Average Error: 0.3 → 0.3
Time: 11.8s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right)\right) + \left(a - 0.5\right) \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{t}}\right) \cdot 2 + \log \left(\sqrt[3]{t}\right)\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right)\right) + \left(a - 0.5\right) \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{t}}\right) \cdot 2 + \log \left(\sqrt[3]{t}\right)\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r63989 = x;
        double r63990 = y;
        double r63991 = r63989 + r63990;
        double r63992 = log(r63991);
        double r63993 = z;
        double r63994 = log(r63993);
        double r63995 = r63992 + r63994;
        double r63996 = t;
        double r63997 = r63995 - r63996;
        double r63998 = a;
        double r63999 = 0.5;
        double r64000 = r63998 - r63999;
        double r64001 = log(r63996);
        double r64002 = r64000 * r64001;
        double r64003 = r63997 + r64002;
        return r64003;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r64004 = x;
        double r64005 = y;
        double r64006 = r64004 + r64005;
        double r64007 = log(r64006);
        double r64008 = z;
        double r64009 = log(r64008);
        double r64010 = r64007 + r64009;
        double r64011 = t;
        double r64012 = r64010 - r64011;
        double r64013 = a;
        double r64014 = 0.5;
        double r64015 = r64013 - r64014;
        double r64016 = 2.0;
        double r64017 = cbrt(r64011);
        double r64018 = cbrt(r64017);
        double r64019 = r64018 * r64018;
        double r64020 = log(r64019);
        double r64021 = r64016 * r64020;
        double r64022 = r64015 * r64021;
        double r64023 = log(r64018);
        double r64024 = r64023 * r64016;
        double r64025 = log(r64017);
        double r64026 = r64024 + r64025;
        double r64027 = r64015 * r64026;
        double r64028 = r64022 + r64027;
        double r64029 = r64012 + r64028;
        return r64029;
}

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

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

  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-lft-in0.3

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

  6. Simplified0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\color{blue}{\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right)} + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\]
  7. Using strategy rm

  8. Applied add-cube-cbrt0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \color{blue}{\left(\left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right) \cdot \sqrt[3]{\sqrt[3]{t}}\right)}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\]

  9. Applied log-prod0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \color{blue}{\left(\log \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right) + \log \left(\sqrt[3]{\sqrt[3]{t}}\right)\right)}\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\]

  10. Applied distribute-lft-in0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(a - 0.5\right) \cdot \color{blue}{\left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right) + 2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}}\right)\right)} + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\]

  11. Applied distribute-lft-in0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\color{blue}{\left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right)\right) + \left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}}\right)\right)\right)} + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\]

  12. Applied associate-+l+0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{\left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right)\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}}\right)\right) + \left(a - 0.5\right) \cdot \log \left(\sqrt[3]{t}\right)\right)\right)}\]

  13. Simplified0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right)\right) + \color{blue}{\left(a - 0.5\right) \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{t}}\right) \cdot 2 + \log \left(\sqrt[3]{t}\right)\right)}\right)\]

  14. Final simplification0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(a - 0.5\right) \cdot \left(2 \cdot \log \left(\sqrt[3]{\sqrt[3]{t}} \cdot \sqrt[3]{\sqrt[3]{t}}\right)\right) + \left(a - 0.5\right) \cdot \left(\log \left(\sqrt[3]{\sqrt[3]{t}}\right) \cdot 2 + \log \left(\sqrt[3]{t}\right)\right)\right)\]

Reproduce

herbie shell --seed 2019354 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64
  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))