Average Error: 2.8 → 1.2
Time: 14.5s
Precision: binary64
Cost: 78016
\[x \geq 0.5\]
\[\left(\frac{1}{\sqrt{\pi}} \cdot e^{\left|x\right| \cdot \left|x\right|}\right) \cdot \left(\left(\left(\frac{1}{\left|x\right|} + \frac{1}{2} \cdot \left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{3}{4} \cdot \left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) + \frac{15}{8} \cdot \left(\left(\left(\left(\left(\left(\frac{1}{\left|x\right|} \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right) \cdot \frac{1}{\left|x\right|}\right)\right) \]
↓
\[\frac{\frac{{\left(e^{x}\right)}^{x} \cdot \mathsf{fma}\left({x}^{-5}, \mathsf{fma}\left(1.875, {x}^{-2}, 0.75\right), \frac{\mathsf{fma}\left(0.5, {x}^{-2}, 1\right)}{x}\right)}{{\pi}^{0.25}}}{{\pi}^{0.25}} \]
(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)
    (fma
     (pow x -5.0)
     (fma 1.875 (pow x -2.0) 0.75)
     (/ (fma 0.5 (pow x -2.0) 1.0) x)))
   (pow PI 0.25))
  (pow PI 0.25)))
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) * fma(pow(x, -5.0), fma(1.875, pow(x, -2.0), 0.75), (fma(0.5, pow(x, -2.0), 1.0) / x))) / pow(((double) M_PI), 0.25)) / pow(((double) M_PI), 0.25);
}

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(Float64((exp(x) ^ x) * fma((x ^ -5.0), fma(1.875, (x ^ -2.0), 0.75), Float64(fma(0.5, (x ^ -2.0), 1.0) / x))) / (pi ^ 0.25)) / (pi ^ 0.25))
end

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[(N[Power[N[Exp[x], $MachinePrecision], x], $MachinePrecision] * N[(N[Power[x, -5.0], $MachinePrecision] * N[(1.875 * N[Power[x, -2.0], $MachinePrecision] + 0.75), $MachinePrecision] + N[(N[(0.5 * N[Power[x, -2.0], $MachinePrecision] + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[Pi, 0.25], $MachinePrecision]), $MachinePrecision] / N[Power[Pi, 0.25], $MachinePrecision]), $MachinePrecision]

\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{\frac{{\left(e^{x}\right)}^{x} \cdot \mathsf{fma}\left({x}^{-5}, \mathsf{fma}\left(1.875, {x}^{-2}, 0.75\right), \frac{\mathsf{fma}\left(0.5, {x}^{-2}, 1\right)}{x}\right)}{{\pi}^{0.25}}}{{\pi}^{0.25}}

Error

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. Simplified2.8

    \[\leadsto \color{blue}{e^{x \cdot x} \cdot \frac{\frac{1 + \frac{0.5}{x \cdot x}}{\left|x\right|} + {\left(\frac{1}{\left|x\right|}\right)}^{5} \cdot \left(0.75 + \frac{1.875}{x \cdot x}\right)}{\sqrt{\pi}}} \]
    Proof
    (*.f64 (exp.f64 (*.f64 x x)) (/.f64 (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (*.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
    (*.f64 (exp.f64 (Rewrite<= sqr-abs_binary64 (*.f64 (fabs.f64 x) (fabs.f64 x)))) (/.f64 (+.f64 (/.f64 (+.f64 1 (/.f64 1/2 (*.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 42 points increase in error, 0 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.f64 (+.f64 (/.f64 (+.f64 1 (/.f64 (Rewrite<= metadata-eval (*.f64 1/2 1)) (*.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 42 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.f64 (+.f64 (/.f64 (+.f64 1 (/.f64 (*.f64 (Rewrite<= metadata-eval (/.f64 1 2)) 1) (*.f64 x x))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 42 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.f64 (+.f64 (/.f64 (+.f64 1 (/.f64 (*.f64 (/.f64 1 2) 1) (Rewrite<= sqr-abs_binary64 (*.f64 (fabs.f64 x) (fabs.f64 x))))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 42 points increase in error, 0 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.f64 (+.f64 (/.f64 (+.f64 1 (Rewrite<= associate-*r/_binary64 (*.f64 (/.f64 1 2) (/.f64 1 (*.f64 (fabs.f64 x) (fabs.f64 x)))))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 42 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.f64 (+.f64 (/.f64 (+.f64 1 (*.f64 (/.f64 1 2) (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 1 (fabs.f64 x)) (fabs.f64 x))))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 40 points increase in error, 0 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.f64 (+.f64 (/.f64 (+.f64 1 (*.f64 (/.f64 1 2) (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 1 (fabs.f64 x)))) (fabs.f64 x)))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 38 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.f64 (+.f64 (/.f64 (+.f64 1 (*.f64 (/.f64 1 2) (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 33 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.f64 (+.f64 (/.f64 (+.f64 1 (Rewrite<= *-rgt-identity_binary64 (*.f64 (*.f64 (/.f64 1 2) (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) 1))) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 42 points increase in error, 0 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.f64 (+.f64 (/.f64 (Rewrite=> distribute-rgt1-in_binary64 (*.f64 (+.f64 (*.f64 (/.f64 1 2) (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) 1) 1)) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 2 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.f64 (+.f64 (/.f64 (Rewrite=> *-rgt-identity_binary64 (+.f64 (*.f64 (/.f64 1 2) (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) 1)) (fabs.f64 x)) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 42 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.f64 (+.f64 (/.f64 (+.f64 (*.f64 (/.f64 1 2) (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) 1) (Rewrite<= /-rgt-identity_binary64 (/.f64 (fabs.f64 x) 1))) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 42 points increase in error, 0 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.f64 (+.f64 (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (+.f64 (*.f64 (/.f64 1 2) (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) 1) 1) (fabs.f64 x))) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 42 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.f64 (+.f64 (Rewrite<= associate-*r/_binary64 (*.f64 (+.f64 (*.f64 (/.f64 1 2) (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) 1) (/.f64 1 (fabs.f64 x)))) (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 42 points increase in error, 0 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.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 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 42 points increase in error, 0 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.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 (pow.f64 (/.f64 1 (fabs.f64 x)) 5) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 42 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.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 (pow.f64 (/.f64 1 (fabs.f64 x)) (Rewrite<= metadata-eval (+.f64 4 1))) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 42 points increase in error, 0 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.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 (Rewrite<= pow-plus_binary64 (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 4) (/.f64 1 (fabs.f64 x)))) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 42 points increase in error, 0 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.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 (pow.f64 (/.f64 1 (fabs.f64 x)) (Rewrite<= metadata-eval (+.f64 3 1))) (/.f64 1 (fabs.f64 x))) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 42 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.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 (Rewrite<= pow-plus_binary64 (*.f64 (pow.f64 (/.f64 1 (fabs.f64 x)) 3) (/.f64 1 (fabs.f64 x)))) (/.f64 1 (fabs.f64 x))) (+.f64 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 42 points increase in error, 0 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.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 (*.f64 (Rewrite=> unpow3_binary64 (*.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 3/4 (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 42 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.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 (*.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 (Rewrite<= metadata-eval (/.f64 3 4)) (/.f64 15/8 (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 29 points increase in error, 4 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.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 (*.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 3 4) (/.f64 (Rewrite<= metadata-eval (*.f64 1 15/8)) (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 1 points increase in error, 26 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.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 (*.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 3 4) (/.f64 (*.f64 1 (Rewrite<= metadata-eval (/.f64 15 8))) (*.f64 x x))))) (sqrt.f64 (PI.f64)))): 42 points increase in error, 0 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.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 (*.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 3 4) (/.f64 (*.f64 1 (/.f64 15 8)) (Rewrite<= sqr-abs_binary64 (*.f64 (fabs.f64 x) (fabs.f64 x))))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 42 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.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 (*.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 3 4) (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.f64 15 8)))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 42 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.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 (*.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 3 4) (*.f64 (Rewrite<= associate-/l/_binary64 (/.f64 (/.f64 1 (fabs.f64 x)) (fabs.f64 x))) (/.f64 15 8))))) (sqrt.f64 (PI.f64)))): 42 points increase in error, 0 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.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 (*.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 3 4) (*.f64 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (/.f64 1 (fabs.f64 x)))) (fabs.f64 x)) (/.f64 15 8))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 42 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.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 (*.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 3 4) (*.f64 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) (/.f64 15 8))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 22 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.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))))) (Rewrite<= distribute-lft-out_binary64 (+.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 3 4)) (*.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 (*.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 15 8)))))) (sqrt.f64 (PI.f64)))): 42 points increase in error, 0 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.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 (Rewrite<= *-commutative_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 (*.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 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x))) (/.f64 15 8))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 42 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.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 (/.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)))) (Rewrite<= associate-*l*_binary64 (*.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 (/.f64 1 (fabs.f64 x)) (/.f64 1 (fabs.f64 x)))) (/.f64 15 8))))) (sqrt.f64 (PI.f64)))): 42 points increase in error, 0 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.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 (/.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 (Rewrite<= associate-*l*_binary64 (*.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 15 8)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 42 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.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 (/.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)))) (Rewrite<= *-commutative_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))))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 42 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.f64 (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)))))) (sqrt.f64 (PI.f64)))): 34 points increase in error, 7 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (/.f64 (+.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))))) (Rewrite<= /-rgt-identity_binary64 (/.f64 (sqrt.f64 (PI.f64)) 1)))): 42 points increase in error, 0 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 (+.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))))) 1) (sqrt.f64 (PI.f64))))): 0 points increase in error, 42 points decrease in error
    (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (Rewrite<= associate-*r/_binary64 (*.f64 (+.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))))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 32 points increase in error, 1 points decrease in error
    (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (+.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)))))) (/.f64 1 (sqrt.f64 (PI.f64))))): 42 points increase in error, 0 points decrease in error
    (Rewrite<= *-commutative_binary64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (*.f64 (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x))) (+.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)))))))): 42 points increase in error, 0 points decrease in error
    (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (exp.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)))) (+.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))))))): 0 points increase in error, 42 points decrease in error

  3. Applied egg-rr1.2

    \[\leadsto \color{blue}{\frac{\frac{{\left(e^{x}\right)}^{x} \cdot \mathsf{fma}\left({x}^{-5}, \mathsf{fma}\left(1.875, {x}^{-2}, 0.75\right), \frac{\mathsf{fma}\left(0.5, {x}^{-2}, 1\right)}{x}\right)}{{\pi}^{0.25}}}{{\pi}^{0.25}}} \]

  4. Final simplification1.2

    \[\leadsto \frac{\frac{{\left(e^{x}\right)}^{x} \cdot \mathsf{fma}\left({x}^{-5}, \mathsf{fma}\left(1.875, {x}^{-2}, 0.75\right), \frac{\mathsf{fma}\left(0.5, {x}^{-2}, 1\right)}{x}\right)}{{\pi}^{0.25}}}{{\pi}^{0.25}} \]

Alternatives

Alternative 1
Error1.2
Cost33536
\[\frac{{\left(e^{x}\right)}^{x}}{x \cdot \sqrt{\pi}} \cdot \left(1 + \left(\frac{1.875}{{x}^{6}} + \frac{0.5 + \frac{0.75}{x \cdot x}}{x \cdot x}\right)\right) \]
Alternative 2
Error2.7
Cost27200
\[\left(1 + \left(\frac{1.875}{{x}^{6}} + \frac{0.5 + \frac{0.75}{x \cdot x}}{x \cdot x}\right)\right) \cdot \frac{e^{x \cdot x}}{x \cdot \sqrt{\pi}} \]
Alternative 3
Error44.7
Cost26560
\[\sqrt{\frac{1}{\pi}} \cdot \left(\left(1 + \frac{0.5}{x \cdot x}\right) \cdot \frac{{\left(e^{x}\right)}^{x}}{x}\right) \]
Alternative 4
Error47.9
Cost26432
\[\frac{e^{x \cdot x}}{\sqrt{\pi}} \cdot \left(\frac{0.75}{{x}^{5}} + \frac{1}{x}\right) \]
Alternative 5
Error48.3
Cost26048
\[\sqrt{\frac{1}{\pi}} \cdot \frac{{\left(e^{x}\right)}^{x}}{x} \]
Alternative 6
Error48.3
Cost26048
\[\frac{{\left(e^{x}\right)}^{x}}{\frac{x}{\sqrt{\frac{1}{\pi}}}} \]
Alternative 7
Error48.3
Cost19712
\[\sqrt{\frac{1}{\pi}} \cdot \frac{e^{x \cdot x}}{x} \]
Alternative 8
Error56.8
Cost19648
\[1.875 \cdot \frac{\sqrt{\frac{1}{\pi}}}{{x}^{7}} \]
Alternative 9
Error57.1
Cost13312
\[\frac{\frac{0.5}{x}}{x \cdot \left(x \cdot \sqrt{\pi}\right)} \]

Error

Reproduce

herbie shell --seed 2022340 
(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)))))))