From Warwick Tucker's Validated Numerics

?

Percentage Accurate: 9.2% → 100.0%
Time: 1.9s
Precision: binary64
Cost: 64

?

\[\left(\left(333.75 \cdot {33096}^{6} + \left(77617 \cdot 77617\right) \cdot \left(\left(\left(\left(11 \cdot \left(77617 \cdot 77617\right)\right) \cdot \left(33096 \cdot 33096\right) + \left(-{33096}^{6}\right)\right) + -121 \cdot {33096}^{4}\right) + -2\right)\right) + 5.5 \cdot {33096}^{8}\right) + \frac{77617}{2 \cdot 33096} \]
↓
\[-0.8273960599468214 \]
(FPCore ()
 :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)
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;
}

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

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;
}

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

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

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

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

\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

Local Percentage Accuracy vs ?

The average percentage accuracy by input value. Horizontal axis shows value of an input variable; the variable is choosen in the title. Vertical axis is accuracy; higher is better. Red represent the original program, while blue represents Herbie's suggestion. These can be toggled with buttons below the plot. The line is an average while dots represent individual samples.

Herbie found 1 alternatives:

AlternativeAccuracySpeedup

Accuracy vs Speed

The accuracy (vertical axis) and speed (horizontal axis) of each alternatives. Up and to the right is better. The red square shows the initial program, and each blue circle shows an alternative.The line shows the best available speed-accuracy tradeoffs.

Bogosity?

Bogosity

Try it out?

Your Program's Arguments

    Results

    Enter valid numbers for all inputs

    Derivation?

    1. Initial program 9.2%

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

    2. Simplified100.0%

      \[\leadsto \color{blue}{-0.8273960599468214} \]
      Step-by-step derivation

      [Start]9.2%

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

    3. Final simplification100.0%

      \[\leadsto -0.8273960599468214 \]

    Reproduce?

    herbie shell --seed 2023178 
(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))))