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

Average Error: 0.1 → 0.1

Time: 19.9s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b) {
        double r294187 = x;
        double r294188 = y;
        double r294189 = r294187 + r294188;
        double r294190 = z;
        double r294191 = r294189 + r294190;
        double r294192 = t;
        double r294193 = log(r294192);
        double r294194 = r294190 * r294193;
        double r294195 = r294191 - r294194;
        double r294196 = a;
        double r294197 = 0.5;
        double r294198 = r294196 - r294197;
        double r294199 = b;
        double r294200 = r294198 * r294199;
        double r294201 = r294195 + r294200;
        return r294201;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r294202 = a;
        double r294203 = 0.5;
        double r294204 = r294202 - r294203;
        double r294205 = b;
        double r294206 = r294204 * r294205;
        double r294207 = x;
        double r294208 = y;
        double r294209 = r294207 + r294208;
        double r294210 = z;
        double r294211 = r294209 + r294210;
        double r294212 = r294206 + r294211;
        double r294213 = 3.0;
        double r294214 = r294213 * r294210;
        double r294215 = t;
        double r294216 = cbrt(r294215);
        double r294217 = r294216 * r294216;
        double r294218 = cbrt(r294217);
        double r294219 = log(r294218);
        double r294220 = cbrt(r294216);
        double r294221 = log(r294220);
        double r294222 = r294219 + r294221;
        double r294223 = r294214 * r294222;
        double r294224 = r294212 - r294223;
        return r294224;
}

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-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-rgt-in 0.1

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

6. Simplified 0.1

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

8. Applied distribute-rgt-out 0.1

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

9. Simplified 0.1

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

11. Applied add-cube-cbrt 0.1

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

12. Applied cbrt-prod 0.1

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

13. Applied log-prod 0.1

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

14. Applied distribute-lft-in 0.1

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

15. Applied distribute-rgt-in 0.1

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

16. Simplified 0.1

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

17. Simplified 0.1

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

18. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019291 
(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)))