Average Error: 0.1 → 0.1
Time: 19.5s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[b \cdot \left(a - 0.5\right) + \left(\left(\left(z - z \cdot \log \left(\sqrt{t}\right)\right) - z \cdot \log \left(\sqrt{t}\right)\right) + \left(y + x\right)\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
b \cdot \left(a - 0.5\right) + \left(\left(\left(z - z \cdot \log \left(\sqrt{t}\right)\right) - z \cdot \log \left(\sqrt{t}\right)\right) + \left(y + x\right)\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r19437420 = x;
        double r19437421 = y;
        double r19437422 = r19437420 + r19437421;
        double r19437423 = z;
        double r19437424 = r19437422 + r19437423;
        double r19437425 = t;
        double r19437426 = log(r19437425);
        double r19437427 = r19437423 * r19437426;
        double r19437428 = r19437424 - r19437427;
        double r19437429 = a;
        double r19437430 = 0.5;
        double r19437431 = r19437429 - r19437430;
        double r19437432 = b;
        double r19437433 = r19437431 * r19437432;
        double r19437434 = r19437428 + r19437433;
        return r19437434;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r19437435 = b;
        double r19437436 = a;
        double r19437437 = 0.5;
        double r19437438 = r19437436 - r19437437;
        double r19437439 = r19437435 * r19437438;
        double r19437440 = z;
        double r19437441 = t;
        double r19437442 = sqrt(r19437441);
        double r19437443 = log(r19437442);
        double r19437444 = r19437440 * r19437443;
        double r19437445 = r19437440 - r19437444;
        double r19437446 = r19437445 - r19437444;
        double r19437447 = y;
        double r19437448 = x;
        double r19437449 = r19437447 + r19437448;
        double r19437450 = r19437446 + r19437449;
        double r19437451 = r19437439 + r19437450;
        return r19437451;
}

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 associate--l+0.1

    \[\leadsto \color{blue}{\left(\left(x + y\right) + \left(z - z \cdot \log t\right)\right)} + \left(a - 0.5\right) \cdot b\]
  4. Using strategy rm

  5. Applied add-sqr-sqrt0.1

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

  6. Applied log-prod0.1

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

  7. Applied distribute-rgt-in0.1

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

  8. Applied associate--r+0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019192 
(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)))