Average Error: 0.3 → 0.3
Time: 32.1s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(2 \cdot \left(\log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right) + \log z\right) - \left(t - \log \left(x + y\right)\right)\]
\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t
↓
\left(2 \cdot \left(\log \left(\sqrt{t}\right) \cdot \left(a - 0.5\right)\right) + \log z\right) - \left(t - \log \left(x + y\right)\right)
double f(double x, double y, double z, double t, double a) {
        double r57092 = x;
        double r57093 = y;
        double r57094 = r57092 + r57093;
        double r57095 = log(r57094);
        double r57096 = z;
        double r57097 = log(r57096);
        double r57098 = r57095 + r57097;
        double r57099 = t;
        double r57100 = r57098 - r57099;
        double r57101 = a;
        double r57102 = 0.5;
        double r57103 = r57101 - r57102;
        double r57104 = log(r57099);
        double r57105 = r57103 * r57104;
        double r57106 = r57100 + r57105;
        return r57106;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r57107 = 2.0;
        double r57108 = t;
        double r57109 = sqrt(r57108);
        double r57110 = log(r57109);
        double r57111 = a;
        double r57112 = 0.5;
        double r57113 = r57111 - r57112;
        double r57114 = r57110 * r57113;
        double r57115 = r57107 * r57114;
        double r57116 = z;
        double r57117 = log(r57116);
        double r57118 = r57115 + r57117;
        double r57119 = x;
        double r57120 = y;
        double r57121 = r57119 + r57120;
        double r57122 = log(r57121);
        double r57123 = r57108 - r57122;
        double r57124 = r57118 - r57123;
        return r57124;
}

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-sqr-sqrt0.3

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

  4. Applied log-prod0.3

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

  5. Applied distribute-rgt-in0.3

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

  6. Applied associate-+r+0.3

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

  8. Applied sub-neg0.3

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

  9. Applied distribute-lft-in0.3

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

  10. Applied associate-+r+0.3

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

  11. Simplified0.3

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

  12. Final simplification0.3

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

Reproduce

herbie shell --seed 2019298 
(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))))