Average Error: 0.1 → 0.1
Time: 28.0s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(x + y\right) + z \cdot \left(1 - \log \left(\sqrt{t}\right) \cdot 2\right)\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(x + y\right) + z \cdot \left(1 - \log \left(\sqrt{t}\right) \cdot 2\right)\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r260162 = x;
        double r260163 = y;
        double r260164 = r260162 + r260163;
        double r260165 = z;
        double r260166 = r260164 + r260165;
        double r260167 = t;
        double r260168 = log(r260167);
        double r260169 = r260165 * r260168;
        double r260170 = r260166 - r260169;
        double r260171 = a;
        double r260172 = 0.5;
        double r260173 = r260171 - r260172;
        double r260174 = b;
        double r260175 = r260173 * r260174;
        double r260176 = r260170 + r260175;
        return r260176;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r260177 = x;
        double r260178 = y;
        double r260179 = r260177 + r260178;
        double r260180 = z;
        double r260181 = 1.0;
        double r260182 = t;
        double r260183 = sqrt(r260182);
        double r260184 = log(r260183);
        double r260185 = 2.0;
        double r260186 = r260184 * r260185;
        double r260187 = r260181 - r260186;
        double r260188 = r260180 * r260187;
        double r260189 = r260179 + r260188;
        double r260190 = a;
        double r260191 = 0.5;
        double r260192 = r260190 - r260191;
        double r260193 = b;
        double r260194 = r260192 * r260193;
        double r260195 = r260189 + r260194;
        return r260195;
}

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. Using strategy rm

  5. Applied add-sqr-sqrt0.1

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

  6. Applied log-prod0.1

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

  7. Applied distribute-lft-in0.1

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

  8. Applied associate--r+0.1

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

  9. Simplified0.1

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

  11. Applied *-un-lft-identity0.1

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

  12. Applied distribute-rgt-out--0.1

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

  13. Applied distribute-lft-out--0.1

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

  14. Simplified0.1

    \[\leadsto \left(\left(x + y\right) + z \cdot \color{blue}{\left(1 - \log \left(\sqrt{t}\right) \cdot 2\right)}\right) + \left(a - 0.5\right) \cdot b\]

  15. Final simplification0.1

    \[\leadsto \left(\left(x + y\right) + z \cdot \left(1 - \log \left(\sqrt{t}\right) \cdot 2\right)\right) + \left(a - 0.5\right) \cdot b\]

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)))