Average Error: 0.1 → 0.1
Time: 8.5s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(x + y\right) + \left(\left(z - \left(z \cdot \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right)\right) + \left(a - 0.5\right) \cdot b\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(x + y\right) + \left(\left(z - \left(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\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r361174 = x;
        double r361175 = y;
        double r361176 = r361174 + r361175;
        double r361177 = z;
        double r361178 = r361176 + r361177;
        double r361179 = t;
        double r361180 = log(r361179);
        double r361181 = r361177 * r361180;
        double r361182 = r361178 - r361181;
        double r361183 = a;
        double r361184 = 0.5;
        double r361185 = r361183 - r361184;
        double r361186 = b;
        double r361187 = r361185 * r361186;
        double r361188 = r361182 + r361187;
        return r361188;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r361189 = x;
        double r361190 = y;
        double r361191 = r361189 + r361190;
        double r361192 = z;
        double r361193 = 2.0;
        double r361194 = t;
        double r361195 = cbrt(r361194);
        double r361196 = log(r361195);
        double r361197 = r361193 * r361196;
        double r361198 = r361192 * r361197;
        double r361199 = r361192 * r361196;
        double r361200 = r361198 + r361199;
        double r361201 = r361192 - r361200;
        double r361202 = a;
        double r361203 = 0.5;
        double r361204 = r361202 - r361203;
        double r361205 = b;
        double r361206 = r361204 * r361205;
        double r361207 = r361201 + r361206;
        double r361208 = r361191 + r361207;
        return r361208;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.1
Target0.5
Herbie0.1
\[\left(\left(x + y\right) + \frac{\left(1 - {\left(\log t\right)}^{2}\right) \cdot z}{1 + \log t}\right) + \left(a - 0.5\right) \cdot b\]

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 associate--l+0.1

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

  4. Applied associate-+l+0.1

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

  6. Applied add-cube-cbrt0.1

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

  7. Applied log-prod0.1

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

  8. Applied distribute-lft-in0.1

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

  9. Simplified0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019322 
(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)))