Average Error: 0.1 → 0.1
Time: 25.2s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(\left(x + \left(\left(y + z\right) - \left(\log \left(\sqrt[3]{t}\right) \cdot z + \log \left(\sqrt[3]{t}\right) \cdot z\right)\right)\right) - \log \left(\sqrt[3]{t}\right) \cdot z\right) + b \cdot \left(a - 0.5\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(\left(x + \left(\left(y + z\right) - \left(\log \left(\sqrt[3]{t}\right) \cdot z + \log \left(\sqrt[3]{t}\right) \cdot z\right)\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 r30065410 = x;
        double r30065411 = y;
        double r30065412 = r30065410 + r30065411;
        double r30065413 = z;
        double r30065414 = r30065412 + r30065413;
        double r30065415 = t;
        double r30065416 = log(r30065415);
        double r30065417 = r30065413 * r30065416;
        double r30065418 = r30065414 - r30065417;
        double r30065419 = a;
        double r30065420 = 0.5;
        double r30065421 = r30065419 - r30065420;
        double r30065422 = b;
        double r30065423 = r30065421 * r30065422;
        double r30065424 = r30065418 + r30065423;
        return r30065424;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r30065425 = x;
        double r30065426 = y;
        double r30065427 = z;
        double r30065428 = r30065426 + r30065427;
        double r30065429 = t;
        double r30065430 = cbrt(r30065429);
        double r30065431 = log(r30065430);
        double r30065432 = r30065431 * r30065427;
        double r30065433 = r30065432 + r30065432;
        double r30065434 = r30065428 - r30065433;
        double r30065435 = r30065425 + r30065434;
        double r30065436 = r30065435 - r30065432;
        double r30065437 = b;
        double r30065438 = a;
        double r30065439 = 0.5;
        double r30065440 = r30065438 - r30065439;
        double r30065441 = r30065437 * r30065440;
        double r30065442 = r30065436 + r30065441;
        return r30065442;
}

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

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019171 
(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)))