Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Average Error: 0.3 → 0.3

Time: 1.3m

Precision: 64

Math

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

↓

\[\left(\left(\left(\log z + \log \left({\left(x + y\right)}^{\frac{1}{3}}\right)\right) + \log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

C

double f(double x, double y, double z, double t, double a) {
        double r19395203 = x;
        double r19395204 = y;
        double r19395205 = r19395203 + r19395204;
        double r19395206 = log(r19395205);
        double r19395207 = z;
        double r19395208 = log(r19395207);
        double r19395209 = r19395206 + r19395208;
        double r19395210 = t;
        double r19395211 = r19395209 - r19395210;
        double r19395212 = a;
        double r19395213 = 0.5;
        double r19395214 = r19395212 - r19395213;
        double r19395215 = log(r19395210);
        double r19395216 = r19395214 * r19395215;
        double r19395217 = r19395211 + r19395216;
        return r19395217;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r19395218 = z;
        double r19395219 = log(r19395218);
        double r19395220 = x;
        double r19395221 = y;
        double r19395222 = r19395220 + r19395221;
        double r19395223 = 0.3333333333333333;
        double r19395224 = pow(r19395222, r19395223);
        double r19395225 = log(r19395224);
        double r19395226 = r19395219 + r19395225;
        double r19395227 = cbrt(r19395222);
        double r19395228 = r19395227 * r19395227;
        double r19395229 = log(r19395228);
        double r19395230 = r19395226 + r19395229;
        double r19395231 = t;
        double r19395232 = r19395230 - r19395231;
        double r19395233 = a;
        double r19395234 = 0.5;
        double r19395235 = r19395233 - r19395234;
        double r19395236 = log(r19395231);
        double r19395237 = r19395235 * r19395236;
        double r19395238 = r19395232 + r19395237;
        return r19395238;
}

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

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

4. Applied log-prod 0.3

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

5. Applied associate-+l+ 0.3

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

7. Applied pow1/3 0.3

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

8. Final simplification 0.3

   \[\leadsto \left(\left(\left(\log z + \log \left({\left(x + y\right)}^{\frac{1}{3}}\right)\right) + \log \left(\sqrt[3]{x + y} \cdot \sqrt[3]{x + y}\right)\right) - t\right) + \left(a - 0.5\right) \cdot \log t\]

Reproduce

herbie shell --seed 2019200 
(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))))