Average Error: 28.8 → 28.8
Time: 9.6s
Precision: binary64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(\left(y \cdot \left(y \cdot \left(y + a\right)\right) + y \cdot b\right) + c\right) + i}\]
\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{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(\left(y \cdot \left(y \cdot \left(y + a\right)\right) + y \cdot b\right) + c\right) + i}
(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t)
  (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))
↓
(FPCore (x y z t a b c i)
 :precision binary64
 (/
  (+ (* y (+ (* y (+ (* y (+ (* x y) z)) 27464.7644705)) 230661.510616)) t)
  (+ (* y (+ (+ (* y (* y (+ y a))) (* y b)) c)) i)))
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i);
}
↓
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return ((y * ((y * ((y * ((x * y) + z)) + 27464.7644705)) + 230661.510616)) + t) / ((y * (((y * (y * (y + a))) + (y * b)) + c)) + i);
}

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 28.8

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

  3. Applied div-inv_binary6428.9

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  4. Simplified28.9

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t\right) \cdot \color{blue}{\frac{1}{y \cdot \left(y \cdot \left(y \cdot \left(y + a\right) + b\right) + c\right) + i}}\]
  5. Using strategy rm

  6. Applied distribute-rgt-in_binary6428.9

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t\right) \cdot \frac{1}{y \cdot \left(\color{blue}{\left(\left(y \cdot \left(y + a\right)\right) \cdot y + b \cdot y\right)} + c\right) + i}\]

  7. Simplified28.9

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t\right) \cdot \frac{1}{y \cdot \left(\left(\color{blue}{y \cdot \left(y \cdot \left(y + a\right)\right)} + b \cdot y\right) + c\right) + i}\]

  8. Simplified28.9

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t\right) \cdot \frac{1}{y \cdot \left(\left(y \cdot \left(y \cdot \left(y + a\right)\right) + \color{blue}{y \cdot b}\right) + c\right) + i}\]
  9. Using strategy rm

  10. Applied un-div-inv_binary6428.8

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

  11. Final simplification28.8

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

Reproduce

herbie shell --seed 2020253 
(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)))