Average Error: 0.3 → 0.3
Time: 31.2s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\left(\log \left(x + y\right) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)\]
\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) + \left(\log \left(\sqrt[3]{z}\right) + \log \left(\sqrt[3]{z}\right)\right)\right) + \log \left(\sqrt[3]{z}\right)\right) - t\right) + \log t \cdot \left(a - 0.5\right)
double f(double x, double y, double z, double t, double a) {
        double r1137566 = x;
        double r1137567 = y;
        double r1137568 = r1137566 + r1137567;
        double r1137569 = log(r1137568);
        double r1137570 = z;
        double r1137571 = log(r1137570);
        double r1137572 = r1137569 + r1137571;
        double r1137573 = t;
        double r1137574 = r1137572 - r1137573;
        double r1137575 = a;
        double r1137576 = 0.5;
        double r1137577 = r1137575 - r1137576;
        double r1137578 = log(r1137573);
        double r1137579 = r1137577 * r1137578;
        double r1137580 = r1137574 + r1137579;
        return r1137580;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r1137581 = x;
        double r1137582 = y;
        double r1137583 = r1137581 + r1137582;
        double r1137584 = log(r1137583);
        double r1137585 = z;
        double r1137586 = cbrt(r1137585);
        double r1137587 = log(r1137586);
        double r1137588 = r1137587 + r1137587;
        double r1137589 = r1137584 + r1137588;
        double r1137590 = r1137589 + r1137587;
        double r1137591 = t;
        double r1137592 = r1137590 - r1137591;
        double r1137593 = log(r1137591);
        double r1137594 = a;
        double r1137595 = 0.5;
        double r1137596 = r1137594 - r1137595;
        double r1137597 = r1137593 * r1137596;
        double r1137598 = r1137592 + r1137597;
        return r1137598;
}

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 add-cube-cbrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied associate-+r+0.3

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

  6. Simplified0.3

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

  7. Final simplification0.3

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

Reproduce

herbie shell --seed 2019156 
(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))))