Average Error: 28.4 → 28.4
Time: 29.0s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(230661.510616 + \left(27464.7644705 + \left(y \cdot \left(x \cdot y\right) + z \cdot y\right)\right) \cdot y\right) \cdot y + t}{i + y \cdot \left(\left(\left(a + y\right) \cdot y + b\right) \cdot y + c\right)}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{\left(230661.510616 + \left(27464.7644705 + \left(y \cdot \left(x \cdot y\right) + z \cdot y\right)\right) \cdot y\right) \cdot y + t}{i + y \cdot \left(\left(\left(a + y\right) \cdot y + b\right) \cdot y + c\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3314451 = x;
        double r3314452 = y;
        double r3314453 = r3314451 * r3314452;
        double r3314454 = z;
        double r3314455 = r3314453 + r3314454;
        double r3314456 = r3314455 * r3314452;
        double r3314457 = 27464.7644705;
        double r3314458 = r3314456 + r3314457;
        double r3314459 = r3314458 * r3314452;
        double r3314460 = 230661.510616;
        double r3314461 = r3314459 + r3314460;
        double r3314462 = r3314461 * r3314452;
        double r3314463 = t;
        double r3314464 = r3314462 + r3314463;
        double r3314465 = a;
        double r3314466 = r3314452 + r3314465;
        double r3314467 = r3314466 * r3314452;
        double r3314468 = b;
        double r3314469 = r3314467 + r3314468;
        double r3314470 = r3314469 * r3314452;
        double r3314471 = c;
        double r3314472 = r3314470 + r3314471;
        double r3314473 = r3314472 * r3314452;
        double r3314474 = i;
        double r3314475 = r3314473 + r3314474;
        double r3314476 = r3314464 / r3314475;
        return r3314476;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3314477 = 230661.510616;
        double r3314478 = 27464.7644705;
        double r3314479 = y;
        double r3314480 = x;
        double r3314481 = r3314480 * r3314479;
        double r3314482 = r3314479 * r3314481;
        double r3314483 = z;
        double r3314484 = r3314483 * r3314479;
        double r3314485 = r3314482 + r3314484;
        double r3314486 = r3314478 + r3314485;
        double r3314487 = r3314486 * r3314479;
        double r3314488 = r3314477 + r3314487;
        double r3314489 = r3314488 * r3314479;
        double r3314490 = t;
        double r3314491 = r3314489 + r3314490;
        double r3314492 = i;
        double r3314493 = a;
        double r3314494 = r3314493 + r3314479;
        double r3314495 = r3314494 * r3314479;
        double r3314496 = b;
        double r3314497 = r3314495 + r3314496;
        double r3314498 = r3314497 * r3314479;
        double r3314499 = c;
        double r3314500 = r3314498 + r3314499;
        double r3314501 = r3314479 * r3314500;
        double r3314502 = r3314492 + r3314501;
        double r3314503 = r3314491 / r3314502;
        return r3314503;
}

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 28.4

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  2. Taylor expanded around 0 28.4

    \[\leadsto \frac{\left(\left(\color{blue}{\left(x \cdot {y}^{2} + z \cdot y\right)} + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  3. Simplified28.4

    \[\leadsto \frac{\left(\left(\color{blue}{\left(z \cdot y + y \cdot \left(y \cdot x\right)\right)} + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  4. Final simplification28.4

    \[\leadsto \frac{\left(230661.510616 + \left(27464.7644705 + \left(y \cdot \left(x \cdot y\right) + z \cdot y\right)\right) \cdot y\right) \cdot y + t}{i + y \cdot \left(\left(\left(a + y\right) \cdot y + b\right) \cdot y + c\right)}\]

Reproduce

herbie shell --seed 2019165 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))