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

Average Error: 0.1 → 0.1

Time: 21.8s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t, double a, double b) {
        double r19286130 = x;
        double r19286131 = y;
        double r19286132 = r19286130 + r19286131;
        double r19286133 = z;
        double r19286134 = r19286132 + r19286133;
        double r19286135 = t;
        double r19286136 = log(r19286135);
        double r19286137 = r19286133 * r19286136;
        double r19286138 = r19286134 - r19286137;
        double r19286139 = a;
        double r19286140 = 0.5;
        double r19286141 = r19286139 - r19286140;
        double r19286142 = b;
        double r19286143 = r19286141 * r19286142;
        double r19286144 = r19286138 + r19286143;
        return r19286144;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r19286145 = a;
        double r19286146 = 0.5;
        double r19286147 = r19286145 - r19286146;
        double r19286148 = b;
        double r19286149 = r19286147 * r19286148;
        double r19286150 = z;
        double r19286151 = x;
        double r19286152 = y;
        double r19286153 = r19286151 + r19286152;
        double r19286154 = r19286150 + r19286153;
        double r19286155 = t;
        double r19286156 = cbrt(r19286155);
        double r19286157 = log(r19286156);
        double r19286158 = r19286150 + r19286150;
        double r19286159 = r19286157 * r19286158;
        double r19286160 = r19286154 - r19286159;
        double r19286161 = cbrt(r19286156);
        double r19286162 = log(r19286161);
        double r19286163 = r19286162 * r19286150;
        double r19286164 = r19286161 * r19286161;
        double r19286165 = log(r19286164);
        double r19286166 = r19286150 * r19286165;
        double r19286167 = r19286163 + r19286166;
        double r19286168 = r19286160 - r19286167;
        double r19286169 = r19286149 + r19286168;
        return r19286169;
}

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. Applied associate--r+ 0.1

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

7. Simplified 0.1

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

9. Applied add-cube-cbrt 0.1

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

10. Applied log-prod 0.1

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

11. Applied distribute-lft-in 0.1

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

12. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019162 
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"

  :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)))