Average Error: 0.2 → 0.3
Time: 30.7s
Precision: 64
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
↓
\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \left(\sqrt[3]{t}\right) \cdot \left(3 \cdot a - 1.5\right)\]
\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) + \log \left(\sqrt[3]{t}\right) \cdot \left(3 \cdot a - 1.5\right)
double f(double x, double y, double z, double t, double a) {
        double r301804 = x;
        double r301805 = y;
        double r301806 = r301804 + r301805;
        double r301807 = log(r301806);
        double r301808 = z;
        double r301809 = log(r301808);
        double r301810 = r301807 + r301809;
        double r301811 = t;
        double r301812 = r301810 - r301811;
        double r301813 = a;
        double r301814 = 0.5;
        double r301815 = r301813 - r301814;
        double r301816 = log(r301811);
        double r301817 = r301815 * r301816;
        double r301818 = r301812 + r301817;
        return r301818;
}
↓
double f(double x, double y, double z, double t, double a) {
        double r301819 = x;
        double r301820 = y;
        double r301821 = r301819 + r301820;
        double r301822 = log(r301821);
        double r301823 = z;
        double r301824 = log(r301823);
        double r301825 = r301822 + r301824;
        double r301826 = t;
        double r301827 = r301825 - r301826;
        double r301828 = cbrt(r301826);
        double r301829 = log(r301828);
        double r301830 = 3.0;
        double r301831 = a;
        double r301832 = r301830 * r301831;
        double r301833 = 1.5;
        double r301834 = r301832 - r301833;
        double r301835 = r301829 * r301834;
        double r301836 = r301827 + r301835;
        return r301836;
}

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

Target

Original0.2
Target0.2
Herbie0.3
\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

Derivation

  1. Initial program 0.2

    \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.2

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

  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

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

  7. Simplified0.3

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

  8. Taylor expanded around 0 0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{\left(3 \cdot \left(a \cdot \log \left({t}^{\frac{1}{3}}\right)\right) - 1.5 \cdot \log \left({t}^{\frac{1}{3}}\right)\right)}\]

  9. Simplified0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \color{blue}{\log \left(\sqrt[3]{t}\right) \cdot \left(3 \cdot a - 1.5\right)}\]

  10. Final simplification0.3

    \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \log \left(\sqrt[3]{t}\right) \cdot \left(3 \cdot a - 1.5\right)\]

Reproduce

herbie shell --seed 2019198 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"

  :herbie-target
  (+ (log (+ x y)) (+ (- (log z) t) (* (- a 0.5) (log t))))

  (+ (- (+ (log (+ x y)) (log z)) t) (* (- a 0.5) (log t))))