Average Error: 58.1 → 0
Time: 2.1s
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

Error

Try it out

Your Program's Arguments

    Results

    Enter valid numbers for all inputs

    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. Simplified0

      \[\leadsto \color{blue}{-0.8273960599468214} \]
      Proof
      -54767/66192: 0 points increase in error, 0 points decrease in error
      (Rewrite<= metadata-eval (+.f64 -2 77617/66192)): 256 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= metadata-eval (+.f64 -7917111340668961361101134701524942850 7917111340668961361101134701524942848)) 77617/66192): 256 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (Rewrite<= metadata-eval (+.f64 438605750846393161930703831040 -7917111779274712207494296632228773890)) 7917111340668961361101134701524942848) 77617/66192): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (Rewrite<= metadata-eval (*.f64 1335/4 1314174534371215466459037696)) -7917111779274712207494296632228773890) 7917111340668961361101134701524942848) 77617/66192): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 1335/4 (Rewrite<= metadata-eval (pow.f64 33096 6))) -7917111779274712207494296632228773890) 7917111340668961361101134701524942848) 77617/66192): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 1335/4 (pow.f64 33096 6)) (Rewrite<= metadata-eval (*.f64 6024398689 -1314174606957974558362483010))) 7917111340668961361101134701524942848) 77617/66192): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 1335/4 (pow.f64 33096 6)) (*.f64 (Rewrite<= metadata-eval (*.f64 77617 77617)) -1314174606957974558362483010)) 7917111340668961361101134701524942848) 77617/66192): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 1335/4 (pow.f64 33096 6)) (*.f64 (*.f64 77617 77617) (Rewrite<= metadata-eval (+.f64 -1314174606957974558362483008 -2)))) 7917111340668961361101134701524942848) 77617/66192): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 1335/4 (pow.f64 33096 6)) (*.f64 (*.f64 77617 77617) (+.f64 (Rewrite<= metadata-eval (+.f64 -1314174461784456350457997632 -145173518207904485376)) -2))) 7917111340668961361101134701524942848) 77617/66192): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 1335/4 (pow.f64 33096 6)) (*.f64 (*.f64 77617 77617) (+.f64 (+.f64 (Rewrite<= metadata-eval (+.f64 72586759116001040064 -1314174534371215466459037696)) -145173518207904485376) -2))) 7917111340668961361101134701524942848) 77617/66192): 0 points increase in error, 256 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 1335/4 (pow.f64 33096 6)) (*.f64 (*.f64 77617 77617) (+.f64 (+.f64 (+.f64 (Rewrite<= metadata-eval (*.f64 66268385579 1095345216)) -1314174534371215466459037696) -145173518207904485376) -2))) 7917111340668961361101134701524942848) 77617/66192): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 1335/4 (pow.f64 33096 6)) (*.f64 (*.f64 77617 77617) (+.f64 (+.f64 (+.f64 (*.f64 (Rewrite<= metadata-eval (*.f64 11 6024398689)) 1095345216) -1314174534371215466459037696) -145173518207904485376) -2))) 7917111340668961361101134701524942848) 77617/66192): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 1335/4 (pow.f64 33096 6)) (*.f64 (*.f64 77617 77617) (+.f64 (+.f64 (+.f64 (*.f64 (*.f64 11 (Rewrite<= metadata-eval (*.f64 77617 77617))) 1095345216) -1314174534371215466459037696) -145173518207904485376) -2))) 7917111340668961361101134701524942848) 77617/66192): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 1335/4 (pow.f64 33096 6)) (*.f64 (*.f64 77617 77617) (+.f64 (+.f64 (+.f64 (*.f64 (*.f64 11 (*.f64 77617 77617)) (Rewrite<= metadata-eval (*.f64 33096 33096))) -1314174534371215466459037696) -145173518207904485376) -2))) 7917111340668961361101134701524942848) 77617/66192): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 1335/4 (pow.f64 33096 6)) (*.f64 (*.f64 77617 77617) (+.f64 (+.f64 (+.f64 (*.f64 (*.f64 11 (*.f64 77617 77617)) (*.f64 33096 33096)) (Rewrite<= metadata-eval (neg.f64 1314174534371215466459037696))) -145173518207904485376) -2))) 7917111340668961361101134701524942848) 77617/66192): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 1335/4 (pow.f64 33096 6)) (*.f64 (*.f64 77617 77617) (+.f64 (+.f64 (+.f64 (*.f64 (*.f64 11 (*.f64 77617 77617)) (*.f64 33096 33096)) (neg.f64 (Rewrite<= metadata-eval (pow.f64 33096 6)))) -145173518207904485376) -2))) 7917111340668961361101134701524942848) 77617/66192): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 1335/4 (pow.f64 33096 6)) (*.f64 (*.f64 77617 77617) (+.f64 (+.f64 (+.f64 (*.f64 (*.f64 11 (*.f64 77617 77617)) (*.f64 33096 33096)) (neg.f64 (pow.f64 33096 6))) (Rewrite<= metadata-eval (*.f64 -121 1199781142214086656))) -2))) 7917111340668961361101134701524942848) 77617/66192): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 1335/4 (pow.f64 33096 6)) (*.f64 (*.f64 77617 77617) (+.f64 (+.f64 (+.f64 (*.f64 (*.f64 11 (*.f64 77617 77617)) (*.f64 33096 33096)) (neg.f64 (pow.f64 33096 6))) (*.f64 -121 (Rewrite<= metadata-eval (pow.f64 33096 4)))) -2))) 7917111340668961361101134701524942848) 77617/66192): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 1335/4 (pow.f64 33096 6)) (*.f64 (*.f64 77617 77617) (+.f64 (+.f64 (+.f64 (*.f64 (*.f64 11 (*.f64 77617 77617)) (*.f64 33096 33096)) (neg.f64 (pow.f64 33096 6))) (*.f64 -121 (pow.f64 33096 4))) -2))) (Rewrite<= metadata-eval (*.f64 11/2 1439474789212538429291115400277262336))) 77617/66192): 0 points increase in error, 256 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 1335/4 (pow.f64 33096 6)) (*.f64 (*.f64 77617 77617) (+.f64 (+.f64 (+.f64 (*.f64 (*.f64 11 (*.f64 77617 77617)) (*.f64 33096 33096)) (neg.f64 (pow.f64 33096 6))) (*.f64 -121 (pow.f64 33096 4))) -2))) (*.f64 11/2 (Rewrite<= metadata-eval (pow.f64 33096 8)))) 77617/66192): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 1335/4 (pow.f64 33096 6)) (*.f64 (*.f64 77617 77617) (+.f64 (+.f64 (+.f64 (*.f64 (*.f64 11 (*.f64 77617 77617)) (*.f64 33096 33096)) (neg.f64 (pow.f64 33096 6))) (*.f64 -121 (pow.f64 33096 4))) -2))) (*.f64 11/2 (pow.f64 33096 8))) (Rewrite<= metadata-eval (/.f64 77617 66192))): 0 points increase in error, 0 points decrease in error
      (+.f64 (+.f64 (+.f64 (*.f64 1335/4 (pow.f64 33096 6)) (*.f64 (*.f64 77617 77617) (+.f64 (+.f64 (+.f64 (*.f64 (*.f64 11 (*.f64 77617 77617)) (*.f64 33096 33096)) (neg.f64 (pow.f64 33096 6))) (*.f64 -121 (pow.f64 33096 4))) -2))) (*.f64 11/2 (pow.f64 33096 8))) (/.f64 77617 (Rewrite<= metadata-eval (*.f64 2 33096)))): 0 points increase in error, 0 points decrease in error

    3. Final simplification0

      \[\leadsto -0.8273960599468214 \]

    Reproduce

    herbie shell --seed 2022329 
(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))))