Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Average Error: 0.3 → 0.3

Time: 12.2s

Precision: 64

Math

\[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r380005 = x;
        double r380006 = y;
        double r380007 = r380005 + r380006;
        double r380008 = log(r380007);
        double r380009 = z;
        double r380010 = log(r380009);
        double r380011 = r380008 + r380010;
        double r380012 = t;
        double r380013 = r380011 - r380012;
        double r380014 = a;
        double r380015 = 0.5;
        double r380016 = r380014 - r380015;
        double r380017 = log(r380012);
        double r380018 = r380016 * r380017;
        double r380019 = r380013 + r380018;
        return r380019;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r380020 = x;
        double r380021 = y;
        double r380022 = r380020 + r380021;
        double r380023 = log(r380022);
        double r380024 = z;
        double r380025 = log(r380024);
        double r380026 = t;
        double r380027 = r380025 - r380026;
        double r380028 = cbrt(r380026);
        double r380029 = r380028 * r380028;
        double r380030 = log(r380029);
        double r380031 = a;
        double r380032 = 0.5;
        double r380033 = r380031 - r380032;
        double r380034 = r380030 * r380033;
        double r380035 = r380027 + r380034;
        double r380036 = log(r380028);
        double r380037 = r380033 * r380036;
        double r380038 = r380035 + r380037;
        double r380039 = r380023 + r380038;
        return r380039;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	0.3
Target	0.3
Herbie	0.3

\[\log \left(x + y\right) + \left(\left(\log z - t\right) + \left(a - 0.5\right) \cdot \log t\right)\]

Derivation

1. Initial program 0.3

   \[\left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]
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-cbrt 0.3

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

7. Applied log-prod 0.3

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

8. Applied distribute-lft-in 0.3

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

9. Applied associate-+r+ 0.3

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

10. Simplified 0.3

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

11. Final simplification 0.3

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

Reproduce

herbie shell --seed 2020003 
(FPCore (x y z t a)
  :name "Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2"
  :precision binary64

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

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