Average Error: 29.3 → 29.4
Time: 7.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r84530 = x;
        double r84531 = y;
        double r84532 = r84530 * r84531;
        double r84533 = z;
        double r84534 = r84532 + r84533;
        double r84535 = r84534 * r84531;
        double r84536 = 27464.7644705;
        double r84537 = r84535 + r84536;
        double r84538 = r84537 * r84531;
        double r84539 = 230661.510616;
        double r84540 = r84538 + r84539;
        double r84541 = r84540 * r84531;
        double r84542 = t;
        double r84543 = r84541 + r84542;
        double r84544 = a;
        double r84545 = r84531 + r84544;
        double r84546 = r84545 * r84531;
        double r84547 = b;
        double r84548 = r84546 + r84547;
        double r84549 = r84548 * r84531;
        double r84550 = c;
        double r84551 = r84549 + r84550;
        double r84552 = r84551 * r84531;
        double r84553 = i;
        double r84554 = r84552 + r84553;
        double r84555 = r84543 / r84554;
        return r84555;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r84556 = x;
        double r84557 = y;
        double r84558 = r84556 * r84557;
        double r84559 = z;
        double r84560 = r84558 + r84559;
        double r84561 = r84560 * r84557;
        double r84562 = 27464.7644705;
        double r84563 = r84561 + r84562;
        double r84564 = r84563 * r84557;
        double r84565 = 230661.510616;
        double r84566 = r84564 + r84565;
        double r84567 = r84566 * r84557;
        double r84568 = t;
        double r84569 = r84567 + r84568;
        double r84570 = 1.0;
        double r84571 = a;
        double r84572 = r84557 + r84571;
        double r84573 = r84572 * r84557;
        double r84574 = b;
        double r84575 = r84573 + r84574;
        double r84576 = r84575 * r84557;
        double r84577 = c;
        double r84578 = r84576 + r84577;
        double r84579 = r84578 * r84557;
        double r84580 = i;
        double r84581 = r84579 + r84580;
        double r84582 = r84570 / r84581;
        double r84583 = r84569 * r84582;
        return r84583;
}

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

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.3

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied div-inv29.4

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  4. Final simplification29.4

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2020024 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))