Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A

Average Error: 0.1 → 0.1

Time: 12.8s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b) {
        double r266297 = x;
        double r266298 = y;
        double r266299 = r266297 + r266298;
        double r266300 = z;
        double r266301 = r266299 + r266300;
        double r266302 = t;
        double r266303 = log(r266302);
        double r266304 = r266300 * r266303;
        double r266305 = r266301 - r266304;
        double r266306 = a;
        double r266307 = 0.5;
        double r266308 = r266306 - r266307;
        double r266309 = b;
        double r266310 = r266308 * r266309;
        double r266311 = r266305 + r266310;
        return r266311;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r266312 = a;
        double r266313 = 0.5;
        double r266314 = r266312 - r266313;
        double r266315 = b;
        double r266316 = r266314 * r266315;
        double r266317 = x;
        double r266318 = y;
        double r266319 = r266317 + r266318;
        double r266320 = z;
        double r266321 = r266319 + r266320;
        double r266322 = r266316 + r266321;
        double r266323 = t;
        double r266324 = sqrt(r266323);
        double r266325 = log(r266324);
        double r266326 = cbrt(r266323);
        double r266327 = r266326 * r266326;
        double r266328 = sqrt(r266327);
        double r266329 = log(r266328);
        double r266330 = sqrt(r266326);
        double r266331 = log(r266330);
        double r266332 = r266329 + r266331;
        double r266333 = r266325 + r266332;
        double r266334 = r266320 * r266333;
        double r266335 = r266322 - r266334;
        return r266335;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Target

Original	0.1
Target	0.4
Herbie	0.1

\[\left(\left(x + y\right) + \frac{\left(1 - {\left(\log t\right)}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b\]

Derivation

1. Initial program 0.1

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

3. Applied add-sqr-sqrt 0.1

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

4. Applied log-prod 0.1

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

5. Applied distribute-lft-in 0.1

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

6. Applied associate--r+ 0.1

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

7. Simplified 0.1

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

9. Applied add-cube-cbrt 0.1

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

10. Applied sqrt-prod 0.1

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

11. Applied log-prod 0.1

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

12. Applied distribute-lft-in 0.1

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

13. Final simplification 0.1

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

Reproduce

herbie shell --seed 1978988140 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"
  :precision binary64

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1 (pow (log t) 2)) z) (+ 1 (log t)))) (* (- a 0.5) b))

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