Average Error: 0.3 → 0.3
Time: 39.0s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\log \left(y + x\right) + \left(\left(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \left(\log \left(\sqrt[3]{z}\right) - t\right)\right) + \log t \cdot \left(a - 0.5\right)\right)\]
\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(\log \left(\sqrt[3]{z} \cdot \sqrt[3]{z}\right) + \left(\log \left(\sqrt[3]{z}\right) - t\right)\right) + \log t \cdot \left(a - 0.5\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r2832558 = x;
        double r2832559 = y;
        double r2832560 = r2832558 + r2832559;
        double r2832561 = log(r2832560);
        double r2832562 = z;
        double r2832563 = log(r2832562);
        double r2832564 = r2832561 + r2832563;
        double r2832565 = t;
        double r2832566 = r2832564 - r2832565;
        double r2832567 = a;
        double r2832568 = 0.5;
        double r2832569 = r2832567 - r2832568;
        double r2832570 = log(r2832565);
        double r2832571 = r2832569 * r2832570;
        double r2832572 = r2832566 + r2832571;
        return r2832572;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r2832573 = y;
        double r2832574 = x;
        double r2832575 = r2832573 + r2832574;
        double r2832576 = log(r2832575);
        double r2832577 = z;
        double r2832578 = cbrt(r2832577);
        double r2832579 = r2832578 * r2832578;
        double r2832580 = log(r2832579);
        double r2832581 = log(r2832578);
        double r2832582 = t;
        double r2832583 = r2832581 - r2832582;
        double r2832584 = r2832580 + r2832583;
        double r2832585 = log(r2832582);
        double r2832586 = a;
        double r2832587 = 0.5;
        double r2832588 = r2832586 - r2832587;
        double r2832589 = r2832585 * r2832588;
        double r2832590 = r2832584 + r2832589;
        double r2832591 = r2832576 + r2832590;
        return r2832591;
}

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

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

  7. Applied log-prod0.3

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

  8. Applied associate--l+0.3

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

  9. Final simplification0.3

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

Reproduce

herbie shell --seed 2019172 
(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))))