Average Error: 0.1 → 0.1
Time: 29.0s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(z + \left(y + x\right)\right) - \log \left({t}^{\frac{2}{3}}\right) \cdot z\right) - \left(\log \left(\sqrt[3]{t}\right) \cdot z - \left(a - 0.5\right) \cdot b\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(z + \left(y + x\right)\right) - \log \left({t}^{\frac{2}{3}}\right) \cdot z\right) - \left(\log \left(\sqrt[3]{t}\right) \cdot z - \left(a - 0.5\right) \cdot b\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r33440157 = x;
        double r33440158 = y;
        double r33440159 = r33440157 + r33440158;
        double r33440160 = z;
        double r33440161 = r33440159 + r33440160;
        double r33440162 = t;
        double r33440163 = log(r33440162);
        double r33440164 = r33440160 * r33440163;
        double r33440165 = r33440161 - r33440164;
        double r33440166 = a;
        double r33440167 = 0.5;
        double r33440168 = r33440166 - r33440167;
        double r33440169 = b;
        double r33440170 = r33440168 * r33440169;
        double r33440171 = r33440165 + r33440170;
        return r33440171;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r33440172 = z;
        double r33440173 = y;
        double r33440174 = x;
        double r33440175 = r33440173 + r33440174;
        double r33440176 = r33440172 + r33440175;
        double r33440177 = t;
        double r33440178 = 0.6666666666666666;
        double r33440179 = pow(r33440177, r33440178);
        double r33440180 = log(r33440179);
        double r33440181 = r33440180 * r33440172;
        double r33440182 = r33440176 - r33440181;
        double r33440183 = cbrt(r33440177);
        double r33440184 = log(r33440183);
        double r33440185 = r33440184 * r33440172;
        double r33440186 = a;
        double r33440187 = 0.5;
        double r33440188 = r33440186 - r33440187;
        double r33440189 = b;
        double r33440190 = r33440188 * r33440189;
        double r33440191 = r33440185 - r33440190;
        double r33440192 = r33440182 - r33440191;
        return r33440192;
}

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
Target0.3
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 add-cube-cbrt0.1

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

  4. Applied log-prod0.1

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

  5. Applied distribute-rgt-in0.1

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

  6. Applied associate--r+0.1

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

  7. Applied associate-+l-0.1

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

  9. Applied pow1/30.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - \log \left(\sqrt[3]{t} \cdot \color{blue}{{t}^{\frac{1}{3}}}\right) \cdot z\right) - \left(\log \left(\sqrt[3]{t}\right) \cdot z - \left(a - 0.5\right) \cdot b\right)\]

  10. Applied pow1/30.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - \log \left(\color{blue}{{t}^{\frac{1}{3}}} \cdot {t}^{\frac{1}{3}}\right) \cdot z\right) - \left(\log \left(\sqrt[3]{t}\right) \cdot z - \left(a - 0.5\right) \cdot b\right)\]

  11. Applied pow-prod-up0.1

    \[\leadsto \left(\left(\left(x + y\right) + z\right) - \log \color{blue}{\left({t}^{\left(\frac{1}{3} + \frac{1}{3}\right)}\right)} \cdot z\right) - \left(\log \left(\sqrt[3]{t}\right) \cdot z - \left(a - 0.5\right) \cdot b\right)\]

  12. Simplified0.1

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

  13. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 
(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)))