Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Average Error: 0.3 → 0.3

Time: 29.4s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r17003132 = x;
        double r17003133 = y;
        double r17003134 = r17003132 + r17003133;
        double r17003135 = log(r17003134);
        double r17003136 = z;
        double r17003137 = log(r17003136);
        double r17003138 = r17003135 + r17003137;
        double r17003139 = t;
        double r17003140 = r17003138 - r17003139;
        double r17003141 = a;
        double r17003142 = 0.5;
        double r17003143 = r17003141 - r17003142;
        double r17003144 = log(r17003139);
        double r17003145 = r17003143 * r17003144;
        double r17003146 = r17003140 + r17003145;
        return r17003146;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r17003147 = t;
        double r17003148 = cbrt(r17003147);
        double r17003149 = log(r17003148);
        double r17003150 = r17003149 + r17003149;
        double r17003151 = a;
        double r17003152 = 0.5;
        double r17003153 = r17003151 - r17003152;
        double r17003154 = r17003150 * r17003153;
        double r17003155 = r17003153 * r17003149;
        double r17003156 = r17003154 + r17003155;
        double r17003157 = y;
        double r17003158 = x;
        double r17003159 = r17003157 + r17003158;
        double r17003160 = log(r17003159);
        double r17003161 = z;
        double r17003162 = log(r17003161);
        double r17003163 = r17003160 + r17003162;
        double r17003164 = r17003163 - r17003147;
        double r17003165 = r17003156 + r17003164;
        return r17003165;
}

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 add-cube-cbrt 0.3

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

4. Applied log-prod 0.3

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

5. Applied distribute-rgt-in 0.3

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

6. Simplified 0.3

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

8. Applied pow1/3 0.3

   \[\leadsto \left(\left(\log \left(x + y\right) + \log z\right) - t\right) + \left(\left(a - 0.5\right) \cdot \left(\log \left(\sqrt[3]{t}\right) + \log \left(\sqrt[3]{t}\right)\right) + \log \color{blue}{\left({t}^{\frac{1}{3}}\right)} \cdot \left(a - 0.5\right)\right)\]
9. Using strategy rm

10. Applied unpow1/3 0.3

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

11. Final simplification 0.3

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

Reproduce

herbie shell --seed 2019192 
(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))))