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

Average Error: 0.1 → 0.1

Time: 19.2s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b) {
        double r510151 = x;
        double r510152 = y;
        double r510153 = r510151 + r510152;
        double r510154 = z;
        double r510155 = r510153 + r510154;
        double r510156 = t;
        double r510157 = log(r510156);
        double r510158 = r510154 * r510157;
        double r510159 = r510155 - r510158;
        double r510160 = a;
        double r510161 = 0.5;
        double r510162 = r510160 - r510161;
        double r510163 = b;
        double r510164 = r510162 * r510163;
        double r510165 = r510159 + r510164;
        return r510165;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r510166 = x;
        double r510167 = y;
        double r510168 = r510166 + r510167;
        double r510169 = z;
        double r510170 = r510168 + r510169;
        double r510171 = 2.0;
        double r510172 = t;
        double r510173 = cbrt(r510172);
        double r510174 = log(r510173);
        double r510175 = r510171 * r510174;
        double r510176 = r510169 * r510175;
        double r510177 = 0.6666666666666666;
        double r510178 = pow(r510172, r510177);
        double r510179 = cbrt(r510178);
        double r510180 = log(r510179);
        double r510181 = r510169 * r510180;
        double r510182 = cbrt(r510173);
        double r510183 = log(r510182);
        double r510184 = r510169 * r510183;
        double r510185 = r510181 + r510184;
        double r510186 = r510176 + r510185;
        double r510187 = r510170 - r510186;
        double r510188 = a;
        double r510189 = 0.5;
        double r510190 = r510188 - r510189;
        double r510191 = b;
        double r510192 = r510190 * r510191;
        double r510193 = r510187 + r510192;
        return r510193;
}

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-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 add-cube-cbrt 0.1

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

9. Applied cbrt-prod 0.1

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

10. Applied log-prod 0.1

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

11. Applied distribute-lft-in 0.1

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

12. Simplified 0.1

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

13. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(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)))