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

Average Accuracy: 95.5% → 98.0%

Time: 16.3s

Precision: binary64

Cost: 46464

\[x \geq 0.5\]

Math

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

↓

\[\frac{{\left(e^{x}\right)}^{x}}{\left|x\right| \cdot {\left({\pi}^{0.25}\right)}^{2}} \cdot \left(\frac{0.5 + \frac{0.75}{x \cdot x}}{x \cdot x} + \left(1 + \frac{1.875}{{x}^{6}}\right)\right) \]

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
 (*
  (/ (pow (exp x) x) (* (fabs x) (pow (pow PI 0.25) 2.0)))
  (+ (/ (+ 0.5 (/ 0.75 (* x x))) (* x x)) (+ 1.0 (/ 1.875 (pow x 6.0))))))

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 (pow(exp(x), x) / (fabs(x) * pow(pow(((double) M_PI), 0.25), 2.0))) * (((0.5 + (0.75 / (x * x))) / (x * x)) + (1.0 + (1.875 / pow(x, 6.0))));
}

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.pow(Math.exp(x), x) / (Math.abs(x) * Math.pow(Math.pow(Math.PI, 0.25), 2.0))) * (((0.5 + (0.75 / (x * x))) / (x * x)) + (1.0 + (1.875 / Math.pow(x, 6.0))));
}

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.pow(math.exp(x), x) / (math.fabs(x) * math.pow(math.pow(math.pi, 0.25), 2.0))) * (((0.5 + (0.75 / (x * x))) / (x * x)) + (1.0 + (1.875 / math.pow(x, 6.0))))

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(Float64((exp(x) ^ x) / Float64(abs(x) * ((pi ^ 0.25) ^ 2.0))) * Float64(Float64(Float64(0.5 + Float64(0.75 / Float64(x * x))) / Float64(x * x)) + Float64(1.0 + Float64(1.875 / (x ^ 6.0)))))
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 = ((exp(x) ^ x) / (abs(x) * ((pi ^ 0.25) ^ 2.0))) * (((0.5 + (0.75 / (x * x))) / (x * x)) + (1.0 + (1.875 / (x ^ 6.0))));
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[(N[Power[N[Exp[x], $MachinePrecision], x], $MachinePrecision] / N[(N[Abs[x], $MachinePrecision] * N[Power[N[Power[Pi, 0.25], $MachinePrecision], 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[(N[(N[(0.5 + N[(0.75 / N[(x * x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[(x * x), $MachinePrecision]), $MachinePrecision] + N[(1.0 + N[(1.875 / N[Power[x, 6.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 95.5%

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

2. Simplified 97.9%

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

   [Start] 95.5	\[ \left(\frac{1}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\left(\frac{1}{\left|x\right|} + \frac{1}{2} \cdot \left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{3}{4} \cdot \left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{15}{8} \cdot \left(\left(\left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) \]
   distribute-lft-in [=>] 95.5	\[ \color{blue}{\left(\frac{1}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\frac{1}{\left|x\right|} + \frac{1}{2} \cdot \left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{3}{4} \cdot \left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \left(\frac{1}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\frac{15}{8} \cdot \left(\left(\left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right)} \]
   +-commutative [=>] 95.5	\[ \color{blue}{\left(\frac{1}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\frac{15}{8} \cdot \left(\left(\left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \left(\frac{1}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\frac{1}{\left|x\right|} + \frac{1}{2} \cdot \left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{3}{4} \cdot \left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right)} \]

3. Applied egg-rr 98.0%

   \[\leadsto \frac{{\left(e^{x}\right)}^{x}}{\left|x\right| \cdot \color{blue}{{\left({\pi}^{0.25}\right)}^{2}}} \cdot \left(\frac{0.5 + \frac{0.75}{x \cdot x}}{x \cdot x} + \left(1 + \frac{1.875}{{x}^{6}}\right)\right) \]
   Proof

   [Start] 97.9	\[ \frac{{\left(e^{x}\right)}^{x}}{\left|x\right| \cdot \sqrt{\pi}} \cdot \left(\frac{0.5 + \frac{0.75}{x \cdot x}}{x \cdot x} + \left(1 + \frac{1.875}{{x}^{6}}\right)\right) \]
   add-sqr-sqrt [=>] 98.0	\[ \frac{{\left(e^{x}\right)}^{x}}{\left|x\right| \cdot \color{blue}{\left(\sqrt{\sqrt{\pi}} \cdot \sqrt{\sqrt{\pi}}\right)}} \cdot \left(\frac{0.5 + \frac{0.75}{x \cdot x}}{x \cdot x} + \left(1 + \frac{1.875}{{x}^{6}}\right)\right) \]
   pow2 [=>] 98.0	\[ \frac{{\left(e^{x}\right)}^{x}}{\left|x\right| \cdot \color{blue}{{\left(\sqrt{\sqrt{\pi}}\right)}^{2}}} \cdot \left(\frac{0.5 + \frac{0.75}{x \cdot x}}{x \cdot x} + \left(1 + \frac{1.875}{{x}^{6}}\right)\right) \]
   pow1/2 [=>] 98.0	\[ \frac{{\left(e^{x}\right)}^{x}}{\left|x\right| \cdot {\left(\sqrt{\color{blue}{{\pi}^{0.5}}}\right)}^{2}} \cdot \left(\frac{0.5 + \frac{0.75}{x \cdot x}}{x \cdot x} + \left(1 + \frac{1.875}{{x}^{6}}\right)\right) \]
   sqrt-pow1 [=>] 98.0	\[ \frac{{\left(e^{x}\right)}^{x}}{\left|x\right| \cdot {\color{blue}{\left({\pi}^{\left(\frac{0.5}{2}\right)}\right)}}^{2}} \cdot \left(\frac{0.5 + \frac{0.75}{x \cdot x}}{x \cdot x} + \left(1 + \frac{1.875}{{x}^{6}}\right)\right) \]
   metadata-eval [=>] 98.0	\[ \frac{{\left(e^{x}\right)}^{x}}{\left|x\right| \cdot {\left({\pi}^{\color{blue}{0.25}}\right)}^{2}} \cdot \left(\frac{0.5 + \frac{0.75}{x \cdot x}}{x \cdot x} + \left(1 + \frac{1.875}{{x}^{6}}\right)\right) \]

4. Final simplification 98.0%

   \[\leadsto \frac{{\left(e^{x}\right)}^{x}}{\left|x\right| \cdot {\left({\pi}^{0.25}\right)}^{2}} \cdot \left(\frac{0.5 + \frac{0.75}{x \cdot x}}{x \cdot x} + \left(1 + \frac{1.875}{{x}^{6}}\right)\right) \]

Alternatives

Alternative 1
Accuracy	98.0%
Cost	46208

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

Alternative 2
Accuracy	98.0%
Cost	33664

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

Alternative 3
Accuracy	97.9%
Cost	33536

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

Alternative 4
Accuracy	98.0%
Cost	33536

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

Alternative 5
Accuracy	97.9%
Cost	33536

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

Alternative 6
Accuracy	97.9%
Cost	33536

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

Alternative 7
Accuracy	95.7%
Cost	27200

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

Alternative 8
Accuracy	95.7%
Cost	27200

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

Alternative 9
Accuracy	95.7%
Cost	27200

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

Alternative 10
Accuracy	36.2%
Cost	26688

\[\frac{\frac{e^{x \cdot x + \left(\frac{0.5}{x \cdot x} + \frac{0.625}{{x}^{4}}\right)}}{x}}{\sqrt{\pi}} \]

Alternative 11
Accuracy	30.5%
Cost	19968

\[\frac{\frac{e^{x \cdot x + \frac{0.5}{x \cdot x}}}{x}}{\sqrt{\pi}} \]

Alternative 12
Accuracy	24.6%
Cost	19584

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

Alternative 13
Accuracy	10.8%
Cost	13312

\[\frac{\frac{0.5}{x}}{x \cdot \left(x \cdot \sqrt{\pi}\right)} \]

Reproduce

herbie shell --seed 2023133 
(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)))))))