Average Error: 0.1 → 0.1
Time: 8.1s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(x + y\right) + \left(\frac{1 - {\left(\log t\right)}^{3}}{\log t \cdot \left(\log t + 1\right) + 1} \cdot z + \left(a - 0.5\right) \cdot b\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(x + y\right) + \left(\frac{1 - {\left(\log t\right)}^{3}}{\log t \cdot \left(\log t + 1\right) + 1} \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 r441600 = x;
        double r441601 = y;
        double r441602 = r441600 + r441601;
        double r441603 = z;
        double r441604 = r441602 + r441603;
        double r441605 = t;
        double r441606 = log(r441605);
        double r441607 = r441603 * r441606;
        double r441608 = r441604 - r441607;
        double r441609 = a;
        double r441610 = 0.5;
        double r441611 = r441609 - r441610;
        double r441612 = b;
        double r441613 = r441611 * r441612;
        double r441614 = r441608 + r441613;
        return r441614;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r441615 = x;
        double r441616 = y;
        double r441617 = r441615 + r441616;
        double r441618 = 1.0;
        double r441619 = t;
        double r441620 = log(r441619);
        double r441621 = 3.0;
        double r441622 = pow(r441620, r441621);
        double r441623 = r441618 - r441622;
        double r441624 = r441620 + r441618;
        double r441625 = r441620 * r441624;
        double r441626 = r441625 + r441618;
        double r441627 = r441623 / r441626;
        double r441628 = z;
        double r441629 = r441627 * r441628;
        double r441630 = a;
        double r441631 = 0.5;
        double r441632 = r441630 - r441631;
        double r441633 = b;
        double r441634 = r441632 * r441633;
        double r441635 = r441629 + r441634;
        double r441636 = r441617 + r441635;
        return r441636;
}

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. Taylor expanded around 0 0.1

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

  6. Simplified0.1

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

  8. Applied flip3--0.1

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

  9. Simplified0.1

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

  10. Simplified0.1

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

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019353 
(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)))