Average Error: 0.1 → 0.1
Time: 20.7s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(z + \left(\left(x + y\right) - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\right) - z \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot b\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(z + \left(\left(x + y\right) - \left(2 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\right) - z \cdot \log \left(\sqrt[3]{t}\right)\right) + \left(a - 0.5\right) \cdot b
double f(double x, double y, double z, double t, double a, double b) {
        double r445616 = x;
        double r445617 = y;
        double r445618 = r445616 + r445617;
        double r445619 = z;
        double r445620 = r445618 + r445619;
        double r445621 = t;
        double r445622 = log(r445621);
        double r445623 = r445619 * r445622;
        double r445624 = r445620 - r445623;
        double r445625 = a;
        double r445626 = 0.5;
        double r445627 = r445625 - r445626;
        double r445628 = b;
        double r445629 = r445627 * r445628;
        double r445630 = r445624 + r445629;
        return r445630;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r445631 = z;
        double r445632 = x;
        double r445633 = y;
        double r445634 = r445632 + r445633;
        double r445635 = 2.0;
        double r445636 = t;
        double r445637 = cbrt(r445636);
        double r445638 = log(r445637);
        double r445639 = r445635 * r445638;
        double r445640 = r445639 * r445631;
        double r445641 = r445634 - r445640;
        double r445642 = r445631 + r445641;
        double r445643 = r445631 * r445638;
        double r445644 = r445642 - r445643;
        double r445645 = a;
        double r445646 = 0.5;
        double r445647 = r445645 - r445646;
        double r445648 = b;
        double r445649 = r445647 * r445648;
        double r445650 = r445644 + r445649;
        return r445650;
}

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 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-lft-in0.1

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

  6. Applied associate--r+0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 
(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)))