Average Error: 0.1 → 0.1
Time: 16.7s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(x + y\right) + z\right) + \left(\left(a - 0.5\right) \cdot b - \left(3 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)\]
\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\right) + \left(\left(a - 0.5\right) \cdot b - \left(3 \cdot \log \left(\sqrt[3]{t}\right)\right) \cdot z\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r297618 = x;
        double r297619 = y;
        double r297620 = r297618 + r297619;
        double r297621 = z;
        double r297622 = r297620 + r297621;
        double r297623 = t;
        double r297624 = log(r297623);
        double r297625 = r297621 * r297624;
        double r297626 = r297622 - r297625;
        double r297627 = a;
        double r297628 = 0.5;
        double r297629 = r297627 - r297628;
        double r297630 = b;
        double r297631 = r297629 * r297630;
        double r297632 = r297626 + r297631;
        return r297632;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r297633 = x;
        double r297634 = y;
        double r297635 = r297633 + r297634;
        double r297636 = z;
        double r297637 = r297635 + r297636;
        double r297638 = a;
        double r297639 = 0.5;
        double r297640 = r297638 - r297639;
        double r297641 = b;
        double r297642 = r297640 * r297641;
        double r297643 = 3.0;
        double r297644 = t;
        double r297645 = cbrt(r297644);
        double r297646 = log(r297645);
        double r297647 = r297643 * r297646;
        double r297648 = r297647 * r297636;
        double r297649 = r297642 - r297648;
        double r297650 = r297637 + r297649;
        return r297650;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019298 
(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)))