);
        double r2075572 = r2075570 * r2075571;
        double r2075573 = r2075567 + r2075572;
        return r2075573;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2075574 = y;
        double r2075575 = x;
        double r2075576 = r2075574 + r2075575;
        double r2075577 = log(r2075576);
        double r2075578 = a;
        double r2075579 = 0.5;
        double r2075580 = r2075578 - r2075579;
        double r2075581 = t;
        double r2075582 = 0.3333333333333333;
        double r2075583 = sqrt(r2075582);
        double r2075584 = pow(r2075581, r2075583);
        double r2075585 = pow(r2075584, r2075583);
        double r2075586 = log(r2075585);
        double r2075587 = r2075580 * r2075586;
        double r2075588 = cbrt(r2075581);
        double r2075589 = r2075588 * r2075588;
        double r2075590 = log(r2075589);
        double r2075591 = r2075590 * r2075580;
        double r2075592 = z;
        double r2075593 = log(r2075592);
        double r2075594 = r2075593 - r2075581;
        double r2075595 = r2075591 + r2075594;
        double r2075596 = r2075587 + r2075595;
        double r2075597 = r2075577 + r2075596;
        return r2075597;
}

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 0.3

    \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
  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"
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))