Average Error: 0.1 → 0.1
Time: 28.3s
Precision: 64
\[\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b\]
↓
\[\left(z + \left(y + x\right)\right) + \left(\left(b \cdot a + \left(-0.5\right) \cdot b\right) - z \cdot \log t\right)\]
\left(\left(\left(x + y\right) + z\right) - z \cdot \log t\right) + \left(a - 0.5\right) \cdot b
↓
\left(z + \left(y + x\right)\right) + \left(\left(b \cdot a + \left(-0.5\right) \cdot b\right) - z \cdot \log t\right)
double f(double x, double y, double z, double t, double a, double b) {
        double r19041462 = x;
        double r19041463 = y;
        double r19041464 = r19041462 + r19041463;
        double r19041465 = z;
        double r19041466 = r19041464 + r19041465;
        double r19041467 = t;
        double r19041468 = log(r19041467);
        double r19041469 = r19041465 * r19041468;
        double r19041470 = r19041466 - r19041469;
        double r19041471 = a;
        double r19041472 = 0.5;
        double r19041473 = r19041471 - r19041472;
        double r19041474 = b;
        double r19041475 = r19041473 * r19041474;
        double r19041476 = r19041470 + r19041475;
        return r19041476;
}
↓
double f(double x, double y, double z, double t, double a, double b) {
        double r19041477 = z;
        double r19041478 = y;
        double r19041479 = x;
        double r19041480 = r19041478 + r19041479;
        double r19041481 = r19041477 + r19041480;
        double r19041482 = b;
        double r19041483 = a;
        double r19041484 = r19041482 * r19041483;
        double r19041485 = 0.5;
        double r19041486 = -r19041485;
        double r19041487 = r19041486 * r19041482;
        double r19041488 = r19041484 + r19041487;
        double r19041489 = t;
        double r19041490 = log(r19041489);
        double r19041491 = r19041477 * r19041490;
        double r19041492 = r19041488 - r19041491;
        double r19041493 = r19041481 + r19041492;
        return r19041493;
}

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 sub-neg0.1

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

  4. Applied associate-+l+0.1

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

  5. Simplified0.1

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

  7. Applied sub-neg0.1

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

  8. Applied distribute-lft-in0.1

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

  9. Final simplification0.1

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

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)))