Average Error: 28.6 → 28.6
Time: 26.3s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + y \cdot \left(\left(\left(z + y \cdot x\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right)}{i + \left(y \cdot \left(y \cdot \left(y \cdot \left(a + y\right) + b\right)\right) + y \cdot c\right)}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{t + y \cdot \left(\left(\left(z + y \cdot x\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right)}{i + \left(y \cdot \left(y \cdot \left(y \cdot \left(a + y\right) + b\right)\right) + y \cdot c\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r61547 = x;
        double r61548 = y;
        double r61549 = r61547 * r61548;
        double r61550 = z;
        double r61551 = r61549 + r61550;
        double r61552 = r61551 * r61548;
        double r61553 = 27464.7644705;
        double r61554 = r61552 + r61553;
        double r61555 = r61554 * r61548;
        double r61556 = 230661.510616;
        double r61557 = r61555 + r61556;
        double r61558 = r61557 * r61548;
        double r61559 = t;
        double r61560 = r61558 + r61559;
        double r61561 = a;
        double r61562 = r61548 + r61561;
        double r61563 = r61562 * r61548;
        double r61564 = b;
        double r61565 = r61563 + r61564;
        double r61566 = r61565 * r61548;
        double r61567 = c;
        double r61568 = r61566 + r61567;
        double r61569 = r61568 * r61548;
        double r61570 = i;
        double r61571 = r61569 + r61570;
        double r61572 = r61560 / r61571;
        return r61572;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r61573 = t;
        double r61574 = y;
        double r61575 = z;
        double r61576 = x;
        double r61577 = r61574 * r61576;
        double r61578 = r61575 + r61577;
        double r61579 = r61578 * r61574;
        double r61580 = 27464.7644705;
        double r61581 = r61579 + r61580;
        double r61582 = r61581 * r61574;
        double r61583 = 230661.510616;
        double r61584 = r61582 + r61583;
        double r61585 = r61574 * r61584;
        double r61586 = r61573 + r61585;
        double r61587 = i;
        double r61588 = a;
        double r61589 = r61588 + r61574;
        double r61590 = r61574 * r61589;
        double r61591 = b;
        double r61592 = r61590 + r61591;
        double r61593 = r61574 * r61592;
        double r61594 = r61574 * r61593;
        double r61595 = c;
        double r61596 = r61574 * r61595;
        double r61597 = r61594 + r61596;
        double r61598 = r61587 + r61597;
        double r61599 = r61586 / r61598;
        return r61599;
}

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 28.6

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  2. Simplified28.6

    \[\leadsto \color{blue}{\frac{y \cdot \left(\left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) + t}{i + y \cdot \left(y \cdot \left(\left(y + a\right) \cdot y + b\right) + c\right)}}\]
  3. Using strategy rm

  4. Applied distribute-rgt-in28.6

    \[\leadsto \frac{y \cdot \left(\left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) + t}{i + \color{blue}{\left(\left(y \cdot \left(\left(y + a\right) \cdot y + b\right)\right) \cdot y + c \cdot y\right)}}\]

  5. Simplified28.6

    \[\leadsto \frac{y \cdot \left(\left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) + t}{i + \left(\color{blue}{y \cdot \left(y \cdot \left(b + y \cdot \left(a + y\right)\right)\right)} + c \cdot y\right)}\]

  6. Simplified28.6

    \[\leadsto \frac{y \cdot \left(\left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) + t}{i + \left(y \cdot \left(y \cdot \left(b + y \cdot \left(a + y\right)\right)\right) + \color{blue}{y \cdot c}\right)}\]

  7. Final simplification28.6

    \[\leadsto \frac{t + y \cdot \left(\left(\left(z + y \cdot x\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right)}{i + \left(y \cdot \left(y \cdot \left(y \cdot \left(a + y\right) + b\right)\right) + y \cdot c\right)}\]

Reproduce

herbie shell --seed 2019195 
(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)))