Jmat.Real.erfi, branch x greater than or equal to 5

Average Error: 2.8 → 1.2

Time: 15.7s

Precision: binary64

Cost: 52992

\[x \geq 0.5\]

Math

\[\left(\frac{1}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\left(\frac{1}{\left|x\right|} + \frac{1}{2} \cdot \left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{3}{4} \cdot \left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{15}{8} \cdot \left(\left(\left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) \]

↓

\[\sqrt{\frac{1}{\pi}} \cdot \left({\left(e^{x}\right)}^{x} \cdot \left(\frac{1}{x} + \left(\frac{0.75}{{x}^{5}} + \frac{0.5}{{x}^{3}}\right)\right) + 1.875 \cdot \frac{e^{x \cdot x}}{{x}^{7}}\right) \]

FPCore

(FPCore (x)
 :precision binary64
 (*
  (* (/ 1.0 (sqrt PI)) (exp (* (fabs x) (fabs x))))
  (+
   (+
    (+
     (/ 1.0 (fabs x))
     (*
      (/ 1.0 2.0)
      (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))))
    (*
     (/ 3.0 4.0)
     (*
      (*
       (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
       (/ 1.0 (fabs x)))
      (/ 1.0 (fabs x)))))
   (*
    (/ 15.0 8.0)
    (*
     (*
      (*
       (*
        (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))
        (/ 1.0 (fabs x)))
       (/ 1.0 (fabs x)))
      (/ 1.0 (fabs x)))
     (/ 1.0 (fabs x)))))))

↓

(FPCore (x)
 :precision binary64
 (*
  (sqrt (/ 1.0 PI))
  (+
   (*
    (pow (exp x) x)
    (+ (/ 1.0 x) (+ (/ 0.75 (pow x 5.0)) (/ 0.5 (pow x 3.0)))))
   (* 1.875 (/ (exp (* x x)) (pow x 7.0))))))

C

double code(double x) {
	return ((1.0 / sqrt(((double) M_PI))) * exp((fabs(x) * fabs(x)))) * ((((1.0 / fabs(x)) + ((1.0 / 2.0) * (((1.0 / fabs(x)) * (1.0 / fabs(x))) * (1.0 / fabs(x))))) + ((3.0 / 4.0) * (((((1.0 / fabs(x)) * (1.0 / fabs(x))) * (1.0 / fabs(x))) * (1.0 / fabs(x))) * (1.0 / fabs(x))))) + ((15.0 / 8.0) * (((((((1.0 / fabs(x)) * (1.0 / fabs(x))) * (1.0 / fabs(x))) * (1.0 / fabs(x))) * (1.0 / fabs(x))) * (1.0 / fabs(x))) * (1.0 / fabs(x)))));
}

↓

double code(double x) {
	return sqrt((1.0 / ((double) M_PI))) * ((pow(exp(x), x) * ((1.0 / x) + ((0.75 / pow(x, 5.0)) + (0.5 / pow(x, 3.0))))) + (1.875 * (exp((x * x)) / pow(x, 7.0))));
}

Java

public static double code(double x) {
	return ((1.0 / Math.sqrt(Math.PI)) * Math.exp((Math.abs(x) * Math.abs(x)))) * ((((1.0 / Math.abs(x)) + ((1.0 / 2.0) * (((1.0 / Math.abs(x)) * (1.0 / Math.abs(x))) * (1.0 / Math.abs(x))))) + ((3.0 / 4.0) * (((((1.0 / Math.abs(x)) * (1.0 / Math.abs(x))) * (1.0 / Math.abs(x))) * (1.0 / Math.abs(x))) * (1.0 / Math.abs(x))))) + ((15.0 / 8.0) * (((((((1.0 / Math.abs(x)) * (1.0 / Math.abs(x))) * (1.0 / Math.abs(x))) * (1.0 / Math.abs(x))) * (1.0 / Math.abs(x))) * (1.0 / Math.abs(x))) * (1.0 / Math.abs(x)))));
}

↓

public static double code(double x) {
	return Math.sqrt((1.0 / Math.PI)) * ((Math.pow(Math.exp(x), x) * ((1.0 / x) + ((0.75 / Math.pow(x, 5.0)) + (0.5 / Math.pow(x, 3.0))))) + (1.875 * (Math.exp((x * x)) / Math.pow(x, 7.0))));
}

Python

def code(x):
	return ((1.0 / math.sqrt(math.pi)) * math.exp((math.fabs(x) * math.fabs(x)))) * ((((1.0 / math.fabs(x)) + ((1.0 / 2.0) * (((1.0 / math.fabs(x)) * (1.0 / math.fabs(x))) * (1.0 / math.fabs(x))))) + ((3.0 / 4.0) * (((((1.0 / math.fabs(x)) * (1.0 / math.fabs(x))) * (1.0 / math.fabs(x))) * (1.0 / math.fabs(x))) * (1.0 / math.fabs(x))))) + ((15.0 / 8.0) * (((((((1.0 / math.fabs(x)) * (1.0 / math.fabs(x))) * (1.0 / math.fabs(x))) * (1.0 / math.fabs(x))) * (1.0 / math.fabs(x))) * (1.0 / math.fabs(x))) * (1.0 / math.fabs(x)))))

↓

def code(x):
	return math.sqrt((1.0 / math.pi)) * ((math.pow(math.exp(x), x) * ((1.0 / x) + ((0.75 / math.pow(x, 5.0)) + (0.5 / math.pow(x, 3.0))))) + (1.875 * (math.exp((x * x)) / math.pow(x, 7.0))))

Julia

function code(x)
	return Float64(Float64(Float64(1.0 / sqrt(pi)) * exp(Float64(abs(x) * abs(x)))) * Float64(Float64(Float64(Float64(1.0 / abs(x)) + Float64(Float64(1.0 / 2.0) * Float64(Float64(Float64(1.0 / abs(x)) * Float64(1.0 / abs(x))) * Float64(1.0 / abs(x))))) + Float64(Float64(3.0 / 4.0) * Float64(Float64(Float64(Float64(Float64(1.0 / abs(x)) * Float64(1.0 / abs(x))) * Float64(1.0 / abs(x))) * Float64(1.0 / abs(x))) * Float64(1.0 / abs(x))))) + Float64(Float64(15.0 / 8.0) * Float64(Float64(Float64(Float64(Float64(Float64(Float64(1.0 / abs(x)) * Float64(1.0 / abs(x))) * Float64(1.0 / abs(x))) * Float64(1.0 / abs(x))) * Float64(1.0 / abs(x))) * Float64(1.0 / abs(x))) * Float64(1.0 / abs(x))))))
end

↓

function code(x)
	return Float64(sqrt(Float64(1.0 / pi)) * Float64(Float64((exp(x) ^ x) * Float64(Float64(1.0 / x) + Float64(Float64(0.75 / (x ^ 5.0)) + Float64(0.5 / (x ^ 3.0))))) + Float64(1.875 * Float64(exp(Float64(x * x)) / (x ^ 7.0)))))
end

MATLAB

function tmp = code(x)
	tmp = ((1.0 / sqrt(pi)) * exp((abs(x) * abs(x)))) * ((((1.0 / abs(x)) + ((1.0 / 2.0) * (((1.0 / abs(x)) * (1.0 / abs(x))) * (1.0 / abs(x))))) + ((3.0 / 4.0) * (((((1.0 / abs(x)) * (1.0 / abs(x))) * (1.0 / abs(x))) * (1.0 / abs(x))) * (1.0 / abs(x))))) + ((15.0 / 8.0) * (((((((1.0 / abs(x)) * (1.0 / abs(x))) * (1.0 / abs(x))) * (1.0 / abs(x))) * (1.0 / abs(x))) * (1.0 / abs(x))) * (1.0 / abs(x)))));
end

↓

function tmp = code(x)
	tmp = sqrt((1.0 / pi)) * (((exp(x) ^ x) * ((1.0 / x) + ((0.75 / (x ^ 5.0)) + (0.5 / (x ^ 3.0))))) + (1.875 * (exp((x * x)) / (x ^ 7.0))));
end

Wolfram

code[x_] := N[(N[(N[(1.0 / N[Sqrt[Pi], $MachinePrecision]), $MachinePrecision] * N[Exp[N[(N[Abs[x], $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(1.0 / N[Abs[x], $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / 2.0), $MachinePrecision] * N[(N[(N[(1.0 / N[Abs[x], $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(3.0 / 4.0), $MachinePrecision] * N[(N[(N[(N[(N[(1.0 / N[Abs[x], $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(15.0 / 8.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[(1.0 / N[Abs[x], $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(1.0 / N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

↓

code[x_] := N[(N[Sqrt[N[(1.0 / Pi), $MachinePrecision]], $MachinePrecision] * N[(N[(N[Power[N[Exp[x], $MachinePrecision], x], $MachinePrecision] * N[(N[(1.0 / x), $MachinePrecision] + N[(N[(0.75 / N[Power[x, 5.0], $MachinePrecision]), $MachinePrecision] + N[(0.5 / N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(1.875 * N[(N[Exp[N[(x * x), $MachinePrecision]], $MachinePrecision] / N[Power[x, 7.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 2.8

   \[\left(\frac{1}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\left(\frac{1}{\left|x\right|} + \frac{1}{2} \cdot \left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{3}{4} \cdot \left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{15}{8} \cdot \left(\left(\left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) \]

2. Simplified 1.3

   \[\leadsto \color{blue}{\frac{\frac{{\left(e^{x}\right)}^{x}}{\left|x\right|}}{\sqrt{\pi}} \cdot \left(1 + \left(\frac{1.875}{{x}^{6}} + \frac{0.5 + \frac{0.75}{x \cdot x}}{x \cdot x}\right)\right)} \]
   Proof
   (*.f64 (/.f64 (/.f64 (pow.f64 (exp.f64 x) x) (fabs.f64 x)) (sqrt.f64 (PI.f64))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (/.f64 (/.f64 (Rewrite<= exp-prod_binary64 (exp.f64 (*.f64 x x))) (fabs.f64 x)) (sqrt.f64 (PI.f64))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 146 points increase in error, 18 points decrease in error
   (*.f64 (/.f64 (/.f64 (exp.f64 (Rewrite<= sqr-abs_binary64 (*.f64 (fabs.f64 x) (fabs.f64 x)))) (fabs.f64 x)) (sqrt.f64 (PI.f64))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (/.f64 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (fabs.f64 x)) (sqrt.f64 (PI.f64))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (/.f64 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (fabs.f64 x)) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (sqrt.f64 (PI.f64))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 17 points increase in error, 30 points decrease in error
   (*.f64 (Rewrite<= associate-*r/_binary64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (sqrt.f64 (PI.f64))))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 40 points increase in error, 36 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (sqrt.f64 (PI.f64)))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))))) (+.f64 1 (+.f64 (/.f64 15/8 (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 45 points increase in error, 68 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (/.f64 (Rewrite<= metadata-eval (*.f64 15/8 1)) (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (/.f64 (*.f64 (Rewrite<= metadata-eval (/.f64 15 8)) 1) (pow.f64 x 6)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (/.f64 (*.f64 (/.f64 15 8) 1) (pow.f64 x (Rewrite<= metadata-eval (*.f64 2 3)))) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (/.f64 (*.f64 (/.f64 15 8) 1) (Rewrite<= pow-sqr_binary64 (*.f64 (pow.f64 x 3) (pow.f64 x 3)))) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 13 points increase in error, 2 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (/.f64 (*.f64 (/.f64 15 8) 1) (Rewrite<= cube-prod_binary64 (pow.f64 (*.f64 x x) 3))) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 9 points increase in error, 14 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (/.f64 (*.f64 (/.f64 15 8) 1) (pow.f64 (Rewrite<= sqr-abs_binary64 (*.f64 (fabs.f64 x) (fabs.f64 x))) 3)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (/.f64 (*.f64 (/.f64 15 8) 1) (pow.f64 (*.f64 (Rewrite<= /-rgt-identity_binary64 (/.f64 (fabs.f64 x) 1)) (fabs.f64 x)) 3)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (/.f64 (*.f64 (/.f64 15 8) 1) (pow.f64 (Rewrite<= associate-/r/_binary64 (/.f64 (fabs.f64 x) (/.f64 1 (fabs.f64 x)))) 3)) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 17 points increase in error, 2 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (/.f64 (*.f64 (/.f64 15 8) 1) (Rewrite=> cube-div_binary64 (/.f64 (pow.f64 (fabs.f64 x) 3) (pow.f64 (/.f64 1 (fabs.f64 x)) 3)))) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 10 points increase in error, 16 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (/.f64 (*.f64 (/.f64 15 8) 1) (/.f64 (Rewrite=> unpow3_binary64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))) (pow.f64 (/.f64 1 (fabs.f64 x)) 3))) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 2 points increase in error, 2 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (/.f64 (*.f64 (/.f64 15 8) 1) (/.f64 (*.f64 (*.f64 (Rewrite<= /-rgt-identity_binary64 (/.f64 (fabs.f64 x) 1)) (fabs.f64 x)) (fabs.f64 x)) (pow.f64 (/.f64 1 (fabs.f64 x)) 3))) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (/.f64 (*.f64 (/.f64 15 8) 1) (/.f64 (*.f64 (Rewrite<= associate-/r/_binary64 (/.f64 (fabs.f64 x) (/.f64 1 (fabs.f64 x)))) (fabs.f64 x)) (pow.f64 (/.f64 1 (fabs.f64 x)) 3))) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 9 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (/.f64 (*.f64 (/.f64 15 8) 1) (/.f64 (Rewrite<= associate-/r/_binary64 (/.f64 (fabs.f64 x) (/.f64 (/.f64 1 (fabs.f64 x)) (fabs.f64 x)))) (pow.f64 (/.f64 1 (fabs.f64 x)) 3))) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 3 points increase in error, 6 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (/.f64 (*.f64 (/.f64 15 8) 1) (/.f64 (/.f64 (fabs.f64 x) (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 1 (fabs.f64 x)))) (fabs.f64 x))) (pow.f64 (/.f64 1 (fabs.f64 x)) 3))) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (/.f64 (*.f64 (/.f64 15 8) 1) (/.f64 (/.f64 (fabs.f64 x) (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))))) (pow.f64 (/.f64 1 (fabs.f64 x)) 3))) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 3 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (/.f64 (*.f64 (/.f64 15 8) 1) (/.f64 (/.f64 (fabs.f64 x) (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) (Rewrite=> unpow3_binary64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))))) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 5 points increase in error, 3 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (/.f64 (*.f64 (/.f64 15 8) 1) (Rewrite<= associate-/r*_binary64 (/.f64 (fabs.f64 x) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))))) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 3 points increase in error, 3 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (/.f64 (*.f64 (/.f64 15 8) 1) (/.f64 (fabs.f64 x) (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))))))) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (/.f64 (*.f64 (/.f64 15 8) 1) (/.f64 (fabs.f64 x) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))))) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 5 points increase in error, 6 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 (/.f64 15 8) (/.f64 1 (/.f64 (fabs.f64 x) (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))))) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 6 points increase in error, 2 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (Rewrite=> associate-/r/_binary64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))))) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 5 points increase in error, 3 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (/.f64 (+.f64 1/2 (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (/.f64 (+.f64 (Rewrite<= metadata-eval (/.f64 1 2)) (/.f64 3/4 (*.f64 x x))) (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (/.f64 (+.f64 (/.f64 1 2) (/.f64 (Rewrite<= metadata-eval (*.f64 1 3/4)) (*.f64 x x))) (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (/.f64 (+.f64 (/.f64 1 2) (/.f64 (*.f64 1 (Rewrite<= metadata-eval (/.f64 3 4))) (*.f64 x x))) (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (/.f64 (+.f64 (/.f64 1 2) (/.f64 (*.f64 1 (/.f64 3 4)) (Rewrite<= sqr-abs_binary64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (/.f64 (+.f64 (/.f64 1 2) (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.f64 3 4)))) (*.f64 x x))))): 2 points increase in error, 2 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (/.f64 (+.f64 (/.f64 1 2) (*.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 1 (fabs.f64 x)) (fabs.f64 x))) (/.f64 3 4))) (*.f64 x x))))): 3 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (/.f64 (+.f64 (/.f64 1 2) (*.f64 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 1 (fabs.f64 x)))) (fabs.f64 x)) (/.f64 3 4))) (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (/.f64 (+.f64 (/.f64 1 2) (*.f64 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) (/.f64 3 4))) (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (+.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 3 4))))) (*.f64 x x))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (/.f64 (*.f64 1 (+.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 3 4)))) (Rewrite<= sqr-abs_binary64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (*.f64 (fabs.f64 x) (fabs.f64 x))) (+.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 3 4)))))))): 2 points increase in error, 2 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (*.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 1 (fabs.f64 x)) (fabs.f64 x))) (+.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 3 4))))))): 7 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (*.f64 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 1 (fabs.f64 x)))) (fabs.f64 x)) (+.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 3 4))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (*.f64 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) (+.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 3 4))))))): 3 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (Rewrite<= distribute-lft-out_binary64 (+.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 2)) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 3 4)))))))): 4 points increase in error, 1 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (/.f64 1 2) (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))))) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 3 4))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (+.f64 (*.f64 (/.f64 1 2) (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) (/.f64 3 4))))))): 1 points increase in error, 5 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (+.f64 (*.f64 (/.f64 1 2) (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) (*.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (/.f64 3 4)))))): 2 points increase in error, 1 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (+.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (+.f64 (*.f64 (/.f64 1 2) (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) (Rewrite<= *-commutative_binary64 (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 (*.f64 (/.f64 1 2) (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 1 (Rewrite=> associate-+l+_binary64 (+.f64 (*.f64 (/.f64 1 2) (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) (+.f64 (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))))))): 9 points increase in error, 3 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 1 (*.f64 (/.f64 1 2) (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))))) (+.f64 (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))))))): 22 points increase in error, 30 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 (/.f64 1 2) (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) 1)) (+.f64 (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))))): 0 points increase in error, 0 points decrease in error
   (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 1 2) (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) 1) (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))))) (*.f64 (+.f64 (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))))))): 57 points increase in error, 52 points decrease in error
   (+.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (+.f64 (*.f64 (/.f64 1 2) (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) 1) (/.f64 1 (fabs.f64 x))) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))))) (*.f64 (+.f64 (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))): 34 points increase in error, 34 points decrease in error
   (+.f64 (*.f64 (Rewrite<= distribute-rgt1-in_binary64 (+.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (*.f64 (/.f64 1 2) (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (*.f64 (+.f64 (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))): 33 points increase in error, 25 points decrease in error
   (+.f64 (*.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (Rewrite<= associate-*r*_binary64 (*.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))))) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (*.f64 (+.f64 (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))): 0 points increase in error, 0 points decrease in error
   (+.f64 (*.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))))))): 0 points increase in error, 0 points decrease in error
   (+.f64 (*.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))))) (*.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))))): 11 points increase in error, 9 points decrease in error
   (+.f64 (*.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (/.f64 1 (fabs.f64 x))) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))))) (*.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))))))): 0 points increase in error, 4 points decrease in error
   (+.f64 (*.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 (*.f64 (Rewrite<= associate-*r*_binary64 (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (*.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (*.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))))))): 3 points increase in error, 2 points decrease in error
   (+.f64 (*.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 (*.f64 (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (/.f64 1 (fabs.f64 x))) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))))))): 5 points increase in error, 9 points decrease in error
   (+.f64 (*.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (+.f64 (*.f64 (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (*.f64 (Rewrite<= associate-*r*_binary64 (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))): 9 points increase in error, 5 points decrease in error
   (+.f64 (*.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (Rewrite<= distribute-rgt-in_binary64 (*.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))) (+.f64 (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))))))): 10 points increase in error, 9 points decrease in error
   (+.f64 (*.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (Rewrite=> *-commutative_binary64 (*.f64 (+.f64 (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))): 0 points increase in error, 0 points decrease in error
   (Rewrite<= distribute-rgt-in_binary64 (*.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))) (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (+.f64 (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))) (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x)))))))): 44 points increase in error, 46 points decrease in error
   (*.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))) (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (*.f64 (/.f64 1 2) (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 3 4) (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))) (*.f64 (/.f64 15 8) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))) (/.f64 1 (fabs.f64 x))))))): 43 points increase in error, 31 points decrease in error

3. Applied egg-rr 1.6

   \[\leadsto \color{blue}{{\left(\sqrt[3]{\frac{\frac{{\left(e^{x}\right)}^{x}}{\sqrt{\pi}}}{x} \cdot \left(1 + \mathsf{fma}\left(1.875, {x}^{-6}, \mathsf{fma}\left(0.75, {x}^{-2}, 0.5\right) \cdot {x}^{-2}\right)\right)}\right)}^{3}} \]

4. Applied egg-rr 1.3

   \[\leadsto \color{blue}{\frac{{\left(e^{x}\right)}^{x}}{x \cdot \sqrt{\pi}} \cdot \left(1 + \mathsf{fma}\left(1.875, {x}^{-6}, {x}^{-2} \cdot \mathsf{fma}\left(0.75, {x}^{-2}, 0.5\right)\right)\right)} \]

5. Taylor expanded in x around inf 2.7

   \[\leadsto \color{blue}{1.875 \cdot \left(\frac{e^{{x}^{2}}}{{x}^{7}} \cdot \sqrt{\frac{1}{\pi}}\right) + \left(0.75 \cdot \left(\frac{e^{{x}^{2}}}{{x}^{5}} \cdot \sqrt{\frac{1}{\pi}}\right) + \left(0.5 \cdot \left(\frac{e^{{x}^{2}}}{{x}^{3}} \cdot \sqrt{\frac{1}{\pi}}\right) + \frac{e^{{x}^{2}}}{x} \cdot \sqrt{\frac{1}{\pi}}\right)\right)} \]

6. Simplified 1.2

   \[\leadsto \color{blue}{\sqrt{\frac{1}{\pi}} \cdot \left({\left(e^{x}\right)}^{x} \cdot \left(\frac{1}{x} + \left(\frac{0.75}{{x}^{5}} + \frac{0.5}{{x}^{3}}\right)\right) + 1.875 \cdot \frac{{\left(e^{x}\right)}^{x}}{{x}^{7}}\right)} \]
   Proof
   (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 (pow.f64 (exp.f64 x) x) (+.f64 (/.f64 1 x) (+.f64 (/.f64 3/4 (pow.f64 x 5)) (/.f64 1/2 (pow.f64 x 3))))) (*.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 7))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 (Rewrite<= exp-prod_binary64 (exp.f64 (*.f64 x x))) (+.f64 (/.f64 1 x) (+.f64 (/.f64 3/4 (pow.f64 x 5)) (/.f64 1/2 (pow.f64 x 3))))) (*.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 7))))): 145 points increase in error, 17 points decrease in error
   (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 (exp.f64 (Rewrite<= unpow2_binary64 (pow.f64 x 2))) (+.f64 (/.f64 1 x) (+.f64 (/.f64 3/4 (pow.f64 x 5)) (/.f64 1/2 (pow.f64 x 3))))) (*.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 7))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (Rewrite<= distribute-lft-out_binary64 (+.f64 (*.f64 (exp.f64 (pow.f64 x 2)) (/.f64 1 x)) (*.f64 (exp.f64 (pow.f64 x 2)) (+.f64 (/.f64 3/4 (pow.f64 x 5)) (/.f64 1/2 (pow.f64 x 3)))))) (*.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 7))))): 35 points increase in error, 36 points decrease in error
   (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (+.f64 (*.f64 (exp.f64 (pow.f64 x 2)) (/.f64 1 x)) (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 (/.f64 3/4 (pow.f64 x 5)) (exp.f64 (pow.f64 x 2))) (*.f64 (/.f64 1/2 (pow.f64 x 3)) (exp.f64 (pow.f64 x 2)))))) (*.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 7))))): 4 points increase in error, 3 points decrease in error
   (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (+.f64 (*.f64 (exp.f64 (pow.f64 x 2)) (/.f64 1 x)) (+.f64 (Rewrite<= associate-/r/_binary64 (/.f64 3/4 (/.f64 (pow.f64 x 5) (exp.f64 (pow.f64 x 2))))) (*.f64 (/.f64 1/2 (pow.f64 x 3)) (exp.f64 (pow.f64 x 2))))) (*.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 7))))): 1 points increase in error, 4 points decrease in error
   (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (+.f64 (*.f64 (exp.f64 (pow.f64 x 2)) (/.f64 1 x)) (+.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 3/4 (exp.f64 (pow.f64 x 2))) (pow.f64 x 5))) (*.f64 (/.f64 1/2 (pow.f64 x 3)) (exp.f64 (pow.f64 x 2))))) (*.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 7))))): 4 points increase in error, 1 points decrease in error
   (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (+.f64 (*.f64 (exp.f64 (pow.f64 x 2)) (/.f64 1 x)) (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 3/4 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5)))) (*.f64 (/.f64 1/2 (pow.f64 x 3)) (exp.f64 (pow.f64 x 2))))) (*.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 7))))): 1 points increase in error, 4 points decrease in error
   (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (+.f64 (*.f64 (exp.f64 (pow.f64 x 2)) (/.f64 1 x)) (+.f64 (*.f64 3/4 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))) (Rewrite<= associate-/r/_binary64 (/.f64 1/2 (/.f64 (pow.f64 x 3) (exp.f64 (pow.f64 x 2))))))) (*.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 7))))): 2 points increase in error, 2 points decrease in error
   (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (+.f64 (*.f64 (exp.f64 (pow.f64 x 2)) (/.f64 1 x)) (+.f64 (*.f64 3/4 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 1/2 (exp.f64 (pow.f64 x 2))) (pow.f64 x 3))))) (*.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 7))))): 1 points increase in error, 0 points decrease in error
   (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (+.f64 (*.f64 (exp.f64 (pow.f64 x 2)) (/.f64 1 x)) (+.f64 (*.f64 3/4 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))) (Rewrite<= associate-*r/_binary64 (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3)))))) (*.f64 15/8 (/.f64 (pow.f64 (exp.f64 x) x) (pow.f64 x 7))))): 0 points increase in error, 0 points decrease in error
   (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (+.f64 (*.f64 (exp.f64 (pow.f64 x 2)) (/.f64 1 x)) (+.f64 (*.f64 3/4 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))) (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3))))) (*.f64 15/8 (/.f64 (Rewrite<= exp-prod_binary64 (exp.f64 (*.f64 x x))) (pow.f64 x 7))))): 6 points increase in error, 2 points decrease in error
   (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (+.f64 (*.f64 (exp.f64 (pow.f64 x 2)) (/.f64 1 x)) (+.f64 (*.f64 3/4 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))) (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3))))) (*.f64 15/8 (/.f64 (exp.f64 (Rewrite<= unpow2_binary64 (pow.f64 x 2))) (pow.f64 x 7))))): 0 points increase in error, 0 points decrease in error
   (Rewrite<= distribute-lft-out_binary64 (+.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 (exp.f64 (pow.f64 x 2)) (/.f64 1 x)) (+.f64 (*.f64 3/4 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))) (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3)))))) (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (*.f64 15/8 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 7)))))): 37 points increase in error, 50 points decrease in error
   (+.f64 (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 (*.f64 (exp.f64 (pow.f64 x 2)) (/.f64 1 x)) (sqrt.f64 (/.f64 1 (PI.f64)))) (*.f64 (+.f64 (*.f64 3/4 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))) (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3)))) (sqrt.f64 (/.f64 1 (PI.f64)))))) (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (*.f64 15/8 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 7))))): 37 points increase in error, 30 points decrease in error
   (+.f64 (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 (exp.f64 (pow.f64 x 2)) (*.f64 (/.f64 1 x) (sqrt.f64 (/.f64 1 (PI.f64)))))) (*.f64 (+.f64 (*.f64 3/4 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))) (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3)))) (sqrt.f64 (/.f64 1 (PI.f64))))) (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (*.f64 15/8 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 7))))): 25 points increase in error, 31 points decrease in error
   (+.f64 (+.f64 (*.f64 (exp.f64 (pow.f64 x 2)) (Rewrite<= associate-/r/_binary64 (/.f64 1 (/.f64 x (sqrt.f64 (/.f64 1 (PI.f64))))))) (*.f64 (+.f64 (*.f64 3/4 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))) (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3)))) (sqrt.f64 (/.f64 1 (PI.f64))))) (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (*.f64 15/8 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 7))))): 32 points increase in error, 23 points decrease in error
   (+.f64 (+.f64 (Rewrite=> associate-*r/_binary64 (/.f64 (*.f64 (exp.f64 (pow.f64 x 2)) 1) (/.f64 x (sqrt.f64 (/.f64 1 (PI.f64)))))) (*.f64 (+.f64 (*.f64 3/4 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))) (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3)))) (sqrt.f64 (/.f64 1 (PI.f64))))) (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (*.f64 15/8 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 7))))): 20 points increase in error, 30 points decrease in error
   (+.f64 (+.f64 (/.f64 (Rewrite=> *-rgt-identity_binary64 (exp.f64 (pow.f64 x 2))) (/.f64 x (sqrt.f64 (/.f64 1 (PI.f64))))) (*.f64 (+.f64 (*.f64 3/4 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))) (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3)))) (sqrt.f64 (/.f64 1 (PI.f64))))) (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (*.f64 15/8 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 7))))): 0 points increase in error, 0 points decrease in error
   (+.f64 (+.f64 (Rewrite=> associate-/r/_binary64 (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) x) (sqrt.f64 (/.f64 1 (PI.f64))))) (*.f64 (+.f64 (*.f64 3/4 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))) (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3)))) (sqrt.f64 (/.f64 1 (PI.f64))))) (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (*.f64 15/8 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 7))))): 36 points increase in error, 27 points decrease in error
   (+.f64 (+.f64 (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) x) (sqrt.f64 (/.f64 1 (PI.f64)))) (Rewrite<= *-commutative_binary64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 3/4 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))) (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3))))))) (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (*.f64 15/8 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 7))))): 0 points increase in error, 0 points decrease in error
   (+.f64 (+.f64 (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) x) (sqrt.f64 (/.f64 1 (PI.f64)))) (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 (*.f64 3/4 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5))) (sqrt.f64 (/.f64 1 (PI.f64)))) (*.f64 (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3))) (sqrt.f64 (/.f64 1 (PI.f64))))))) (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (*.f64 15/8 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 7))))): 6 points increase in error, 3 points decrease in error
   (+.f64 (+.f64 (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) x) (sqrt.f64 (/.f64 1 (PI.f64)))) (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 3/4 (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5)) (sqrt.f64 (/.f64 1 (PI.f64)))))) (*.f64 (*.f64 1/2 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3))) (sqrt.f64 (/.f64 1 (PI.f64)))))) (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (*.f64 15/8 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 7))))): 5 points increase in error, 2 points decrease in error
   (+.f64 (+.f64 (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) x) (sqrt.f64 (/.f64 1 (PI.f64)))) (+.f64 (*.f64 3/4 (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (Rewrite<= associate-*r*_binary64 (*.f64 1/2 (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3)) (sqrt.f64 (/.f64 1 (PI.f64)))))))) (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (*.f64 15/8 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 7))))): 0 points increase in error, 0 points decrease in error
   (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 (*.f64 3/4 (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (*.f64 1/2 (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3)) (sqrt.f64 (/.f64 1 (PI.f64)))))) (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) x) (sqrt.f64 (/.f64 1 (PI.f64)))))) (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (*.f64 15/8 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 7))))): 0 points increase in error, 0 points decrease in error
   (+.f64 (Rewrite<= associate-+r+_binary64 (+.f64 (*.f64 3/4 (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (*.f64 1/2 (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3)) (sqrt.f64 (/.f64 1 (PI.f64))))) (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) x) (sqrt.f64 (/.f64 1 (PI.f64))))))) (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (*.f64 15/8 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 7))))): 23 points increase in error, 27 points decrease in error
   (+.f64 (+.f64 (*.f64 3/4 (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (*.f64 1/2 (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3)) (sqrt.f64 (/.f64 1 (PI.f64))))) (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) x) (sqrt.f64 (/.f64 1 (PI.f64)))))) (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 15/8 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 7))) (sqrt.f64 (/.f64 1 (PI.f64)))))): 0 points increase in error, 0 points decrease in error
   (+.f64 (+.f64 (*.f64 3/4 (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (*.f64 1/2 (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3)) (sqrt.f64 (/.f64 1 (PI.f64))))) (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) x) (sqrt.f64 (/.f64 1 (PI.f64)))))) (Rewrite<= associate-*r*_binary64 (*.f64 15/8 (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 7)) (sqrt.f64 (/.f64 1 (PI.f64))))))): 10 points increase in error, 11 points decrease in error
   (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 15/8 (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 7)) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (*.f64 3/4 (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 5)) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (*.f64 1/2 (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) (pow.f64 x 3)) (sqrt.f64 (/.f64 1 (PI.f64))))) (*.f64 (/.f64 (exp.f64 (pow.f64 x 2)) x) (sqrt.f64 (/.f64 1 (PI.f64)))))))): 0 points increase in error, 0 points decrease in error

7. Applied egg-rr 1.2

   \[\leadsto \sqrt{\frac{1}{\pi}} \cdot \left({\left(e^{x}\right)}^{x} \cdot \left(\frac{1}{x} + \left(\frac{0.75}{{x}^{5}} + \frac{0.5}{{x}^{3}}\right)\right) + 1.875 \cdot \frac{\color{blue}{e^{x \cdot x}}}{{x}^{7}}\right) \]

8. Final simplification 1.2

   \[\leadsto \sqrt{\frac{1}{\pi}} \cdot \left({\left(e^{x}\right)}^{x} \cdot \left(\frac{1}{x} + \left(\frac{0.75}{{x}^{5}} + \frac{0.5}{{x}^{3}}\right)\right) + 1.875 \cdot \frac{e^{x \cdot x}}{{x}^{7}}\right) \]

Alternatives

Alternative 1
Error	1.3
Cost	46144

\[\frac{{\left(e^{x}\right)}^{x}}{x \cdot \sqrt{\pi}} \cdot \left(1 + \mathsf{fma}\left(1.875, {x}^{-6}, \frac{0.75}{{x}^{4}} + \frac{0.5}{x \cdot x}\right)\right) \]

Alternative 2
Error	1.2
Cost	40000

\[\sqrt{\frac{1}{\pi}} \cdot \left(\frac{{\left(e^{x}\right)}^{x}}{x} \cdot \left(\frac{1.875}{{x}^{6}} + \left(\frac{0.75}{{x}^{4}} + \left(1 + \frac{0.5}{x \cdot x}\right)\right)\right)\right) \]

Alternative 3
Error	1.3
Cost	39936

\[\frac{\frac{{\left(e^{x}\right)}^{x}}{\left|x\right|}}{\sqrt{\pi}} \cdot \left(1 + \left(\frac{1.875}{{x}^{6}} + \frac{0.5 + \frac{0.75}{x \cdot x}}{x \cdot x}\right)\right) \]

Alternative 4
Error	2.7
Cost	33664

\[\left(\sqrt{\frac{1}{\pi}} \cdot \frac{e^{x \cdot x}}{x}\right) \cdot \left(\frac{1.875}{{x}^{6}} + \left(1 + \left(\frac{0.75}{{x}^{4}} + \frac{0.5}{x \cdot x}\right)\right)\right) \]

Alternative 5
Error	2.7
Cost	33600

\[\left(1 + \left(\frac{1.875}{{x}^{6}} + \frac{0.5 + \frac{0.75}{x \cdot x}}{x \cdot x}\right)\right) \cdot \frac{\frac{e^{x \cdot x}}{\left|x\right|}}{\sqrt{\pi}} \]

Alternative 6
Error	41.2
Cost	26944

\[\left(\sqrt{\frac{1}{\pi}} \cdot \frac{e^{x \cdot x}}{x}\right) \cdot \left(1 + \left(\frac{0.75}{{x}^{4}} + \frac{0.5}{x \cdot x}\right)\right) \]

Alternative 7
Error	44.5
Cost	20224

\[\left(1 + \frac{0.5}{x \cdot x}\right) \cdot \left(\sqrt{\frac{1}{\pi}} \cdot \frac{e^{x \cdot x}}{x}\right) \]

Alternative 8
Error	48.2
Cost	19712

\[\sqrt{\frac{1}{\pi}} \cdot \frac{e^{x \cdot x}}{x} \]

Alternative 9
Error	56.7
Cost	13056

\[\frac{\frac{2.1875}{x}}{\sqrt{\pi}} \]

Reproduce

herbie shell --seed 2022310 
(FPCore (x)
  :name "Jmat.Real.erfi, branch x greater than or equal to 5"
  :precision binary64
  :pre (>= x 0.5)
  (* (* (/ 1.0 (sqrt PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1.0 (fabs x)) (* (/ 1.0 2.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))) (* (/ 3.0 4.0) (* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))) (* (/ 15.0 8.0) (* (* (* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x)))))))