Average Error: 0.1 → 0.1
Time: 27.7s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(\left(\left(y + z\right) + x\right) - \left(\log \left(\sqrt[3]{t}\right) \cdot z + \log \left(\sqrt[3]{t}\right) \cdot z\right)\right) - \log \left(\sqrt[3]{t}\right) \cdot z\right) + b \cdot \left(a - 0.5\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(\left(\left(y + z\right) + x\right) - \left(\log \left(\sqrt[3]{t}\right) \cdot z + \log \left(\sqrt[3]{t}\right) \cdot z\right)\right) - \log \left(\sqrt[3]{t}\right) \cdot z\right) + b \cdot \left(a - 0.5\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r17502979 = x;
        double r17502980 = y;
        double r17502981 = r17502979 + r17502980;
        double r17502982 = z;
        double r17502983 = r17502981 + r17502982;
        double r17502984 = t;
        double r17502985 = log(r17502984);
        double r17502986 = r17502982 * r17502985;
        double r17502987 = r17502983 - r17502986;
        double r17502988 = a;
        double r17502989 = 0.5;
        double r17502990 = r17502988 - r17502989;
        double r17502991 = b;
        double r17502992 = r17502990 * r17502991;
        double r17502993 = r17502987 + r17502992;
        return r17502993;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r17502994 = y;
        double r17502995 = z;
        double r17502996 = r17502994 + r17502995;
        double r17502997 = x;
        double r17502998 = r17502996 + r17502997;
        double r17502999 = t;
        double r17503000 = cbrt(r17502999);
        double r17503001 = log(r17503000);
        double r17503002 = r17503001 * r17502995;
        double r17503003 = r17503002 + r17503002;
        double r17503004 = r17502998 - r17503003;
        double r17503005 = r17503004 - r17503002;
        double r17503006 = b;
        double r17503007 = a;
        double r17503008 = 0.5;
        double r17503009 = r17503007 - r17503008;
        double r17503010 = r17503006 * r17503009;
        double r17503011 = r17503005 + r17503010;
        return r17503011;
}

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

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (x y z t a b)
  :name "Numeric.SpecFunctions:logBeta from math-functions-0.1.5.2, A"

  :herbie-target
  (+ (+ (+ x y) (/ (* (- 1.0 (pow (log t) 2.0)) z) (+ 1.0 (log t)))) (* (- a 0.5) b))

  (+ (- (+ (+ x y) z) (* z (log t))) (* (- a 0.5) b)))