Average Error: 0.1 → 0.1
Time: 7.2s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(x + y\right) + \left(\left(\left(z - \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot z\right) - \log \left(\sqrt[3]{t}\right) \cdot z\right) + \left(a - 0.5\right) \cdot b\right)\]
\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(\left(z - \log \left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot z\right) - \log \left(\sqrt[3]{t}\right) \cdot z\right) + \left(a - 0.5\right) \cdot b\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r396225 = x;
        double r396226 = y;
        double r396227 = r396225 + r396226;
        double r396228 = z;
        double r396229 = r396227 + r396228;
        double r396230 = t;
        double r396231 = log(r396230);
        double r396232 = r396228 * r396231;
        double r396233 = r396229 - r396232;
        double r396234 = a;
        double r396235 = 0.5;
        double r396236 = r396234 - r396235;
        double r396237 = b;
        double r396238 = r396236 * r396237;
        double r396239 = r396233 + r396238;
        return r396239;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r396240 = x;
        double r396241 = y;
        double r396242 = r396240 + r396241;
        double r396243 = z;
        double r396244 = t;
        double r396245 = cbrt(r396244);
        double r396246 = r396245 * r396245;
        double r396247 = log(r396246);
        double r396248 = r396247 * r396243;
        double r396249 = r396243 - r396248;
        double r396250 = log(r396245);
        double r396251 = r396250 * r396243;
        double r396252 = r396249 - r396251;
        double r396253 = a;
        double r396254 = 0.5;
        double r396255 = r396253 - r396254;
        double r396256 = b;
        double r396257 = r396255 * r396256;
        double r396258 = r396252 + r396257;
        double r396259 = r396242 + r396258;
        return r396259;
}

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
Target0.4
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-rgt-in0.1

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

  9. Applied associate--r+0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2020018 
(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)))