Average Error: 0.1 → 0.7
Time: 9.5s
Precision: binary64
Cost: 39428
\[x \leq 0.5\]
\[\left|\frac{1}{\sqrt{\pi}} \cdot \left(\left(\left(2 \cdot \left|x\right| + \frac{2}{3} \cdot \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{5} \cdot \left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{21} \cdot \left(\left(\left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right)\right| \]
↓
\[\begin{array}{l} t_0 := 0.2 \cdot {x}^{5}\\ \mathbf{if}\;x \leq -12226.198624689428:\\ \;\;\;\;\left|\frac{t_0 + 0.047619047619047616 \cdot {x}^{7}}{\sqrt{\pi}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\mathsf{fma}\left(2, x, 0.6666666666666666 \cdot {x}^{3} + t_0\right) \cdot \sqrt{\frac{1}{\pi}}\right|\\ \end{array} \]
(FPCore (x)
 :precision binary64
 (fabs
  (*
   (/ 1.0 (sqrt PI))
   (+
    (+
     (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x))))
     (*
      (/ 1.0 5.0)
      (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x))))
    (*
     (/ 1.0 21.0)
     (*
      (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))
      (fabs x)))))))
↓
(FPCore (x)
 :precision binary64
 (let* ((t_0 (* 0.2 (pow x 5.0))))
   (if (<= x -12226.198624689428)
     (fabs (/ (+ t_0 (* 0.047619047619047616 (pow x 7.0))) (sqrt PI)))
     (fabs
      (*
       (fma 2.0 x (+ (* 0.6666666666666666 (pow x 3.0)) t_0))
       (sqrt (/ 1.0 PI)))))))
double code(double x) {
	return fabs(((1.0 / sqrt(((double) M_PI))) * ((((2.0 * fabs(x)) + ((2.0 / 3.0) * ((fabs(x) * fabs(x)) * fabs(x)))) + ((1.0 / 5.0) * ((((fabs(x) * fabs(x)) * fabs(x)) * fabs(x)) * fabs(x)))) + ((1.0 / 21.0) * ((((((fabs(x) * fabs(x)) * fabs(x)) * fabs(x)) * fabs(x)) * fabs(x)) * fabs(x))))));
}
↓
double code(double x) {
	double t_0 = 0.2 * pow(x, 5.0);
	double tmp;
	if (x <= -12226.198624689428) {
		tmp = fabs(((t_0 + (0.047619047619047616 * pow(x, 7.0))) / sqrt(((double) M_PI))));
	} else {
		tmp = fabs((fma(2.0, x, ((0.6666666666666666 * pow(x, 3.0)) + t_0)) * sqrt((1.0 / ((double) M_PI)))));
	}
	return tmp;
}

function code(x)
	return abs(Float64(Float64(1.0 / sqrt(pi)) * Float64(Float64(Float64(Float64(2.0 * abs(x)) + Float64(Float64(2.0 / 3.0) * Float64(Float64(abs(x) * abs(x)) * abs(x)))) + Float64(Float64(1.0 / 5.0) * Float64(Float64(Float64(Float64(abs(x) * abs(x)) * abs(x)) * abs(x)) * abs(x)))) + Float64(Float64(1.0 / 21.0) * Float64(Float64(Float64(Float64(Float64(Float64(abs(x) * abs(x)) * abs(x)) * abs(x)) * abs(x)) * abs(x)) * abs(x))))))
end
↓
function code(x)
	t_0 = Float64(0.2 * (x ^ 5.0))
	tmp = 0.0
	if (x <= -12226.198624689428)
		tmp = abs(Float64(Float64(t_0 + Float64(0.047619047619047616 * (x ^ 7.0))) / sqrt(pi)));
	else
		tmp = abs(Float64(fma(2.0, x, Float64(Float64(0.6666666666666666 * (x ^ 3.0)) + t_0)) * sqrt(Float64(1.0 / pi))));
	end
	return tmp
end

code[x_] := N[Abs[N[(N[(1.0 / N[Sqrt[Pi], $MachinePrecision]), $MachinePrecision] * N[(N[(N[(N[(2.0 * N[Abs[x], $MachinePrecision]), $MachinePrecision] + N[(N[(2.0 / 3.0), $MachinePrecision] * N[(N[(N[Abs[x], $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / 5.0), $MachinePrecision] * N[(N[(N[(N[(N[Abs[x], $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / 21.0), $MachinePrecision] * N[(N[(N[(N[(N[(N[(N[Abs[x], $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision] * N[Abs[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]
↓
code[x_] := Block[{t$95$0 = N[(0.2 * N[Power[x, 5.0], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, -12226.198624689428], N[Abs[N[(N[(t$95$0 + N[(0.047619047619047616 * N[Power[x, 7.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Sqrt[Pi], $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[Abs[N[(N[(2.0 * x + N[(N[(0.6666666666666666 * N[Power[x, 3.0], $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision] * N[Sqrt[N[(1.0 / Pi), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]], $MachinePrecision]]]

\left|\frac{1}{\sqrt{\pi}} \cdot \left(\left(\left(2 \cdot \left|x\right| + \frac{2}{3} \cdot \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{5} \cdot \left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{21} \cdot \left(\left(\left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right)\right|
↓
\begin{array}{l}
t_0 := 0.2 \cdot {x}^{5}\\
\mathbf{if}\;x \leq -12226.198624689428:\\
\;\;\;\;\left|\frac{t_0 + 0.047619047619047616 \cdot {x}^{7}}{\sqrt{\pi}}\right|\\

\mathbf{else}:\\
\;\;\;\;\left|\mathsf{fma}\left(2, x, 0.6666666666666666 \cdot {x}^{3} + t_0\right) \cdot \sqrt{\frac{1}{\pi}}\right|\\


\end{array}

Error

Derivation

  1. Split input into 2 regimes

  2. if x < -12226.1986246894285

    1. Initial program 0.9

      \[\left|\frac{1}{\sqrt{\pi}} \cdot \left(\left(\left(2 \cdot \left|x\right| + \frac{2}{3} \cdot \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{5} \cdot \left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{21} \cdot \left(\left(\left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right)\right| \]

    2. Simplified0.6

      \[\leadsto \color{blue}{\left|\frac{\mathsf{fma}\left(0.2, {x}^{5}, \mathsf{fma}\left(x, \mathsf{fma}\left(0.6666666666666666, x \cdot x, 2\right), 0.047619047619047616 \cdot {x}^{7}\right)\right)}{\sqrt{\pi}}\right|} \]
      Proof
      (fabs.f64 (/.f64 (fma.f64 1/5 (pow.f64 x 5) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (Rewrite<= metadata-eval (/.f64 1 5)) (pow.f64 x 5) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (pow.f64 (Rewrite<= unpow1_binary64 (pow.f64 x 1)) 5) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (pow.f64 (Rewrite=> sqr-pow_binary64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2)))) 5) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 134 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (pow.f64 (Rewrite<= fabs-sqr_binary64 (fabs.f64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2))))) 5) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (pow.f64 (fabs.f64 (Rewrite<= sqr-pow_binary64 (pow.f64 x 1))) 5) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 134 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (pow.f64 (fabs.f64 (Rewrite=> unpow1_binary64 x)) 5) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (pow.f64 (fabs.f64 x) (Rewrite<= metadata-eval (+.f64 4 1))) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (pow.f64 (fabs.f64 x) (+.f64 (Rewrite<= metadata-eval (+.f64 3 1)) 1)) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (Rewrite<= pow-plus_binary64 (*.f64 (pow.f64 (fabs.f64 x) (+.f64 3 1)) (fabs.f64 x))) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (Rewrite<= pow-plus_binary64 (*.f64 (pow.f64 (fabs.f64 x) 3) (fabs.f64 x))) (fabs.f64 x)) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (Rewrite=> unpow3_binary64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (Rewrite<= unpow1_binary64 (pow.f64 x 1)) (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (Rewrite=> sqr-pow_binary64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2)))) (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 166 points increase in error, 16 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (Rewrite<= fabs-sqr_binary64 (fabs.f64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2))))) (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 (Rewrite<= sqr-pow_binary64 (pow.f64 x 1))) (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 16 points increase in error, 166 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 (Rewrite=> unpow1_binary64 x)) (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (fma.f64 (Rewrite<= metadata-eval (/.f64 2 3)) (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (fma.f64 (/.f64 2 3) (Rewrite<= sqr-abs_binary64 (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2)) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (Rewrite=> +-commutative_binary64 (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))))) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (Rewrite<= metadata-eval (/.f64 1 21)) (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (pow.f64 (Rewrite<= unpow1_binary64 (pow.f64 x 1)) 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (pow.f64 (Rewrite=> sqr-pow_binary64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2)))) 7)))) (sqrt.f64 (PI.f64)))): 134 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (pow.f64 (Rewrite<= fabs-sqr_binary64 (fabs.f64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2))))) 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (pow.f64 (fabs.f64 (Rewrite<= sqr-pow_binary64 (pow.f64 x 1))) 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 134 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (pow.f64 (fabs.f64 (Rewrite=> unpow1_binary64 x)) 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (pow.f64 (fabs.f64 x) (Rewrite<= metadata-eval (+.f64 6 1)))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (pow.f64 (fabs.f64 x) (+.f64 (Rewrite<= metadata-eval (*.f64 2 3)) 1))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (Rewrite<= pow-plus_binary64 (*.f64 (pow.f64 (fabs.f64 x) (*.f64 2 3)) (fabs.f64 x)))))) (sqrt.f64 (PI.f64)))): 2 points increase in error, 2 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (Rewrite<= pow-sqr_binary64 (*.f64 (pow.f64 (fabs.f64 x) 3) (pow.f64 (fabs.f64 x) 3))) (fabs.f64 x))))) (sqrt.f64 (PI.f64)))): 7 points increase in error, 1 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (Rewrite<= cube-prod_binary64 (pow.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) 3)) (fabs.f64 x))))) (sqrt.f64 (PI.f64)))): 8 points increase in error, 5 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (Rewrite=> unpow3_binary64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (*.f64 (fabs.f64 x) (fabs.f64 x))) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (fabs.f64 x))))) (sqrt.f64 (PI.f64)))): 4 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (fabs.f64 x) (fabs.f64 x))) (fabs.f64 x))))) (sqrt.f64 (PI.f64)))): 2 points increase in error, 6 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (fabs.f64 x))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 3 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (+.f64 (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 1 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (Rewrite<= associate-*r*_binary64 (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 1 points decrease in error
      (fabs.f64 (/.f64 (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))): 33 points increase in error, 129 points decrease in error
      (fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (Rewrite=> associate-+l+_binary64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))))): 1 points increase in error, 0 points decrease in error
      (fabs.f64 (Rewrite=> distribute-rgt-in_binary64 (+.f64 (*.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64))))))): 1 points increase in error, 1 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))) (*.f64 2 (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (+.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) (fabs.f64 x))) (*.f64 2 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (Rewrite=> distribute-rgt-out_binary64 (*.f64 (fabs.f64 x) (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 1 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (Rewrite=> associate-*l*_binary64 (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64))))) (*.f64 (+.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64))))) (*.f64 (+.f64 (*.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (fabs.f64 x)) (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 4 points increase in error, 2 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64))))) (*.f64 (Rewrite=> distribute-rgt-out_binary64 (*.f64 (fabs.f64 x) (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64))))) (Rewrite=> associate-*l*_binary64 (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))))))): 3 points increase in error, 3 points decrease in error
      (fabs.f64 (Rewrite=> distribute-lft-out_binary64 (*.f64 (fabs.f64 x) (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (*.f64 (fabs.f64 (Rewrite<= unpow1_binary64 (pow.f64 x 1))) (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64))))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (*.f64 (fabs.f64 (Rewrite=> sqr-pow_binary64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2))))) (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64))))))): 176 points increase in error, 1 points decrease in error
      (fabs.f64 (*.f64 (Rewrite=> fabs-sqr_binary64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2)))) (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64))))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (*.f64 (Rewrite<= sqr-pow_binary64 (pow.f64 x 1)) (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64))))))): 1 points increase in error, 176 points decrease in error
      (fabs.f64 (*.f64 (Rewrite=> unpow1_binary64 x) (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64))))))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> fabs-mul_binary64 (*.f64 (fabs.f64 x) (fabs.f64 (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (Rewrite<= fabs-fabs_binary64 (fabs.f64 (fabs.f64 x))) (fabs.f64 (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fabs-mul_binary64 (fabs.f64 (*.f64 (fabs.f64 x) (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (Rewrite<= distribute-lft-out_binary64 (+.f64 (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64))))) (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (fabs.f64 x) (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))) (/.f64 1 (sqrt.f64 (PI.f64))))) (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64))))))): 3 points increase in error, 3 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (fabs.f64 x)) (*.f64 (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64))))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (fabs.f64 x))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64))))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (Rewrite<= associate-*r*_binary64 (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64))))))): 2 points increase in error, 4 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (fabs.f64 x) (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2)) (/.f64 1 (sqrt.f64 (PI.f64))))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) (fabs.f64 x)) (*.f64 2 (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 0 points increase in error, 1 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 2 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (Rewrite<= distribute-rgt-in_binary64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))))))): 1 points increase in error, 1 points decrease in error
      (fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))): 0 points increase in error, 1 points decrease in error

    3. Taylor expanded in x around inf 0.8

      \[\leadsto \left|\color{blue}{0.2 \cdot \left({x}^{5} \cdot \sqrt{\frac{1}{\pi}}\right) + 0.047619047619047616 \cdot \left({x}^{7} \cdot \sqrt{\frac{1}{\pi}}\right)}\right| \]

    4. Simplified0.8

      \[\leadsto \left|\color{blue}{\sqrt{\frac{1}{\pi}} \cdot \mathsf{fma}\left(0.047619047619047616, {x}^{7}, 0.2 \cdot {x}^{5}\right)}\right| \]
      Proof
      (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 1/21 (pow.f64 x 7) (*.f64 1/5 (pow.f64 x 5)))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 1/21 (pow.f64 x 7)) (*.f64 1/5 (pow.f64 x 5))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 1/5 (pow.f64 x 5)) (*.f64 1/21 (pow.f64 x 7))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 (*.f64 1/5 (pow.f64 x 5)) (sqrt.f64 (/.f64 1 (PI.f64)))) (*.f64 (*.f64 1/21 (pow.f64 x 7)) (sqrt.f64 (/.f64 1 (PI.f64)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 1/5 (*.f64 (pow.f64 x 5) (sqrt.f64 (/.f64 1 (PI.f64)))))) (*.f64 (*.f64 1/21 (pow.f64 x 7)) (sqrt.f64 (/.f64 1 (PI.f64))))): 6 points increase in error, 11 points decrease in error
      (+.f64 (*.f64 1/5 (*.f64 (pow.f64 x 5) (sqrt.f64 (/.f64 1 (PI.f64))))) (Rewrite<= associate-*r*_binary64 (*.f64 1/21 (*.f64 (pow.f64 x 7) (sqrt.f64 (/.f64 1 (PI.f64))))))): 7 points increase in error, 1 points decrease in error

    5. Applied egg-rr0.6

      \[\leadsto \left|\color{blue}{\frac{\mathsf{fma}\left(0.047619047619047616, {x}^{7}, 0.2 \cdot {x}^{5}\right)}{\sqrt{\pi}}}\right| \]

    6. Taylor expanded in x around 0 0.6

      \[\leadsto \left|\frac{\color{blue}{0.2 \cdot {x}^{5} + 0.047619047619047616 \cdot {x}^{7}}}{\sqrt{\pi}}\right| \]

    if -12226.1986246894285 < x

    1. Initial program 0.1

      \[\left|\frac{1}{\sqrt{\pi}} \cdot \left(\left(\left(2 \cdot \left|x\right| + \frac{2}{3} \cdot \left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{5} \cdot \left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right) + \frac{1}{21} \cdot \left(\left(\left(\left(\left(\left(\left|x\right| \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right) \cdot \left|x\right|\right)\right)\right| \]

    2. Simplified0.5

      \[\leadsto \color{blue}{\left|\frac{\mathsf{fma}\left(0.2, {x}^{5}, \mathsf{fma}\left(x, \mathsf{fma}\left(0.6666666666666666, x \cdot x, 2\right), 0.047619047619047616 \cdot {x}^{7}\right)\right)}{\sqrt{\pi}}\right|} \]
      Proof
      (fabs.f64 (/.f64 (fma.f64 1/5 (pow.f64 x 5) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (Rewrite<= metadata-eval (/.f64 1 5)) (pow.f64 x 5) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (pow.f64 (Rewrite<= unpow1_binary64 (pow.f64 x 1)) 5) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (pow.f64 (Rewrite=> sqr-pow_binary64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2)))) 5) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 134 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (pow.f64 (Rewrite<= fabs-sqr_binary64 (fabs.f64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2))))) 5) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (pow.f64 (fabs.f64 (Rewrite<= sqr-pow_binary64 (pow.f64 x 1))) 5) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 134 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (pow.f64 (fabs.f64 (Rewrite=> unpow1_binary64 x)) 5) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (pow.f64 (fabs.f64 x) (Rewrite<= metadata-eval (+.f64 4 1))) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (pow.f64 (fabs.f64 x) (+.f64 (Rewrite<= metadata-eval (+.f64 3 1)) 1)) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (Rewrite<= pow-plus_binary64 (*.f64 (pow.f64 (fabs.f64 x) (+.f64 3 1)) (fabs.f64 x))) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (Rewrite<= pow-plus_binary64 (*.f64 (pow.f64 (fabs.f64 x) 3) (fabs.f64 x))) (fabs.f64 x)) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (Rewrite=> unpow3_binary64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 x (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (Rewrite<= unpow1_binary64 (pow.f64 x 1)) (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (Rewrite=> sqr-pow_binary64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2)))) (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 166 points increase in error, 16 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (Rewrite<= fabs-sqr_binary64 (fabs.f64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2))))) (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 (Rewrite<= sqr-pow_binary64 (pow.f64 x 1))) (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 16 points increase in error, 166 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 (Rewrite=> unpow1_binary64 x)) (fma.f64 2/3 (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (fma.f64 (Rewrite<= metadata-eval (/.f64 2 3)) (*.f64 x x) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (fma.f64 (/.f64 2 3) (Rewrite<= sqr-abs_binary64 (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2)) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (Rewrite=> +-commutative_binary64 (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))))) (*.f64 1/21 (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (Rewrite<= metadata-eval (/.f64 1 21)) (pow.f64 x 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (pow.f64 (Rewrite<= unpow1_binary64 (pow.f64 x 1)) 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (pow.f64 (Rewrite=> sqr-pow_binary64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2)))) 7)))) (sqrt.f64 (PI.f64)))): 134 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (pow.f64 (Rewrite<= fabs-sqr_binary64 (fabs.f64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2))))) 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (pow.f64 (fabs.f64 (Rewrite<= sqr-pow_binary64 (pow.f64 x 1))) 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 134 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (pow.f64 (fabs.f64 (Rewrite=> unpow1_binary64 x)) 7)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (pow.f64 (fabs.f64 x) (Rewrite<= metadata-eval (+.f64 6 1)))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (pow.f64 (fabs.f64 x) (+.f64 (Rewrite<= metadata-eval (*.f64 2 3)) 1))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (Rewrite<= pow-plus_binary64 (*.f64 (pow.f64 (fabs.f64 x) (*.f64 2 3)) (fabs.f64 x)))))) (sqrt.f64 (PI.f64)))): 2 points increase in error, 2 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (Rewrite<= pow-sqr_binary64 (*.f64 (pow.f64 (fabs.f64 x) 3) (pow.f64 (fabs.f64 x) 3))) (fabs.f64 x))))) (sqrt.f64 (PI.f64)))): 7 points increase in error, 1 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (Rewrite<= cube-prod_binary64 (pow.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) 3)) (fabs.f64 x))))) (sqrt.f64 (PI.f64)))): 8 points increase in error, 5 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (Rewrite=> unpow3_binary64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (*.f64 (fabs.f64 x) (fabs.f64 x))) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (fabs.f64 x))))) (sqrt.f64 (PI.f64)))): 4 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (fabs.f64 x) (fabs.f64 x))) (fabs.f64 x))))) (sqrt.f64 (PI.f64)))): 2 points increase in error, 6 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fma.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (fabs.f64 x))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 3 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (fabs.f64 x) (+.f64 2 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (+.f64 (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 1 points decrease in error
      (fabs.f64 (/.f64 (fma.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (Rewrite<= associate-*r*_binary64 (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (Rewrite<= fma-def_binary64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 1 points decrease in error
      (fabs.f64 (/.f64 (+.f64 (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (/.f64 (Rewrite<= *-lft-identity_binary64 (*.f64 1 (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))) (sqrt.f64 (PI.f64)))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (Rewrite<= associate-*l/_binary64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))): 33 points increase in error, 129 points decrease in error
      (fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (Rewrite=> associate-+l+_binary64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))))): 1 points increase in error, 0 points decrease in error
      (fabs.f64 (Rewrite=> distribute-rgt-in_binary64 (+.f64 (*.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64))))))): 1 points increase in error, 1 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (Rewrite=> +-commutative_binary64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))) (*.f64 2 (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (+.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) (fabs.f64 x))) (*.f64 2 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (Rewrite=> distribute-rgt-out_binary64 (*.f64 (fabs.f64 x) (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 1 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (Rewrite=> associate-*l*_binary64 (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64))))) (*.f64 (+.f64 (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64))))) (*.f64 (+.f64 (*.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (fabs.f64 x)) (Rewrite=> associate-*r*_binary64 (*.f64 (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 4 points increase in error, 2 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64))))) (*.f64 (Rewrite=> distribute-rgt-out_binary64 (*.f64 (fabs.f64 x) (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64))))) (Rewrite=> associate-*l*_binary64 (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))))))): 3 points increase in error, 3 points decrease in error
      (fabs.f64 (Rewrite=> distribute-lft-out_binary64 (*.f64 (fabs.f64 x) (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (*.f64 (fabs.f64 (Rewrite<= unpow1_binary64 (pow.f64 x 1))) (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64))))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (*.f64 (fabs.f64 (Rewrite=> sqr-pow_binary64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2))))) (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64))))))): 176 points increase in error, 1 points decrease in error
      (fabs.f64 (*.f64 (Rewrite=> fabs-sqr_binary64 (*.f64 (pow.f64 x (/.f64 1 2)) (pow.f64 x (/.f64 1 2)))) (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64))))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (*.f64 (Rewrite<= sqr-pow_binary64 (pow.f64 x 1)) (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64))))))): 1 points increase in error, 176 points decrease in error
      (fabs.f64 (*.f64 (Rewrite=> unpow1_binary64 x) (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64))))))): 0 points increase in error, 0 points decrease in error
      (Rewrite=> fabs-mul_binary64 (*.f64 (fabs.f64 x) (fabs.f64 (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (Rewrite<= fabs-fabs_binary64 (fabs.f64 (fabs.f64 x))) (fabs.f64 (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (fabs.f64 (fabs.f64 x)) (fabs.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= fabs-mul_binary64 (fabs.f64 (*.f64 (fabs.f64 x) (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (Rewrite<= distribute-lft-out_binary64 (+.f64 (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64))))) (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64)))))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (fabs.f64 x) (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))) (/.f64 1 (sqrt.f64 (PI.f64))))) (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64))))))): 3 points increase in error, 3 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (fabs.f64 x)) (*.f64 (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64))))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (fabs.f64 x))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64))))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (Rewrite<= associate-*r*_binary64 (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (fabs.f64 x) (*.f64 (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2) (/.f64 1 (sqrt.f64 (PI.f64))))))): 2 points increase in error, 4 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))) (Rewrite<= associate-*l*_binary64 (*.f64 (*.f64 (fabs.f64 x) (+.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) 2)) (/.f64 1 (sqrt.f64 (PI.f64))))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 (*.f64 (/.f64 2 3) (*.f64 (fabs.f64 x) (fabs.f64 x))) (fabs.f64 x)) (*.f64 2 (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 0 points increase in error, 1 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 2 (fabs.f64 x))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (+.f64 (*.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (/.f64 1 (sqrt.f64 (PI.f64)))) (*.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))))) (/.f64 1 (sqrt.f64 (PI.f64)))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (Rewrite<= distribute-rgt-in_binary64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (+.f64 (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))))))): 1 points increase in error, 1 points decrease in error
      (fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (+.f64 (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))))): 0 points increase in error, 0 points decrease in error
      (fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 (PI.f64))) (Rewrite<= associate-+l+_binary64 (+.f64 (+.f64 (+.f64 (*.f64 2 (fabs.f64 x)) (*.f64 (/.f64 2 3) (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 5) (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (*.f64 (/.f64 1 21) (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x))))))): 0 points increase in error, 1 points decrease in error

    3. Taylor expanded in x around 0 0.7

      \[\leadsto \left|\color{blue}{0.6666666666666666 \cdot \left({x}^{3} \cdot \sqrt{\frac{1}{\pi}}\right) + \left(0.2 \cdot \left({x}^{5} \cdot \sqrt{\frac{1}{\pi}}\right) + 2 \cdot \left(x \cdot \sqrt{\frac{1}{\pi}}\right)\right)}\right| \]

    4. Simplified0.7

      \[\leadsto \left|\color{blue}{\sqrt{\frac{1}{\pi}} \cdot \mathsf{fma}\left(2, x, \mathsf{fma}\left(0.6666666666666666, {x}^{3}, 0.2 \cdot {x}^{5}\right)\right)}\right| \]
      Proof
      (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (fma.f64 2/3 (pow.f64 x 3) (*.f64 1/5 (pow.f64 x 5))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (fma.f64 2 x (Rewrite<= fma-def_binary64 (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 1/5 (pow.f64 x 5)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (Rewrite<= fma-def_binary64 (+.f64 (*.f64 2 x) (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 1/5 (pow.f64 x 5)))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= distribute-lft-out_binary64 (+.f64 (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (*.f64 2 x)) (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 1/5 (pow.f64 x 5)))))): 1 points increase in error, 0 points decrease in error
      (+.f64 (Rewrite<= *-commutative_binary64 (*.f64 (*.f64 2 x) (sqrt.f64 (/.f64 1 (PI.f64))))) (*.f64 (sqrt.f64 (/.f64 1 (PI.f64))) (+.f64 (*.f64 2/3 (pow.f64 x 3)) (*.f64 1/5 (pow.f64 x 5))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (*.f64 2 x) (sqrt.f64 (/.f64 1 (PI.f64)))) (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 (*.f64 2/3 (pow.f64 x 3)) (sqrt.f64 (/.f64 1 (PI.f64)))) (*.f64 (*.f64 1/5 (pow.f64 x 5)) (sqrt.f64 (/.f64 1 (PI.f64))))))): 1 points increase in error, 1 points decrease in error
      (+.f64 (*.f64 (*.f64 2 x) (sqrt.f64 (/.f64 1 (PI.f64)))) (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 2/3 (*.f64 (pow.f64 x 3) (sqrt.f64 (/.f64 1 (PI.f64)))))) (*.f64 (*.f64 1/5 (pow.f64 x 5)) (sqrt.f64 (/.f64 1 (PI.f64)))))): 0 points increase in error, 0 points decrease in error
      (+.f64 (*.f64 (*.f64 2 x) (sqrt.f64 (/.f64 1 (PI.f64)))) (+.f64 (*.f64 2/3 (*.f64 (pow.f64 x 3) (sqrt.f64 (/.f64 1 (PI.f64))))) (Rewrite<= associate-*r*_binary64 (*.f64 1/5 (*.f64 (pow.f64 x 5) (sqrt.f64 (/.f64 1 (PI.f64)))))))): 6 points increase in error, 3 points decrease in error
      (+.f64 (Rewrite<= associate-*r*_binary64 (*.f64 2 (*.f64 x (sqrt.f64 (/.f64 1 (PI.f64)))))) (+.f64 (*.f64 2/3 (*.f64 (pow.f64 x 3) (sqrt.f64 (/.f64 1 (PI.f64))))) (*.f64 1/5 (*.f64 (pow.f64 x 5) (sqrt.f64 (/.f64 1 (PI.f64))))))): 1 points increase in error, 0 points decrease in error
      (Rewrite<= +-commutative_binary64 (+.f64 (+.f64 (*.f64 2/3 (*.f64 (pow.f64 x 3) (sqrt.f64 (/.f64 1 (PI.f64))))) (*.f64 1/5 (*.f64 (pow.f64 x 5) (sqrt.f64 (/.f64 1 (PI.f64)))))) (*.f64 2 (*.f64 x (sqrt.f64 (/.f64 1 (PI.f64))))))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-+r+_binary64 (+.f64 (*.f64 2/3 (*.f64 (pow.f64 x 3) (sqrt.f64 (/.f64 1 (PI.f64))))) (+.f64 (*.f64 1/5 (*.f64 (pow.f64 x 5) (sqrt.f64 (/.f64 1 (PI.f64))))) (*.f64 2 (*.f64 x (sqrt.f64 (/.f64 1 (PI.f64)))))))): 0 points increase in error, 0 points decrease in error

    5. Applied egg-rr0.7

      \[\leadsto \left|\sqrt{\frac{1}{\pi}} \cdot \mathsf{fma}\left(2, x, \color{blue}{0.6666666666666666 \cdot {x}^{3} + 0.2 \cdot {x}^{5}}\right)\right| \]
  3. Recombined 2 regimes into one program.

  4. Final simplification0.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -12226.198624689428:\\ \;\;\;\;\left|\frac{0.2 \cdot {x}^{5} + 0.047619047619047616 \cdot {x}^{7}}{\sqrt{\pi}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\mathsf{fma}\left(2, x, 0.6666666666666666 \cdot {x}^{3} + 0.2 \cdot {x}^{5}\right) \cdot \sqrt{\frac{1}{\pi}}\right|\\ \end{array} \]

Alternatives

Alternative 1
Error0.1
Cost85888
\[\begin{array}{l} t_0 := \left|x\right| \cdot \left(x \cdot x\right)\\ t_1 := \left|x\right| \cdot \left(\left|x\right| \cdot t_0\right)\\ \left|\frac{1}{\sqrt{\pi}} \cdot \left(\left(\left(2 \cdot \left|x\right| + 0.6666666666666666 \cdot t_0\right) + 0.2 \cdot t_1\right) + 0.047619047619047616 \cdot \left(\left|x\right| \cdot \left(\left|x\right| \cdot t_1\right)\right)\right)\right| \end{array} \]
Alternative 2
Error0.5
Cost52288
\[\left|\frac{\mathsf{fma}\left(0.047619047619047616, x \cdot {x}^{6}, \mathsf{fma}\left(2, x, 0.6666666666666666 \cdot {x}^{3} + 0.2 \cdot {x}^{5}\right)\right)}{\sqrt{\pi}}\right| \]
Alternative 3
Error0.5
Cost45824
\[\left|\frac{\mathsf{fma}\left(0.2, {x}^{5}, \mathsf{fma}\left(x, 2 + 0.6666666666666666 \cdot \left(x \cdot x\right), 0.047619047619047616 \cdot {x}^{7}\right)\right)}{\sqrt{\pi}}\right| \]
Alternative 4
Error1.3
Cost45440
\[\left|\frac{\mathsf{fma}\left(0.2, {x}^{5}, \mathsf{fma}\left(x, 2, 0.047619047619047616 \cdot {x}^{7}\right)\right)}{\sqrt{\pi}}\right| \]
Alternative 5
Error0.7
Cost39364
\[\begin{array}{l} t_0 := 0.2 \cdot {x}^{5}\\ \mathbf{if}\;x \leq -12226.198624689428:\\ \;\;\;\;\left|\frac{t_0 + 0.047619047619047616 \cdot {x}^{7}}{\sqrt{\pi}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\sqrt{\frac{1}{\pi}} \cdot \mathsf{fma}\left(x, \mathsf{fma}\left(x, x \cdot 0.6666666666666666, 2\right), t_0\right)\right|\\ \end{array} \]
Alternative 6
Error0.8
Cost32772
\[\begin{array}{l} \mathbf{if}\;x \leq -12226.198624689428:\\ \;\;\;\;\left|\frac{0.2 \cdot {x}^{5} + 0.047619047619047616 \cdot {x}^{7}}{\sqrt{\pi}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\sqrt{\frac{1}{\pi}} \cdot \left(x \cdot \left(2 + 0.6666666666666666 \cdot \left(x \cdot x\right)\right)\right)\right|\\ \end{array} \]
Alternative 7
Error0.8
Cost26052
\[\begin{array}{l} \mathbf{if}\;x \leq -12226.198624689428:\\ \;\;\;\;\left|{x}^{7} \cdot \frac{0.047619047619047616}{\sqrt{\pi}}\right|\\ \mathbf{else}:\\ \;\;\;\;\left|\sqrt{\frac{1}{\pi}} \cdot \left(x \cdot \left(2 + 0.6666666666666666 \cdot \left(x \cdot x\right)\right)\right)\right|\\ \end{array} \]
Alternative 8
Error4.4
Cost19968
\[\left|\sqrt{\frac{1}{\pi}} \cdot \left(x \cdot \left(2 + 0.6666666666666666 \cdot \left(x \cdot x\right)\right)\right)\right| \]
Alternative 9
Error5.2
Cost19456
\[\left|\frac{2}{\frac{\sqrt{\pi}}{x}}\right| \]
Alternative 10
Error4.8
Cost19456
\[\left|x \cdot \frac{2}{\sqrt{\pi}}\right| \]

Error

Reproduce

herbie shell --seed 2022295 
(FPCore (x)
  :name "Jmat.Real.erfi, branch x less than or equal to 0.5"
  :precision binary64
  :pre (<= x 0.5)
  (fabs (* (/ 1.0 (sqrt PI)) (+ (+ (+ (* 2.0 (fabs x)) (* (/ 2.0 3.0) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1.0 5.0) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))))