Numeric.SpecFunctions:logGammaL from math-functions-0.1.5.2

Average Error: 0.3 → 0.3

Time: 33.8s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a) {
        double r21130405 = x;
        double r21130406 = y;
        double r21130407 = r21130405 + r21130406;
        double r21130408 = log(r21130407);
        double r21130409 = z;
        double r21130410 = log(r21130409);
        double r21130411 = r21130408 + r21130410;
        double r21130412 = t;
        double r21130413 = r21130411 - r21130412;
        double r21130414 = a;
        double r21130415 = 0.5;
        double r21130416 = r21130414 - r21130415;
        double r21130417 = log(r21130412);
        double r21130418 = r21130416 * r21130417;
        double r21130419 = r21130413 + r21130418;
        return r21130419;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r21130420 = x;
        double r21130421 = y;
        double r21130422 = r21130420 + r21130421;
        double r21130423 = log(r21130422);
        double r21130424 = z;
        double r21130425 = cbrt(r21130424);
        double r21130426 = log(r21130425);
        double r21130427 = r21130426 + r21130426;
        double r21130428 = r21130423 + r21130427;
        double r21130429 = r21130428 + r21130426;
        double r21130430 = t;
        double r21130431 = r21130429 - r21130430;
        double r21130432 = log(r21130430);
        double r21130433 = a;
        double r21130434 = 0.5;
        double r21130435 = r21130433 - r21130434;
        double r21130436 = r21130432 * r21130435;
        double r21130437 = r21130431 + r21130436;
        return r21130437;
}

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

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

4. Applied log-prod 0.3

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

5. Applied associate-+r+ 0.3

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

6. Simplified 0.3

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

7. Final simplification 0.3

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

Reproduce

herbie shell --seed 2019179 
(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))))