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

Average Error: 0.1 → 0.1

Time: 8.0s

Precision: 64

Math

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

↓

\[\left(\left(\left(x + y\right) + z\right) - \left(z \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + {\left(\log \left({t}^{\frac{1}{3}}\right) \cdot z\right)}^{1}\right)\right) + \left(a - 0.5\right) \cdot b\]

C

double f(double x, double y, double z, double t, double a, double b) {
        double r510301 = x;
        double r510302 = y;
        double r510303 = r510301 + r510302;
        double r510304 = z;
        double r510305 = r510303 + r510304;
        double r510306 = t;
        double r510307 = log(r510306);
        double r510308 = r510304 * r510307;
        double r510309 = r510305 - r510308;
        double r510310 = a;
        double r510311 = 0.5;
        double r510312 = r510310 - r510311;
        double r510313 = b;
        double r510314 = r510312 * r510313;
        double r510315 = r510309 + r510314;
        return r510315;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r510316 = x;
        double r510317 = y;
        double r510318 = r510316 + r510317;
        double r510319 = z;
        double r510320 = r510318 + r510319;
        double r510321 = 2.0;
        double r510322 = t;
        double r510323 = cbrt(r510322);
        double r510324 = log(r510323);
        double r510325 = r510321 * r510324;
        double r510326 = r510319 * r510325;
        double r510327 = 0.3333333333333333;
        double r510328 = pow(r510322, r510327);
        double r510329 = log(r510328);
        double r510330 = r510329 * r510319;
        double r510331 = 1.0;
        double r510332 = pow(r510330, r510331);
        double r510333 = r510326 + r510332;
        double r510334 = r510320 - r510333;
        double r510335 = a;
        double r510336 = 0.5;
        double r510337 = r510335 - r510336;
        double r510338 = b;
        double r510339 = r510337 * r510338;
        double r510340 = r510334 + r510339;
        return r510340;
}

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	0.3
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-cube-cbrt 0.1

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

4. Applied log-prod 0.1

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

5. Applied distribute-lft-in 0.1

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

6. Simplified 0.1

   \[\leadsto \left(\left(\left(x + y\right) + z\right) - \left(\color{blue}{z \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right)} + z \cdot \log \left(\sqrt[3]{t}\right)\right)\right) + \left(a - 0.5\right) \cdot b\]
7. Using strategy rm

8. Applied pow1 0.1

   \[\leadsto \left(\left(\left(x + y\right) + z\right) - \left(z \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + z \cdot \color{blue}{{\left(\log \left(\sqrt[3]{t}\right)\right)}^{1}}\right)\right) + \left(a - 0.5\right) \cdot b\]

9. Applied pow1 0.1

   \[\leadsto \left(\left(\left(x + y\right) + z\right) - \left(z \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + \color{blue}{{z}^{1}} \cdot {\left(\log \left(\sqrt[3]{t}\right)\right)}^{1}\right)\right) + \left(a - 0.5\right) \cdot b\]

10. Applied pow-prod-down 0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - \left(z \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + \color{blue}{{\left(z \cdot \log \left(\sqrt[3]{t}\right)\right)}^{1}}\right)\right) + \left(a - 0.5\right) \cdot b\]

11. Simplified 0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - \left(z \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + {\color{blue}{\left(\log \left({t}^{\frac{1}{3}}\right) \cdot z\right)}}^{1}\right)\right) + \left(a - 0.5\right) \cdot b\]

12. Final simplification 0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - \left(z \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + {\left(\log \left({t}^{\frac{1}{3}}\right) \cdot z\right)}^{1}\right)\right) + \left(a - 0.5\right) \cdot b\]

Reproduce

herbie shell --seed 2020034 
(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)))