From Warwick Tucker's Validated Numerics

Average Error: 58.1 → 0

Time: 1.8s

Precision: binary64

Cost: 64

Math

\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]

↓

\[-0.8273960599468214 \]

FPCore

(FPCore ()
 :precision binary64
 (+
  (+
   (+
    (* 333.75 (pow 33096.0 6.0))
    (*
     (* 77617.0 77617.0)
     (+
      (+
       (+
        (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0))
        (- (pow 33096.0 6.0)))
       (* -121.0 (pow 33096.0 4.0)))
      -2.0)))
   (* 5.5 (pow 33096.0 8.0)))
  (/ 77617.0 (* 2.0 33096.0))))

↓

(FPCore () :precision binary64 -0.8273960599468214)

C

double code() {
	return (((333.75 * pow(33096.0, 6.0)) + ((77617.0 * 77617.0) * (((((11.0 * (77617.0 * 77617.0)) * (33096.0 * 33096.0)) + -pow(33096.0, 6.0)) + (-121.0 * pow(33096.0, 4.0))) + -2.0))) + (5.5 * pow(33096.0, 8.0))) + (77617.0 / (2.0 * 33096.0));
}

↓

double code() {
	return -0.8273960599468214;
}

Fortran

real(8) function code()
    code = (((333.75d0 * (33096.0d0 ** 6.0d0)) + ((77617.0d0 * 77617.0d0) * (((((11.0d0 * (77617.0d0 * 77617.0d0)) * (33096.0d0 * 33096.0d0)) + -(33096.0d0 ** 6.0d0)) + ((-121.0d0) * (33096.0d0 ** 4.0d0))) + (-2.0d0)))) + (5.5d0 * (33096.0d0 ** 8.0d0))) + (77617.0d0 / (2.0d0 * 33096.0d0))
end function

↓

real(8) function code()
    code = -0.8273960599468214d0
end function

Java

public static double code() {
	return (((333.75 * Math.pow(33096.0, 6.0)) + ((77617.0 * 77617.0) * (((((11.0 * (77617.0 * 77617.0)) * (33096.0 * 33096.0)) + -Math.pow(33096.0, 6.0)) + (-121.0 * Math.pow(33096.0, 4.0))) + -2.0))) + (5.5 * Math.pow(33096.0, 8.0))) + (77617.0 / (2.0 * 33096.0));
}

↓

public static double code() {
	return -0.8273960599468214;
}

Python

def code():
	return (((333.75 * math.pow(33096.0, 6.0)) + ((77617.0 * 77617.0) * (((((11.0 * (77617.0 * 77617.0)) * (33096.0 * 33096.0)) + -math.pow(33096.0, 6.0)) + (-121.0 * math.pow(33096.0, 4.0))) + -2.0))) + (5.5 * math.pow(33096.0, 8.0))) + (77617.0 / (2.0 * 33096.0))

↓

def code():
	return -0.8273960599468214

Julia

function code()
	return Float64(Float64(Float64(Float64(333.75 * (33096.0 ^ 6.0)) + Float64(Float64(77617.0 * 77617.0) * Float64(Float64(Float64(Float64(Float64(11.0 * Float64(77617.0 * 77617.0)) * Float64(33096.0 * 33096.0)) + Float64(-(33096.0 ^ 6.0))) + Float64(-121.0 * (33096.0 ^ 4.0))) + -2.0))) + Float64(5.5 * (33096.0 ^ 8.0))) + Float64(77617.0 / Float64(2.0 * 33096.0)))
end

↓

function code()
	return -0.8273960599468214
end

MATLAB

function tmp = code()
	tmp = (((333.75 * (33096.0 ^ 6.0)) + ((77617.0 * 77617.0) * (((((11.0 * (77617.0 * 77617.0)) * (33096.0 * 33096.0)) + -(33096.0 ^ 6.0)) + (-121.0 * (33096.0 ^ 4.0))) + -2.0))) + (5.5 * (33096.0 ^ 8.0))) + (77617.0 / (2.0 * 33096.0));
end

↓

function tmp = code()
	tmp = -0.8273960599468214;
end

Wolfram

code[] := N[(N[(N[(N[(333.75 * N[Power[33096.0, 6.0], $MachinePrecision]), $MachinePrecision] + N[(N[(77617.0 * 77617.0), $MachinePrecision] * N[(N[(N[(N[(N[(11.0 * N[(77617.0 * 77617.0), $MachinePrecision]), $MachinePrecision] * N[(33096.0 * 33096.0), $MachinePrecision]), $MachinePrecision] + (-N[Power[33096.0, 6.0], $MachinePrecision])), $MachinePrecision] + N[(-121.0 * N[Power[33096.0, 4.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + -2.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(5.5 * N[Power[33096.0, 8.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(77617.0 / N[(2.0 * 33096.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[] := -0.8273960599468214

Derivation

1. Initial program 58.1

   \[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]

2. Simplified 0

   \[\leadsto \color{blue}{-0.8273960599468214} \]
   Proof

   [Start] 58.1	\[ \left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]
   metadata-eval [=>] 58.1	\[ \left(\left(333.75 \cdot \color{blue}{1.3141745343712155 \cdot 10^{+27}} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]
   metadata-eval [=>] 58.1	\[ \left(\left(\color{blue}{4.386057508463931 \cdot 10^{+29}} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]
   metadata-eval [=>] 58.1	\[ \left(\left(4.386057508463931 \cdot 10^{+29} + \color{blue}{6024398689} \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]
   metadata-eval [=>] 58.1	\[ \left(\left(4.386057508463931 \cdot 10^{+29} + 6024398689 \cdot \left(\left(\left(\left(11 \cdot \color{blue}{6024398689}\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]
   metadata-eval [=>] 58.1	\[ \left(\left(4.386057508463931 \cdot 10^{+29} + 6024398689 \cdot \left(\left(\left(\color{blue}{66268385579} \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]
   metadata-eval [=>] 58.1	\[ \left(\left(4.386057508463931 \cdot 10^{+29} + 6024398689 \cdot \left(\left(\left(66268385579 \cdot \color{blue}{1095345216} + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]
   metadata-eval [=>] 58.1	\[ \left(\left(4.386057508463931 \cdot 10^{+29} + 6024398689 \cdot \left(\left(\left(\color{blue}{7.258675911600104 \cdot 10^{+19}} + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]
   metadata-eval [=>] 58.1	\[ \left(\left(4.386057508463931 \cdot 10^{+29} + 6024398689 \cdot \left(\left(\left(7.258675911600104 \cdot 10^{+19} + \left(-\color{blue}{1.3141745343712155 \cdot 10^{+27}}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]
   metadata-eval [=>] 58.1	\[ \left(\left(4.386057508463931 \cdot 10^{+29} + 6024398689 \cdot \left(\left(\left(7.258675911600104 \cdot 10^{+19} + \color{blue}{-1.3141745343712155 \cdot 10^{+27}}\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]
   metadata-eval [=>] 63.0	\[ \left(\left(4.386057508463931 \cdot 10^{+29} + 6024398689 \cdot \left(\left(\color{blue}{-1.3141744617844562 \cdot 10^{+27}} + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]
   metadata-eval [=>] 63.0	\[ \left(\left(4.386057508463931 \cdot 10^{+29} + 6024398689 \cdot \left(\left(-1.3141744617844562 \cdot 10^{+27} + -121 \cdot \color{blue}{1199781142214086700}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]
   metadata-eval [=>] 63.0	\[ \left(\left(4.386057508463931 \cdot 10^{+29} + 6024398689 \cdot \left(\left(-1.3141744617844562 \cdot 10^{+27} + \color{blue}{-1.4517351820790448 \cdot 10^{+20}}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]
   metadata-eval [=>] 63.0	\[ \left(\left(4.386057508463931 \cdot 10^{+29} + 6024398689 \cdot \left(\color{blue}{-1.3141746069579746 \cdot 10^{+27}} + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]
   metadata-eval [=>] 63.0	\[ \left(\left(4.386057508463931 \cdot 10^{+29} + 6024398689 \cdot \color{blue}{-1.3141746069579746 \cdot 10^{+27}}\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]
   metadata-eval [=>] 63.0	\[ \left(\left(4.386057508463931 \cdot 10^{+29} + \color{blue}{-7.917111779274712 \cdot 10^{+36}}\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]
   metadata-eval [=>] 63.0	\[ \left(\color{blue}{-7.917111340668961 \cdot 10^{+36}} + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]
   metadata-eval [=>] 63.0	\[ \left(-7.917111340668961 \cdot 10^{+36} + 5.5 \cdot \color{blue}{1.4394747892125385 \cdot 10^{+36}}\right) + \frac{77617}{2 \cdot 33096} \]
   metadata-eval [=>] 63.0	\[ \left(-7.917111340668961 \cdot 10^{+36} + \color{blue}{7.917111340668961 \cdot 10^{+36}}\right) + \frac{77617}{2 \cdot 33096} \]
   metadata-eval [=>] 1.0	\[ \color{blue}{-2} + \frac{77617}{2 \cdot 33096} \]
   metadata-eval [=>] 1.0	\[ -2 + \frac{77617}{\color{blue}{66192}} \]
   metadata-eval [=>] 1.0	\[ -2 + \color{blue}{1.1726039400531787} \]
   metadata-eval [=>] 0	\[ \color{blue}{-0.8273960599468214} \]

3. Final simplification 0

   \[\leadsto -0.8273960599468214 \]

Reproduce

herbie shell --seed 2022354 
(FPCore ()
  :name "From Warwick Tucker's Validated Numerics"
  :precision binary64
  (+ (+ (+ (* 333.75 (pow 33096.0 6.0)) (* (* 77617.0 77617.0) (+ (+ (+ (* (* 11.0 (* 77617.0 77617.0)) (* 33096.0 33096.0)) (- (pow 33096.0 6.0))) (* -121.0 (pow 33096.0 4.0))) -2.0))) (* 5.5 (pow 33096.0 8.0))) (/ 77617.0 (* 2.0 33096.0))))