Average Error: 0.1 → 0.1
Time: 28.8s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(z + \left(x + y\right)\right) - \left(z \cdot \log \left(\sqrt[3]{t}\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right)\right) - z \cdot \log \left(\sqrt[3]{t}\right)\right) + b \cdot \left(a - 0.5\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(z + \left(x + y\right)\right) - \left(z \cdot \log \left(\sqrt[3]{t}\right) + z \cdot \log \left(\sqrt[3]{t}\right)\right)\right) - z \cdot \log \left(\sqrt[3]{t}\right)\right) + b \cdot \left(a - 0.5\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r20675619 = x;
        double r20675620 = y;
        double r20675621 = r20675619 + r20675620;
        double r20675622 = z;
        double r20675623 = r20675621 + r20675622;
        double r20675624 = t;
        double r20675625 = log(r20675624);
        double r20675626 = r20675622 * r20675625;
        double r20675627 = r20675623 - r20675626;
        double r20675628 = a;
        double r20675629 = 0.5;
        double r20675630 = r20675628 - r20675629;
        double r20675631 = b;
        double r20675632 = r20675630 * r20675631;
        double r20675633 = r20675627 + r20675632;
        return r20675633;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r20675634 = z;
        double r20675635 = x;
        double r20675636 = y;
        double r20675637 = r20675635 + r20675636;
        double r20675638 = r20675634 + r20675637;
        double r20675639 = t;
        double r20675640 = cbrt(r20675639);
        double r20675641 = log(r20675640);
        double r20675642 = r20675634 * r20675641;
        double r20675643 = r20675642 + r20675642;
        double r20675644 = r20675638 - r20675643;
        double r20675645 = r20675644 - r20675642;
        double r20675646 = b;
        double r20675647 = a;
        double r20675648 = 0.5;
        double r20675649 = r20675647 - r20675648;
        double r20675650 = r20675646 * r20675649;
        double r20675651 = r20675645 + r20675650;
        return r20675651;
}

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-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

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

  8. Final simplification0.1

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

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)))