Average Error: 29.1 → 29.2
Time: 8.5s
Precision: binary64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(\sqrt[3]{y} \cdot \left(\left(y \cdot \left(y + a\right) + b\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) + c\right) + i}\]
\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(\sqrt[3]{y} \cdot \left(\left(y \cdot \left(y + a\right) + b\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\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 (+ (* (cbrt y) (* (+ (* y (+ y a)) b) (* (cbrt y) (cbrt y)))) c))
   i)))
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((double) (((double) (((double) (((double) (((double) (((double) (((double) (((double) (x * y)) + z)) * y)) + 27464.7644705)) * y)) + 230661.510616)) * y)) + t)) / ((double) (((double) (((double) (((double) (((double) (((double) (((double) (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 (((double) (((double) (y * ((double) (((double) (y * ((double) (((double) (y * ((double) (((double) (x * y)) + z)))) + 27464.7644705)))) + 230661.510616)))) + t)) / ((double) (((double) (y * ((double) (((double) (((double) cbrt(y)) * ((double) (((double) (((double) (y * ((double) (y + a)))) + b)) * ((double) (((double) cbrt(y)) * ((double) cbrt(y)))))))) + 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 29.1

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

  3. Applied add-cube-cbrt29.2

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot \color{blue}{\left(\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}\right)} + c\right) \cdot y + i}\]

  4. Applied associate-*r*29.2

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}} + c\right) \cdot y + i}\]

  5. Simplified29.2

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\color{blue}{\left(\left(y \cdot \left(y + a\right) + b\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right)} \cdot \sqrt[3]{y} + c\right) \cdot y + i}\]

  6. Final simplification29.2

    \[\leadsto \frac{y \cdot \left(y \cdot \left(y \cdot \left(x \cdot y + z\right) + 27464.7644705\right) + 230661.510616\right) + t}{y \cdot \left(\sqrt[3]{y} \cdot \left(\left(y \cdot \left(y + a\right) + b\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) + c\right) + i}\]

Reproduce

herbie shell --seed 2020198 
(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)))