Metrics for ENA, Section 1.4, Exercise 4d

analyze26.0ms (0.3%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	12.8%	87.2%	0%	0%	0%	0
0%	0%	12.8%	87.2%	0%	0%	0%	1
0%	0%	12.8%	87.2%	0%	0%	0%	2
50%	6.4%	6.4%	87.2%	0%	0%	0%	3
57.1%	6.4%	4.8%	87.2%	0%	1.6%	0%	4
69.2%	7.2%	3.2%	87.2%	0%	2.4%	0%	5
75%	7.2%	2.4%	87.2%	0%	3.2%	0%	6
82.6%	7.6%	1.6%	87.2%	0%	3.6%	0%	7
86.4%	7.6%	1.2%	87.2%	0%	4%	0%	8
90.7%	7.8%	0.8%	87.2%	0%	4.2%	0%	9
92.6%	7.8%	0.6%	87.2%	0%	4.4%	0%	10
95%	7.9%	0.4%	87.2%	0%	4.5%	0%	11
96.3%	8%	0.3%	87.2%	0%	4.5%	0%	12

Compiler

Compiled 25 to 17 computations (32% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-<=: 5.0ms (43.4% of total)

ival-sub: 2.0ms (17.4% of total)

ival-mult: 2.0ms (17.4% of total)

ival-sqrt: 2.0ms (17.4% of total)

ival-and: 1.0ms (8.7% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

sample1.6s (16.5%)

Results

544.0ms	4799×	0	valid
516.0ms	2773×	1	valid
165.0ms	684×	2	valid
20.0ms	159×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 774.0ms

ival-<=: 213.0ms (27.5% of total)

ival-mult: 157.0ms (20.3% of total)

ival-sub: 137.0ms (17.7% of total)

ival-sqrt: 113.0ms (14.6% of total)

backward-pass: 83.0ms (10.7% of total)

ival-and: 51.0ms (6.6% of total)

const: 20.0ms (2.6% of total)

Bogosity

preprocess60.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

598×	`fnmadd-define`
520×	`fmsub-define`
502×	`fnmsub-define`
464×	`sum3-define`
440×	`fmm-def`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	48
1	60	46
2	152	43
3	429	43
4	1134	43
5	2073	43
6	2317	43
7	2341	43
0	6	7
1	13	7
2	21	7
3	35	7
4	58	7
5	134	7
6	345	7
7	539	7
8	717	7
9	941	7
10	1105	7
11	1117	7
0	1117	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- x (sqrt (- (* x x) eps)))

Outputs
(- x (sqrt (- (* x x) eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Call 2

Inputs
(- x (sqrt (- (* x x) eps)))
(- (neg x) (sqrt (- (* (neg x) (neg x)) eps)))
(- x (sqrt (- (* x x) (neg eps))))
(neg (- (neg x) (sqrt (- (* (neg x) (neg x)) eps))))
(neg (- x (sqrt (- (* x x) (neg eps)))))
(- eps (sqrt (- (* eps eps) x)))

Outputs
(- x (sqrt (- (* x x) eps)))
(- x (sqrt (- (square x) eps)))
(- (neg x) (sqrt (- (* (neg x) (neg x)) eps)))
(- (neg x) (sqrt (- (square x) eps)))
(- x (sqrt (- (* x x) (neg eps))))
(- x (sqrt (fma x x eps)))
(neg (- (neg x) (sqrt (- (* (neg x) (neg x)) eps))))
(+ x (sqrt (- (square x) eps)))
(neg (- x (sqrt (- (* x x) (neg eps)))))
(- (sqrt (fma x x eps)) x)
(- eps (sqrt (- (* eps eps) x)))
(- eps (sqrt (fmsub eps eps x)))

explain140.0ms (1.4%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
104	-	-	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`
0	-	-	`x`
0	-	-	`(*.f64 x x)`
0	-	-	`(-.f64 (*.f64 x x) eps)`
0	-	-	`(sqrt.f64 (-.f64 (*.f64 x x) eps))`
0	-	-	`eps`

Results

37.0ms	308×	0	valid
30.0ms	168×	1	valid
10.0ms	36×	2	valid

Compiler

Compiled 64 to 20 computations (68.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 33.0ms

ival-sqrt: 13.0ms (39.5% of total)

ival-sub: 8.0ms (24.3% of total)

ival-mult: 7.0ms (21.3% of total)

backward-pass: 5.0ms (15.2% of total)

const: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 10 to 6 computations (40% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	62.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Compiler

Compiled 10 to 6 computations (40% saved)

simplify28.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(-.f64 (*.f64 x x) eps)
✓	cost-diff	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	cost-diff	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Rules

324×	`sum3-define`
296×	`fnmadd-define`
214×	`fma-define`
184×	`fma-lowering-fma.f32`
184×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	20
1	13	20
2	21	20
3	35	20
4	58	20
5	134	20
6	345	20
7	539	20
8	717	20
9	941	20
10	1105	20
11	1117	20
0	1117	20

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- x (sqrt (- (* x x) eps)))
x
(sqrt (- (* x x) eps))
(- (* x x) eps)
(* x x)
eps

Outputs
(- x (sqrt (- (* x x) eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt (- (* x x) eps))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(- (* x x) eps)
(-.f64 (*.f64 x x) eps)
(* x x)
(*.f64 x x)
eps

localize50.0ms (0.5%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(-.f64 (*.f64 x x) eps)
✓	accuracy	100.0%	(sqrt.f64 (-.f64 (*.f64 x x) eps))
✓	accuracy	62.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Results

16.0ms	84×	1	valid
15.0ms	154×	0	valid
5.0ms	18×	2	valid

Compiler

Compiled 27 to 7 computations (74.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-sub: 4.0ms (30.2% of total)

ival-sqrt: 3.0ms (22.6% of total)

ival-mult: 3.0ms (22.6% of total)

backward-pass: 2.0ms (15.1% of total)

const: 0.0ms (0% of total)

series8.0ms (0.1%)

Counts

4 → 84

Calls

Call 1

Inputs
#<alt (- x (sqrt (- (* x x) eps)))>
#<alt (sqrt (- (* x x) eps))>
#<alt (- (* x x) eps)>
#<alt (* x x)>

Outputs
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)>
#<alt (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)>
#<alt (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))>
#<alt x>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))>
#<alt (* -1 eps)>
#<alt (- (pow x 2) eps)>
#<alt (- (pow x 2) eps)>
#<alt (- (pow x 2) eps)>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (* -1 eps)>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* -1 eps)>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>

Calls

21 calls:

Time	Variable		Point	Expression
1.0ms	x	@	inf	(- x (sqrt (- (* x x) eps)))
1.0ms	eps	@	inf	(- x (sqrt (- (* x x) eps)))
1.0ms	eps	@	0	(- x (sqrt (- (* x x) eps)))
1.0ms	eps	@	-inf	(- x (sqrt (- (* x x) eps)))
1.0ms	x	@	0	(- x (sqrt (- (* x x) eps)))

rewrite318.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

2262×	`-lowering-.f32`
2262×	`-lowering-.f64`
1852×	`fma-lowering-fma.f32`
1852×	`fma-lowering-fma.f64`
1702×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	41	18
2	328	18
3	4080	18
0	8354	18

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 209

Calls

Call 1

Inputs
(- x (sqrt (- (* x x) eps)))
(sqrt (- (* x x) eps))
(- (* x x) eps)
(* x x)

Outputs
(+.f64 x (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps))) x)
(+.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (.f64 x x) (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (.f64 x x) (-.f64 (*.f64 x x) eps))))))
(+.f64 (/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(-.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (.f64 x x) (-.f64 (.f64 x x) eps)))) (/.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (.f64 x x) (-.f64 (*.f64 x x) eps)))))
(-.f64 (/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(-.f64 #s(literal 0 binary64) (-.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) x))
(-.f64 (+.f64 x #s(literal 0 binary64)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(fma.f64 x (/.f64 (.f64 x x) (+.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (.f64 x x) (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (.f64 x x) (-.f64 (.f64 x x) eps))))))
(fma.f64 x (/.f64 x (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))))
(fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))))
(fma.f64 (.f64 x x) (/.f64 x (+.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (.f64 x x) (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (.f64 x x) (-.f64 (.f64 x x) eps))))))
(fma.f64 (.f64 x (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (.f64 x x) (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (.f64 x x) (-.f64 (*.f64 x x) eps))))))
(fma.f64 #s(literal -1 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps)) x)
(fma.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) (+.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (.f64 x x) (-.f64 (.f64 x x) eps)))) (neg.f64 (/.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (.f64 x x) (-.f64 (*.f64 x x) eps))))))
(fma.f64 (pow.f64 x #s(literal 1/2 binary64)) (pow.f64 x #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(fma.f64 (/.f64 (.f64 x (.f64 x x)) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (pow.f64 (+.f64 (-.f64 (.f64 x x) eps) (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) #s(literal 3 binary64)))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (+.f64 (-.f64 (.f64 x x) eps) (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (-.f64 (+.f64 (-.f64 (.f64 x x) eps) (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 x x)))) (neg.f64 (/.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)) (+.f64 (.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (.f64 x x) (-.f64 (.f64 x x) eps))))))
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(/.f64 (.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 eps eps) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps eps)))) (+.f64 (.f64 x x) eps)))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 eps (.f64 eps (.f64 eps eps)))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps eps)) (+.f64 (*.f64 x x) eps)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps))))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps))))))
(/.f64 (neg.f64 (+.f64 (neg.f64 (.f64 x (.f64 x (.f64 x x)))) (.f64 eps eps))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps)))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps)))) (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps))))) (+.f64 (.f64 (/.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps)))) (/.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps))))) (.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps)))) (/.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (*.f64 x x) eps))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) eps)) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 eps eps) (+.f64 (.f64 x x) eps)) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) eps)) (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) eps))) (+.f64 (.f64 (/.f64 (.f64 eps eps) (+.f64 (.f64 x x) eps)) (/.f64 (.f64 eps eps) (+.f64 (.f64 x x) eps))) (.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) eps)) (/.f64 (.f64 eps eps) (+.f64 (*.f64 x x) eps))))))
(/.f64 (-.f64 (.f64 eps eps) (.f64 x (.f64 x (.f64 x x)))) (-.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 x x)))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps)))) (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps))))) (.f64 (/.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps)))) (/.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps)))))) (+.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps)))) (/.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (*.f64 x x) eps))))))
(/.f64 (-.f64 (.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) eps)) (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) eps))) (.f64 (/.f64 (.f64 eps eps) (+.f64 (.f64 x x) eps)) (/.f64 (.f64 eps eps) (+.f64 (.f64 x x) eps)))) (+.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 (.f64 x x) eps)) (/.f64 (.f64 eps eps) (+.f64 (.f64 x x) eps))))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps))))) (sqrt.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps)))))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x x) eps)))) (pow.f64 (+.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))
(/.f64 (.f64 (sqrt.f64 (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps)))) (sqrt.f64 (-.f64 (.f64 x x) eps))) (sqrt.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps)))))
(/.f64 (.f64 (sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x x) eps))) (sqrt.f64 (-.f64 (.f64 x x) eps))) (pow.f64 (+.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))
(/.f64 (.f64 (-.f64 (.f64 (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps))))) (+.f64 (.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps))))) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (*.f64 eps eps))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 eps (.f64 eps eps)) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) eps))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 eps eps) (+.f64 (.f64 x (.f64 x (.f64 x x))) (*.f64 eps eps)))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 eps (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) eps))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps eps)))
(pow.f64 (sqrt.f64 (-.f64 (*.f64 x x) eps)) #s(literal 2 binary64))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps))) #s(literal 2 binary64))
(pow.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (*.f64 x x) eps)) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) #s(literal -1 binary64))
(.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(.f64 (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (*.f64 x x) eps)))))
(.f64 (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 x x))))))
(.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps))) (.f64 (-.f64 (.f64 x x) eps) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (*.f64 x x) eps))))))
(.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps)))))
(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 (.f64 x x) eps))) (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 (.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) eps)))
(.f64 (+.f64 (.f64 x x) eps) (.f64 (-.f64 (.f64 x x) eps) (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) eps))))
(.f64 (+.f64 (.f64 x x) eps) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x x) eps)))
(.f64 #s(literal 1 binary64) (-.f64 (.f64 x x) eps))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (*.f64 x x) eps))))))
(.f64 (+.f64 (neg.f64 (.f64 x (.f64 x (.f64 x x)))) (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 x x) eps))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps)))) (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (*.f64 eps eps))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) eps)) (.f64 (-.f64 (.f64 x x) eps) (+.f64 (*.f64 x x) eps)))
(.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) eps)))
(.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) (.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(.f64 (pow.f64 (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (*.f64 x x) eps)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x x) eps)) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 x x) eps)) #s(literal 1 binary64)))
(.f64 (.f64 (sqrt.f64 (-.f64 (.f64 x x) eps)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64))) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)))
(.f64 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -1 binary64)) (sqrt.f64 (-.f64 (.f64 x x) eps)))
(.f64 (/.f64 (.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x x) eps)) (.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x x) eps))) (-.f64 (.f64 x x) eps))
(.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))))) (.f64 (.f64 eps (+.f64 (.f64 x x) eps)) (.f64 eps (.f64 (+.f64 (.f64 x x) eps) (.f64 eps (+.f64 (.f64 x x) eps))))))) (+.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x))))) (.f64 (.f64 eps (+.f64 (.f64 x x) eps)) (-.f64 (.f64 eps (+.f64 (.f64 x x) eps)) (.f64 x (.f64 x (.f64 x x)))))))
(.f64 (/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps))) (.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps))))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 (.f64 x x) eps))))
(.f64 (/.f64 (.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x x) eps)) (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps)))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (-.f64 eps (.f64 x x)))))
(exp.f64 (*.f64 #s(literal 2 binary64) (log.f64 x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 2 binary64))
(*.f64 x x)
(*.f64 (exp.f64 (log.f64 x)) (exp.f64 (log.f64 x)))

simplify274.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

4906×	`-lowering-.f32`
4906×	`-lowering-.f64`
2924×	`+-lowering-+.f64`
2924×	`+-lowering-+.f32`
2068×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	257	1162
1	856	1066
2	3033	1031
0	8035	1031

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

Inputs
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -1 eps)
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)

Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))))
(- x (* (sqrt eps) (sqrt -1)))
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64))))) (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))))) (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 x x))) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (+.f64 (+.f64 (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x))) (.f64 eps #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 x x))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64))) eps)) (+.f64 (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (*.f64 x x)))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (+.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))) #s(literal -2 binary64)) (/.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 x x))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(.f64 (+.f64 (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/16 binary64)) (pow.f64 x #s(literal 6 binary64))) (+.f64 (+.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))) #s(literal -2 binary64)) (/.f64 (.f64 eps #s(literal 1/2 binary64)) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
(* 1/2 (/ eps x))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(/.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 x x))) x)
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 eps (+.f64 (/.f64 (.f64 eps #s(literal 5/128 binary64)) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (-.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (+.f64 (-.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (/.f64 (.f64 (*.f64 x x) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64)))) (+.f64 (-.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (/.f64 (.f64 (.f64 x x) #s(literal -1/2 binary64)) (sqrt.f64 #s(literal -1 binary64)))))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* -1 (* eps (- (* -1 (/ (+ x (* 1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (+.f64 x (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 x x))))) eps)))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (-.f64 x (/.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (-.f64 (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 x x) (.f64 x x)))) (.f64 (.f64 (sqrt.f64 eps) #s(literal 1/2 binary64)) (*.f64 x x)))) eps)) eps)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+.f64 (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 x x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+.f64 (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (.f64 x x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (*.f64 eps eps)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64))))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(+.f64 (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (/.f64 #s(literal 1/8 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/16 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x)) (/.f64 (.f64 (.f64 eps eps) #s(literal -1/8 binary64)) (.f64 (.f64 x x) (.f64 x x))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x)) (+.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal -1/8 binary64)) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64)))))))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(.f64 x (+.f64 #s(literal -1 binary64) (/.f64 (.f64 eps #s(literal 1/2 binary64)) (*.f64 x x))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(.f64 x (+.f64 #s(literal -1 binary64) (+.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 x x)))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x)) (+.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal -1/8 binary64)) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) x))
x
(+ x (* -1/2 (/ eps x)))
(+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+.f64 x (.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 x (.f64 x x))))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+.f64 x (.f64 eps (+.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -1/8 binary64) (.f64 x (*.f64 x x))))) (/.f64 #s(literal -1/2 binary64) x))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (/.f64 (.f64 (*.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64)))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 eps (+.f64 (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (/.f64 (.f64 (.f64 x x) #s(literal 1/2 binary64)) (sqrt.f64 #s(literal -1 binary64))))) (+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (.f64 (.f64 x x) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (.f64 #s(literal 1/16 binary64) (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(*.f64 (sqrt.f64 eps) (-.f64 #s(literal 0 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(-.f64 #s(literal 0 binary64) (.f64 eps (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (*.f64 x x)))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(-.f64 #s(literal 0 binary64) (.f64 eps (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x)) #s(literal 1/2 binary64))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (.f64 x x) (*.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(.f64 eps (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x x))) (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (.f64 x x) (.f64 x x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal 1/16 binary64) (*.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))))))))))
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(pow x 2)
(*.f64 x x)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* eps (- (/ (pow x 2) eps) 1))
(.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps)))
(* eps (- (/ (pow x 2) eps) 1))
(.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps)))
(* eps (- (/ (pow x 2) eps) 1))
(.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps)))
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps)))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps)))
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)

eval44.0ms (0.5%)

Compiler: Compiled 9770 to 1039 computations (89.4% saved)

prune51.0ms (0.5%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	277	16	293
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	277	17	294

Accuracy

99.8%

Counts

294 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	29.8%	(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (-.f64 (.f64 x x) eps) (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x x) (-.f64 (*.f64 x x) eps))))))
	62.5%	(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	35.0%	(/.f64 (+.f64 (+.f64 (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x))) (.f64 eps #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 x x))) x)
	41.0%	(/.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 x x))) x)
	29.1%	(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64))) eps)) (+.f64 (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (*.f64 x x)))) x)
▶	62.5%	(-.f64 (/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
	62.5%	(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)))))
	3.7%	(-.f64 x (+.f64 x (.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 x (.f64 x x)))))))
	6.8%	(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
▶	6.0%	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
✓	62.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
▶	58.3%	(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
▶	62.8%	(-.f64 x (sqrt.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps)))))
	4.3%	(-.f64 x x)
▶	3.5%	(*.f64 x #s(literal 2 binary64))
	25.6%	(.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 eps (+.f64 (/.f64 (.f64 eps #s(literal 5/128 binary64)) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
	43.4%	(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))

Compiler

Compiled 688 to 358 computations (48% saved)

simplify181.0ms (1.9%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
✓	cost-diff	7424	(-.f64 (/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
✓	cost-diff	0	(-.f64 #s(literal 0 binary64) eps)
✓	cost-diff	0	(sqrt.f64 (-.f64 #s(literal 0 binary64) eps))
✓	cost-diff	0	(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
✓	cost-diff	0	(/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x)))
✓	cost-diff	256	(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
✓	cost-diff	512	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
✓	cost-diff	0	(*.f64 x #s(literal 2 binary64))
✓	cost-diff	0	(+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps))
✓	cost-diff	256	(.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps)))
✓	cost-diff	256	(sqrt.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps))))
✓	cost-diff	256	(-.f64 x (sqrt.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps)))))

Rules

1942×	`sum5-define`
1734×	`-lowering-.f32`
1734×	`-lowering-.f64`
1192×	`/-lowering-/.f32`
1192×	`/-lowering-/.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	28	179
1	79	176
2	187	162
3	624	133
4	2333	133
0	8102	133

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(- x (sqrt (* eps (+ -1 (/ (* x x) eps)))))
x
(sqrt (* eps (+ -1 (/ (* x x) eps))))
(* eps (+ -1 (/ (* x x) eps)))
eps
(+ -1 (/ (* x x) eps))
-1
(/ (* x x) eps)
(* x x)
(* x 2)
x
2
(- x (* x (+ 1 (/ (* eps -1/2) (* x x)))))
x
(* x (+ 1 (/ (* eps -1/2) (* x x))))
(+ 1 (/ (* eps -1/2) (* x x)))
1
(/ (* eps -1/2) (* x x))
(* eps -1/2)
eps
-1/2
(* x x)
(- x (sqrt (- 0 eps)))
x
(sqrt (- 0 eps))
(- 0 eps)
0
eps
(- (/ (* x x) (+ x (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (+ x (sqrt (- (* x x) eps)))))
(/ (* x x) (+ x (sqrt (- (* x x) eps))))
(* x x)
x
(+ x (sqrt (- (* x x) eps)))
(sqrt (- (* x x) eps))
(- (* x x) eps)
eps
(/ (- (* x x) eps) (+ x (sqrt (- (* x x) eps))))

Outputs
(- x (sqrt (* eps (+ -1 (/ (* x x) eps)))))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(sqrt (* eps (+ -1 (/ (* x x) eps))))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(* eps (+ -1 (/ (* x x) eps)))
(-.f64 (*.f64 x x) eps)
eps
(+ -1 (/ (* x x) eps))
(+.f64 #s(literal -1 binary64) (/.f64 x (/.f64 eps x)))
-1
#s(literal -1 binary64)
(/ (* x x) eps)
(/.f64 x (/.f64 eps x))
(* x x)
(*.f64 x x)
(* x 2)
(*.f64 x #s(literal 2 binary64))
x
2
#s(literal 2 binary64)
(- x (* x (+ 1 (/ (* eps -1/2) (* x x)))))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
x
(* x (+ 1 (/ (* eps -1/2) (* x x))))
(+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+ 1 (/ (* eps -1/2) (* x x)))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x)))
1
#s(literal 1 binary64)
(/ (* eps -1/2) (* x x))
(/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x))
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
eps
-1/2
#s(literal -1/2 binary64)
(* x x)
(*.f64 x x)
(- x (sqrt (- 0 eps)))
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
x
(sqrt (- 0 eps))
(sqrt.f64 (-.f64 #s(literal 0 binary64) eps))
(- 0 eps)
(-.f64 #s(literal 0 binary64) eps)
0
#s(literal 0 binary64)
eps
(- (/ (* x x) (+ x (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (+ x (sqrt (- (* x x) eps)))))
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/ (* x x) (+ x (sqrt (- (* x x) eps))))
(/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
(* x x)
(*.f64 x x)
x
(+ x (sqrt (- (* x x) eps)))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(sqrt (- (* x x) eps))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(- (* x x) eps)
(-.f64 (*.f64 x x) eps)
eps
(/ (- (* x x) eps) (+ x (sqrt (- (* x x) eps))))
(/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))

localize295.0ms (3%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	accuracy	99.5%	(/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
✓	accuracy	90.8%	(/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
✓	accuracy	82.0%	(-.f64 (/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
✓	accuracy	100.0%	(-.f64 #s(literal 0 binary64) eps)
✓	accuracy	100.0%	(sqrt.f64 (-.f64 #s(literal 0 binary64) eps))
✓	accuracy	100.0%	(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x)))
✓	accuracy	83.6%	(/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x))
✓	accuracy	82.0%	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
✓	accuracy	80.5%	(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
✓	accuracy	100.0%	(*.f64 x #s(literal 2 binary64))
✓	accuracy	100.0%	(sqrt.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps))))
✓	accuracy	99.5%	(.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps)))
✓	accuracy	82.6%	(/.f64 (*.f64 x x) eps)
✓	accuracy	82.0%	(-.f64 x (sqrt.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps)))))

Results

95.0ms	152×	0	valid
75.0ms	11×	2	valid
55.0ms	55×	0	invalid
32.0ms	38×	1	valid

Compiler

Compiled 200 to 29 computations (85.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 46.0ms

ival-mult: 11.0ms (23.8% of total)

ival-div: 10.0ms (21.6% of total)

ival-sub: 9.0ms (19.5% of total)

ival-sqrt: 7.0ms (15.1% of total)

backward-pass: 5.0ms (10.8% of total)

ival-add: 5.0ms (10.8% of total)

const: 1.0ms (2.2% of total)

series51.0ms (0.5%)

Counts

18 → 384

Calls

Call 1

Inputs
#<alt (- x (sqrt (* eps (+ -1 (/ (* x x) eps)))))>
#<alt (sqrt (* eps (+ -1 (/ (* x x) eps))))>
#<alt (* eps (+ -1 (/ (* x x) eps)))>
#<alt (+ -1 (/ (* x x) eps))>
#<alt (* x 2)>
#<alt (- x (* x (+ 1 (/ (* eps -1/2) (* x x)))))>
#<alt (* x (+ 1 (/ (* eps -1/2) (* x x))))>
#<alt (+ 1 (/ (* eps -1/2) (* x x)))>
#<alt (/ (* eps -1/2) (* x x))>
#<alt (- x (sqrt (- 0 eps)))>
#<alt (sqrt (- 0 eps))>
#<alt (- 0 eps)>
#<alt (- (/ (* x x) (+ x (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (+ x (sqrt (- (* x x) eps)))))>
#<alt (/ (* x x) (+ x (sqrt (- (* x x) eps))))>
#<alt (* x x)>
#<alt (+ x (sqrt (- (* x x) eps)))>
#<alt (/ (* x x) eps)>
#<alt (/ (- (* x x) eps) (+ x (sqrt (- (* x x) eps))))>

Outputs
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)>
#<alt (/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)>
#<alt (/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (pow (sqrt -1) 3))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (/ (pow x 4) (sqrt -1)))) (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))>
#<alt x>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt eps) (pow (sqrt -1) 3)))>
#<alt (* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))>
#<alt (* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3))))))>
#<alt (* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))>
#<alt (pow x 2)>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (* -1 eps)>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* eps (- (/ (pow x 2) eps) 1))>
#<alt (* -1 eps)>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))>
#<alt (* -1 eps)>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (+ (* -1 eps) (pow x 2))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt (* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))>
#<alt -1>
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#<alt (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))>
#<alt (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* x (+ (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))))>
#<alt (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* x (+ (* x (- (+ (* -1 (* x (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))))>
#<alt (* 1/2 x)>
#<alt (* x (- (+ 1/2 (* -1/2 (/ eps (pow x 2)))) (* -1/8 (/ eps (pow x 2)))))>
#<alt (* x (- (+ 1/2 (+ (* -1 (/ (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2))) (pow x 4))) (* -1/2 (/ eps (pow x 2))))) (* -1/8 (/ eps (pow x 2)))))>
#<alt (* x (- (+ 1/2 (+ (* -1 (/ (+ (* -1/16 (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps)))) (+ (* -1/64 (pow eps 3)) (* 1/4 (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2))))))) (pow x 6))) (* -1/2 (/ eps (pow x 2))))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* 2 (/ (pow x 3) eps))>
#<alt (* -1 (* (pow x 3) (- (* 5/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 5/8 eps)) (pow x 4))) (* 5/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 5/8 eps)))) (* 5/16 (pow eps 2)))) (pow x 6))) (* 5/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 5/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))))>
#<alt (* 1/2 x)>
#<alt (+ (* -3/8 (/ eps x)) (* 1/2 x))>
#<alt (+ (* 1/2 x) (* eps (- (* -1/16 (/ eps (pow x 3))) (* 3/8 (/ 1 x)))))>
#<alt (+ (* 1/2 x) (* eps (- (* eps (- (* -3/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 3/8 (/ 1 x)))))>
#<alt (* -1 (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* -1 (/ x (pow (sqrt -1) 2))))>
#<alt (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (pow eps 2))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (* -1 (/ x (pow (sqrt -1) 2))))>
#<alt (- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (* 1/2 (/ (* eps (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2)))) (pow eps 3))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* -1 (/ (- (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (+ (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))>

Calls

96 calls:

Time	Variable		Point	Expression
10.0ms	x	@	-inf	(* x 2)
3.0ms	x	@	0	(- x (sqrt (- 0 eps)))
2.0ms	x	@	0	(/ (* x x) (+ x (sqrt (- (* x x) eps))))
2.0ms	eps	@	-inf	(- (/ (* x x) (+ x (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (+ x (sqrt (- (* x x) eps)))))
1.0ms	eps	@	inf	(/ (- (* x x) eps) (+ x (sqrt (- (* x x) eps))))

rewrite400.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2588×	`fma-lowering-fma.f32`
2588×	`fma-lowering-fma.f64`
2538×	`-lowering-.f32`
2538×	`-lowering-.f64`
1762×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	28	129
1	218	126
2	2304	106
0	8482	106

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 665

Calls

Call 1

Inputs
(- x (sqrt (* eps (+ -1 (/ (* x x) eps)))))
(sqrt (* eps (+ -1 (/ (* x x) eps))))
(* eps (+ -1 (/ (* x x) eps)))
(+ -1 (/ (* x x) eps))
(* x 2)
(- x (* x (+ 1 (/ (* eps -1/2) (* x x)))))
(* x (+ 1 (/ (* eps -1/2) (* x x))))
(+ 1 (/ (* eps -1/2) (* x x)))
(/ (* eps -1/2) (* x x))
(- x (sqrt (- 0 eps)))
(sqrt (- 0 eps))
(- 0 eps)
(- (/ (* x x) (+ x (sqrt (- (* x x) eps)))) (/ (- (* x x) eps) (+ x (sqrt (- (* x x) eps)))))
(/ (* x x) (+ x (sqrt (- (* x x) eps))))
(* x x)
(+ x (sqrt (- (* x x) eps)))
(/ (* x x) eps)
(/ (- (* x x) eps) (+ x (sqrt (- (* x x) eps))))

Outputs
(+.f64 x (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(+.f64 (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (-.f64 #s(literal 0 binary64) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))))
(+.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) x)
(+.f64 (-.f64 #s(literal 0 binary64) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))))
(+.f64 (-.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) (+.f64 (.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (-.f64 (.f64 x x) eps)) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))))
(+.f64 (-.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) (fma.f64 (neg.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64))) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))
(+.f64 (-.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) (fma.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(+.f64 (-.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) (fma.f64 (neg.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps)))) (sqrt.f64 eps) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(+.f64 (-.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) (fma.f64 (neg.f64 (sqrt.f64 eps)) (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps))) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(+.f64 (fma.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) #s(literal 1 binary64) (.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64))))
(+.f64 (fma.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) eps))))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))))) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) eps)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 (*.f64 x x) eps)))))
(+.f64 (fma.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (.f64 (+.f64 (.f64 x x) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))))))) (fma.f64 (neg.f64 (+.f64 (.f64 x x) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (.f64 (+.f64 (.f64 x x) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))))))
(+.f64 (fma.f64 x (/.f64 x (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (.f64 (-.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) (/.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)))))) (fma.f64 (neg.f64 (-.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))) (.f64 (-.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) (/.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) (-.f64 (*.f64 x x) eps))))))
(+.f64 (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) #s(literal 1 binary64) (.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64))))
(+.f64 (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) eps))))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))))) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) eps)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) eps)))))
(+.f64 (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (.f64 (+.f64 (.f64 x x) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))))))) (fma.f64 (neg.f64 (+.f64 (.f64 x x) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (.f64 (+.f64 (.f64 x x) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))))))
(+.f64 (fma.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (.f64 (-.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) (/.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)))))) (fma.f64 (neg.f64 (-.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))) (.f64 (-.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) (/.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))))))
(+.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))) (fma.f64 (-.f64 #s(literal 0 binary64) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) #s(literal 1 binary64) (.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 1 binary64))))
(+.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) eps))))) (fma.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))))) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) eps)) (.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) eps)))))
(+.f64 (fma.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (.f64 (+.f64 (.f64 x x) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))))))) (fma.f64 (neg.f64 (+.f64 (.f64 x x) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (.f64 (+.f64 (.f64 x x) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))))))
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(/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps eps)) (.f64 (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) (+.f64 eps (*.f64 x x))))
(/.f64 (-.f64 (.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (.f64 (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) eps)) (pow.f64 (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) #s(literal 2 binary64)))
(/.f64 (-.f64 (.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) (.f64 x x)) eps)) (.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) (.f64 x x)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (.f64 (-.f64 #s(literal 0 binary64) (.f64 x x)) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) eps)) (.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (.f64 (-.f64 (.f64 x x) eps) #s(literal 1 binary64)) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 eps (.f64 eps eps))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 eps (.f64 x x)))) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps eps)) #s(literal 1 binary64)) (.f64 (+.f64 eps (.f64 x x)) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) eps))) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 eps (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 eps (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (.f64 (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 eps (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 eps (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (+.f64 (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 eps (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 (.f64 (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 eps (.f64 eps eps))) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 eps (.f64 x x)))))
(/.f64 (.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps eps)) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (+.f64 eps (*.f64 x x)))
(pow.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (.f64 x x) eps)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (.f64 x x) eps)) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(.f64 (-.f64 (.f64 x x) eps) (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(.f64 (-.f64 #s(literal 0 binary64) (-.f64 (.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (-.f64 (*.f64 x x) eps))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)) #s(literal -1 binary64)))
(.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (+.f64 (.f64 x x) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(.f64 (/.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(.f64 (pow.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (.f64 (.f64 x (.f64 x x)) (.f64 x (.f64 x x))) (.f64 eps (.f64 eps eps)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 eps (.f64 x x))))))
(.f64 (pow.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps eps))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 eps (*.f64 x x))))

simplify337.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

7636×	`-lowering-.f32`
7636×	`-lowering-.f64`
4130×	`+-lowering-+.f64`
4130×	`+-lowering-+.f32`
1220×	`associate-r`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	795	5023
1	2797	4439
0	8995	4439

Stop Event

1×	iter limit
1×	node limit

Counts

384 → 384

Calls

Call 1

Inputs
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 1/2 (/ eps x))
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (pow (sqrt -1) 3))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (/ (pow x 4) (sqrt -1)))) (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* (sqrt eps) (pow (sqrt -1) 3)))
(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3))))))
(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(pow x 2)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -1 eps)
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 eps)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
-1
(- (/ (pow x 2) eps) 1)
(- (/ (pow x 2) eps) 1)
(- (/ (pow x 2) eps) 1)
(/ (pow x 2) eps)
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(/ (pow x 2) eps)
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(/ (pow x 2) eps)
(/ (+ (* -1 eps) (pow x 2)) eps)
(/ (+ (* -1 eps) (pow x 2)) eps)
(/ (+ (* -1 eps) (pow x 2)) eps)
-1
(- (/ (pow x 2) eps) 1)
(- (/ (pow x 2) eps) 1)
(- (/ (pow x 2) eps) 1)
-1
(- (/ (pow x 2) eps) 1)
(- (/ (pow x 2) eps) 1)
(- (/ (pow x 2) eps) 1)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
x
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* -1/2 (/ eps x)))
(+ x (* -1/2 (/ eps x)))
(* -1/2 (/ eps x))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* -1/2 (/ eps x))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
1
(+ 1 (* -1/2 (/ eps (pow x 2))))
(+ 1 (* -1/2 (/ eps (pow x 2))))
(+ 1 (* -1/2 (/ eps (pow x 2))))
(* -1/2 (/ eps (pow x 2)))
(* eps (- (/ 1 eps) (* 1/2 (/ 1 (pow x 2)))))
(* eps (- (/ 1 eps) (* 1/2 (/ 1 (pow x 2)))))
(* eps (- (/ 1 eps) (* 1/2 (/ 1 (pow x 2)))))
(* -1/2 (/ eps (pow x 2)))
(* -1 (* eps (- (* 1/2 (/ 1 (pow x 2))) (/ 1 eps))))
(* -1 (* eps (- (* 1/2 (/ 1 (pow x 2))) (/ 1 eps))))
(* -1 (* eps (- (* 1/2 (/ 1 (pow x 2))) (/ 1 eps))))
(* -1/2 (/ eps (pow x 2)))
(/ (+ (* -1/2 eps) (pow x 2)) (pow x 2))
(/ (+ (* -1/2 eps) (pow x 2)) (pow x 2))
(/ (+ (* -1/2 eps) (pow x 2)) (pow x 2))
1
(+ 1 (* -1/2 (/ eps (pow x 2))))
(+ 1 (* -1/2 (/ eps (pow x 2))))
(+ 1 (* -1/2 (/ eps (pow x 2))))
1
(+ 1 (* -1/2 (/ eps (pow x 2))))
(+ 1 (* -1/2 (/ eps (pow x 2))))
(+ 1 (* -1/2 (/ eps (pow x 2))))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
x
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
x
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (sqrt eps) (sqrt -1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))
(- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))))))) (* -1/2 (* (pow eps 2) (pow x 3)))) eps)) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))
(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))
(* (pow x 2) (+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(* (pow x 2) (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(* (pow x 2) (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(* 1/2 x)
(* x (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4))))))
(* 2 (/ (pow x 3) eps))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2)))) (pow x 6))) (* 1/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))))
(* 1/2 x)
(+ (* 1/8 (/ eps x)) (* 1/2 x))
(+ (* 1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 1/8 (/ 1 x)))))
(+ (* 1/2 x) (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x)))))
(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))
(/ (+ (* -1 (/ (pow x 3) (pow (sqrt -1) 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (/ (pow x 3) (pow (sqrt -1) 2))) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 5)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (pow (sqrt -1) 2))))) eps)
(* -1 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))
(* -1 (/ (+ (* -1 (pow x 3)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(* -1 (/ (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1))))))))) (* -1/2 (* eps (pow x 5)))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(* (sqrt eps) (sqrt -1))
(+ x (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(* 2 x)
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(/ (pow x 2) eps)
(* -1 (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* x (+ (* x (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))))
(+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* x (+ (* x (- (+ (* -1 (* x (+ (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* (sqrt (/ 1 eps)) (/ (- (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))))) (/ 1 (pow (sqrt -1) 2)))))
(* 1/2 x)
(* x (- (+ 1/2 (* -1/2 (/ eps (pow x 2)))) (* -1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (+ (* -1 (/ (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2))) (pow x 4))) (* -1/2 (/ eps (pow x 2))))) (* -1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (+ (* -1 (/ (+ (* -1/16 (* (pow eps 2) (- (* -1/2 eps) (* -1/8 eps)))) (+ (* -1/64 (pow eps 3)) (* 1/4 (* eps (+ (* -1/4 (* eps (- (* -1/2 eps) (* -1/8 eps)))) (* -1/32 (pow eps 2))))))) (pow x 6))) (* -1/2 (/ eps (pow x 2))))) (+ (* -1/4 (/ (* eps (- (* -1/2 eps) (* -1/8 eps))) (pow x 4))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/32 (/ (pow eps 2) (pow x 4)))))))
(* 2 (/ (pow x 3) eps))
(* -1 (* (pow x 3) (- (* 5/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 5/8 eps)) (pow x 4))) (* 5/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 5/8 eps)))) (* 5/16 (pow eps 2)))) (pow x 6))) (* 5/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 5/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))))
(* 1/2 x)
(+ (* -3/8 (/ eps x)) (* 1/2 x))
(+ (* 1/2 x) (* eps (- (* -1/16 (/ eps (pow x 3))) (* 3/8 (/ 1 x)))))
(+ (* 1/2 x) (* eps (- (* eps (- (* -3/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 3/8 (/ 1 x)))))
(* -1 (* (sqrt eps) (/ 1 (sqrt -1))))
(- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* -1 (/ x (pow (sqrt -1) 2))))
(- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (/ (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1)))) (pow eps 2))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (* -1 (/ x (pow (sqrt -1) 2))))
(- (+ (* -1 (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt eps) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))) (sqrt -1)))) (* 1/2 (/ (* eps (* (pow x 2) (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2)))))) (pow (sqrt -1) 2)))) (pow eps 3))) (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1))))) (+ (* -1 (/ x (pow (sqrt -1) 2))) (+ (* -1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 (pow eps 3))) (/ (* x (- (* (sqrt eps) (/ (pow x 2) (sqrt -1))) (* -1 (/ (* eps x) (pow (sqrt -1) 2))))) (sqrt -1))))))
(* (sqrt eps) (sqrt -1))
(+ (* -1 (/ (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
(+ (* -1 (/ (- (+ (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (+ (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
(+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))

Outputs
(* -1 (* (sqrt eps) (sqrt -1)))
(.f64 (sqrt.f64 eps) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(- x (* (sqrt eps) (sqrt -1)))
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* x (+ 1 (* -1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) #s(literal -1/2 binary64))))) (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* x (+ 1 (* x (- (* 1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(-.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x x)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (.f64 #s(literal -1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))))) (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ (- (* 1/8 (/ (pow eps 2) (pow x 2))) (* -1/2 eps)) x)
(/.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (/.f64 (.f64 (.f64 eps eps) #s(literal -1/8 binary64)) (.f64 x x))) x)
(/ (- (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2))))) x)
(/.f64 (+.f64 (/.f64 (.f64 eps (.f64 (.f64 eps eps) #s(literal 1/16 binary64))) (pow.f64 x #s(literal 4 binary64))) (-.f64 (.f64 eps #s(literal 1/2 binary64)) (/.f64 (.f64 (.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 x x)))) x)
(/ (- (* 1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x)
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64)))) (-.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (/.f64 (.f64 (.f64 eps eps) #s(literal -1/8 binary64)) (.f64 x x))) (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64))))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 eps (*.f64 x x))) #s(literal -2 binary64)) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (* 1/8 (/ (pow eps 2) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(.f64 (-.f64 (/.f64 (.f64 eps (.f64 eps #s(literal 1/8 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 2 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (* 1/16 (/ (pow eps 3) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))))
(.f64 (-.f64 (/.f64 (.f64 eps (.f64 (.f64 eps eps) #s(literal 1/16 binary64))) (pow.f64 x #s(literal 6 binary64))) (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x)) (/.f64 (.f64 (.f64 eps eps) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(.f64 eps (+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 eps (+.f64 (/.f64 (.f64 #s(literal 1/16 binary64) eps) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x (*.f64 x x)))))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 eps (+.f64 (/.f64 (.f64 #s(literal 5/128 binary64) eps) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(.f64 (sqrt.f64 eps) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (-.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* eps (- (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (+.f64 (.f64 (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) #s(literal -1/2 binary64))) (-.f64 (/.f64 x eps) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))))
(* eps (- (+ (* 1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ x eps)) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (.f64 #s(literal 1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (-.f64 (-.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (.f64 x x) (sqrt.f64 #s(literal -1 binary64)))))))
(* (sqrt eps) (pow (sqrt -1) 3))
(.f64 (sqrt.f64 eps) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
(.f64 (neg.f64 (-.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (- (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
(-.f64 #s(literal 0 binary64) (.f64 eps (-.f64 (/.f64 (+.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64)))) (-.f64 #s(literal 0 binary64) eps)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 (/ (- (* 1/8 (* (sqrt (/ 1 eps)) (/ (pow x 4) (sqrt -1)))) (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
(.f64 (-.f64 (/.f64 (-.f64 x (/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/8 binary64))) (.f64 (sqrt.f64 eps) (.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64)))) eps)) (-.f64 #s(literal 0 binary64) eps)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (-.f64 #s(literal 0 binary64) eps))
x
(+ x (* -1/2 (/ eps x)))
(+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+.f64 x (.f64 eps (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 eps (.f64 x (.f64 x x)))) (/.f64 #s(literal -1/2 binary64) x))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+.f64 x (.f64 eps (+.f64 (.f64 eps (+.f64 (/.f64 (.f64 #s(literal -1/16 binary64) eps) (pow.f64 x #s(literal 5 binary64))) (/.f64 #s(literal -1/8 binary64) (.f64 x (*.f64 x x))))) (/.f64 #s(literal -1/2 binary64) x))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (*.f64 x x) (sqrt.f64 #s(literal -1 binary64))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
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(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
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(* -1 (* (sqrt eps) (pow (sqrt -1) 3)))
(.f64 (sqrt.f64 eps) (neg.f64 (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))
(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))
(.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (*.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64)))) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3))))))
(.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (sqrt.f64 #s(literal -1 binary64))))))) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (+ (* -1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (sqrt -1)))) (+ (* -1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 3)))) (* (sqrt (/ 1 eps)) (pow (sqrt -1) 3)))))))
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(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
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(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
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(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
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x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x)) (/.f64 (.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
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(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x)) (/.f64 (.f64 (*.f64 eps eps) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
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(pow x 2)
(*.f64 x x)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* eps (- (/ (pow x 2) eps) 1))
(.f64 eps (+.f64 (/.f64 (.f64 x x) eps) #s(literal -1 binary64)))
(* eps (- (/ (pow x 2) eps) 1))
(.f64 eps (+.f64 (/.f64 (.f64 x x) eps) #s(literal -1 binary64)))
(* eps (- (/ (pow x 2) eps) 1))
(.f64 eps (+.f64 (/.f64 (.f64 x x) eps) #s(literal -1 binary64)))
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(-.f64 #s(literal 0 binary64) (.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) eps))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(-.f64 #s(literal 0 binary64) (.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) eps))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(-.f64 #s(literal 0 binary64) (.f64 eps (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) eps))))
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(+ (* -1 eps) (pow x 2))
(-.f64 (*.f64 x x) eps)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 x (.f64 x (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 x (.f64 x (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 x (.f64 x (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 x (.f64 x (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 x (.f64 x (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 x (.f64 x (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x)))))
-1
#s(literal -1 binary64)
(- (/ (pow x 2) eps) 1)
(+.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64))
(- (/ (pow x 2) eps) 1)
(+.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64))
(- (/ (pow x 2) eps) 1)
(+.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64))
(/ (pow x 2) eps)
(/.f64 (*.f64 x x) eps)
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
(.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
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(/.f64 (*.f64 x x) eps)
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(.f64 (.f64 x x) (+.f64 (/.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1 binary64) (*.f64 x x))))
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(* (pow x 2) (- (/ 1 eps) (/ 1 (pow x 2))))
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(/.f64 (*.f64 x x) eps)
(/ (+ (* -1 eps) (pow x 2)) eps)
(/.f64 (-.f64 (*.f64 x x) eps) eps)
(/ (+ (* -1 eps) (pow x 2)) eps)
(/.f64 (-.f64 (*.f64 x x) eps) eps)
(/ (+ (* -1 eps) (pow x 2)) eps)
(/.f64 (-.f64 (*.f64 x x) eps) eps)
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(- (/ (pow x 2) eps) 1)
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#s(literal -1 binary64)
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(- (/ (pow x 2) eps) 1)
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(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
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(* 2 x)
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(* 1/2 (/ eps x))
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(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
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(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
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(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
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(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
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(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* 1/2 (/ eps x))
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(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(.f64 eps (+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
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(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
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(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
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(* -1 (* (sqrt eps) (sqrt -1)))
(.f64 (sqrt.f64 eps) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(- x (* (sqrt eps) (sqrt -1)))
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))
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(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))
(/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))
(* (pow x 2) (+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(.f64 (.f64 x x) (+.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (/.f64 x eps) #s(literal 1 binary64))))
(* (pow x 2) (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
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(* (pow x 2) (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
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(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(* x (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/8 binary64) (/.f64 eps (*.f64 x x)))))
(* x (- (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2)))))
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(* x (- (+ 1/2 (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4))))))
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(* 2 (/ (pow x 3) eps))
(.f64 #s(literal 2 binary64) (/.f64 (.f64 x (*.f64 x x)) eps))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
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(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))
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(* 1/2 x)
(*.f64 x #s(literal 1/2 binary64))
(+ (* 1/8 (/ eps x)) (* 1/2 x))
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(+ (* 1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 1/8 (/ 1 x)))))
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(+ (* 1/2 x) (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x)))))
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(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))
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(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 5)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (pow (sqrt -1) 2))))) eps)
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(* -1 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1 binary64)))
(* -1 (/ (+ (* -1 (pow x 3)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(/.f64 (-.f64 (.f64 (sqrt.f64 eps) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (.f64 x (*.f64 x x))) (-.f64 #s(literal 0 binary64) eps))
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(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(pow x 2)
(*.f64 x x)
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ x (* (sqrt eps) (sqrt -1)))
(+.f64 (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x)
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
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(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
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(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
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(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(.f64 x (+.f64 (+.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x)) (/.f64 (.f64 (.f64 eps eps) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64)))) (+.f64 (/.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps (.f64 eps eps))) (pow.f64 x #s(literal 6 binary64))) #s(literal 2 binary64))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
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(-.f64 (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 (+.f64 (.f64 #s(literal 3/2 binary64) (.f64 (sqrt.f64 eps) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (.f64 (sqrt.f64 eps) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (.f64 eps x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)))) (*.f64 eps x)) eps))
(+ (* -1 (/ (- (+ (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x))))))))))) (* -1/2 (* (pow x 2) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))) (+ (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* x (* (sqrt -1) (- (* (sqrt eps) (* (pow x 2) (sqrt -1))) (* -1 (* eps x)))))))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* -1 (* eps x))) eps)) (* (sqrt eps) (sqrt -1)))
(-.f64 (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (+.f64 (-.f64 (.f64 (sqrt.f64 eps) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (/.f64 (-.f64 (-.f64 (.f64 (+.f64 (.f64 (sqrt.f64 eps) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (.f64 eps x)) (.f64 (.f64 x x) #s(literal -1/2 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (+.f64 (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))) (.f64 (sqrt.f64 eps) (.f64 (+.f64 (.f64 (sqrt.f64 eps) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (.f64 eps x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) x)))) (+.f64 (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))) (.f64 (sqrt.f64 eps) (.f64 (+.f64 (.f64 (sqrt.f64 eps) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64))))) (.f64 eps x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) x))))) eps)) (*.f64 eps x)) eps))

eval197.0ms (2%)

Compiler: Compiled 38981 to 3009 computations (92.3% saved)

prune184.0ms (1.9%)

Pruning

40 alts after pruning (37 fresh and 3 done)

	Pruned	Kept	Total
New	1219	29	1248
Fresh	3	8	11
Picked	3	2	5
Done	0	1	1
Total	1225	40	1265

Accuracy

100.0%

Counts

1265 → 40

Alt Table

Click to see full alt table

Status	Accuracy	Program
	62.2%	(fma.f64 (-.f64 (.f64 x x) eps) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))))
	2.3%	(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))) x)
	5.7%	(/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))) (+.f64 (.f64 x x) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
	62.5%	(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	35.0%	(/.f64 (+.f64 (+.f64 (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x))) (.f64 eps #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 x x))) x)
	29.1%	(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64))) eps)) (+.f64 (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (*.f64 x x)))) x)
	42.9%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
	5.7%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)))) (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))))
	62.4%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (.f64 x x) (-.f64 (*.f64 x x) eps))))
	6.7%	(-.f64 (/.f64 (.f64 x x) (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
✓	62.5%	(-.f64 (/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
	62.4%	(-.f64 (/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (-.f64 (*.f64 x x) eps)))
	6.8%	(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
	3.6%	(-.f64 x (/.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
▶	4.8%	(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
	62.5%	(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)))))
	6.8%	(-.f64 x (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))
	3.7%	(-.f64 x (+.f64 x (.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 x (.f64 x x)))))))
	5.9%	(-.f64 x (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) x))
	4.7%	(-.f64 x (.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
	4.8%	(-.f64 x (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (*.f64 x x)))))))))
	4.8%	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 (.f64 x (.f64 x eps)) eps)))))
	6.0%	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (/.f64 (.f64 x x) eps) eps)))))
	4.8%	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x (*.f64 x eps)) (/.f64 #s(literal 1 binary64) eps))))))
	5.2%	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 eps x) (/.f64 x eps))))))
	6.0%	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) eps) #s(literal -1/2 binary64))))))
	6.6%	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))))
	6.6%	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
	6.7%	(-.f64 x (*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))))
	5.5%	(-.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))
✓	62.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	62.8%	(-.f64 x (sqrt.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps)))))
▶	58.3%	(-.f64 x (sqrt.f64 (neg.f64 eps)))
	4.3%	(-.f64 x x)
▶	99.6%	(+.f64 (-.f64 (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
	43.2%	(.f64 (.f64 (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
	25.6%	(.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 eps (+.f64 (/.f64 (.f64 eps #s(literal 5/128 binary64)) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
▶	38.9%	(.f64 eps (+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
	43.4%	(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
▶	3.5%	x

Compiler

Compiled 1829 to 894 computations (51.1% saved)

simplify206.0ms (2.1%)

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	-64	(neg.f64 eps)
✓	cost-diff	-64	(sqrt.f64 (neg.f64 eps))
✓	cost-diff	-64	(-.f64 x (sqrt.f64 (neg.f64 eps)))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x)))))
✓	cost-diff	256	(.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (*.f64 x x))))) x)
✓	cost-diff	256	(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
✓	cost-diff	256	(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
✓	cost-diff	0	(/.f64 eps (.f64 x (.f64 x x)))
✓	cost-diff	0	(.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (*.f64 x x))))
✓	cost-diff	0	(+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x))
✓	cost-diff	128	(.f64 eps (+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
✓	cost-diff	64	(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
✓	cost-diff	64	(/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))
✓	cost-diff	14336	(-.f64 (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))))
✓	cost-diff	14528	(+.f64 (-.f64 (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))

Rules

3286×	`-lowering-.f32`
3286×	`-lowering-.f64`
1782×	`/-lowering-/.f32`
1782×	`/-lowering-/.f64`
1314×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	34	216
1	101	212
2	267	204
3	767	204
4	2885	203
0	8415	203

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(+ (- (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))) (/ (* x x) (+ x (pow (- (* x x) eps) 1/2)))) (/ eps (+ x (pow (- (* x x) eps) 1/2))))
(- (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))) (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))))
(/ (* x x) (+ x (pow (- (* x x) eps) 1/2)))
(* x x)
x
(+ x (pow (- (* x x) eps) 1/2))
(pow (- (* x x) eps) 1/2)
(- (* x x) eps)
eps
1/2
(/ eps (+ x (pow (- (* x x) eps) 1/2)))
x
(* eps (+ (* 1/8 (/ eps (* x (* x x)))) (/ 1/2 x)))
eps
(+ (* 1/8 (/ eps (* x (* x x)))) (/ 1/2 x))
(* 1/8 (/ eps (* x (* x x))))
1/8
(/ eps (* x (* x x)))
(* x (* x x))
x
(* x x)
(/ 1/2 x)
1/2
(- x (/ (* (- 1 (* 1/4 (* (/ eps (* x x)) (/ eps (* x x))))) x) (- 1 (* eps (/ -1/2 (* x x))))))
x
(/ (* (- 1 (* 1/4 (* (/ eps (* x x)) (/ eps (* x x))))) x) (- 1 (* eps (/ -1/2 (* x x)))))
(* (- 1 (* 1/4 (* (/ eps (* x x)) (/ eps (* x x))))) x)
(- 1 (* 1/4 (* (/ eps (* x x)) (/ eps (* x x)))))
1
(* 1/4 (* (/ eps (* x x)) (/ eps (* x x))))
1/4
(* (/ eps (* x x)) (/ eps (* x x)))
(/ eps (* x x))
eps
(* x x)
(- 1 (* eps (/ -1/2 (* x x))))
(* eps (/ -1/2 (* x x)))
(/ -1/2 (* x x))
-1/2
(- x (sqrt (neg eps)))
x
(sqrt (neg eps))
(neg eps)
eps

Outputs
(+ (- (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))) (/ (* x x) (+ x (pow (- (* x x) eps) 1/2)))) (/ eps (+ x (pow (- (* x x) eps) 1/2))))
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(- (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))) (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))))
#s(literal 0 binary64)
(/ (* x x) (+ x (pow (- (* x x) eps) 1/2)))
(/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))))
(* x x)
(*.f64 x x)
x
(+ x (pow (- (* x x) eps) 1/2))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(pow (- (* x x) eps) 1/2)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(- (* x x) eps)
(-.f64 (*.f64 x x) eps)
eps
1/2
#s(literal 1/2 binary64)
(/ eps (+ x (pow (- (* x x) eps) 1/2)))
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
x
(* eps (+ (* 1/8 (/ eps (* x (* x x)))) (/ 1/2 x)))
(.f64 (/.f64 eps x) (+.f64 (/.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps x)) x) #s(literal 1/2 binary64)))
eps
(+ (* 1/8 (/ eps (* x (* x x)))) (/ 1/2 x))
(+.f64 (/.f64 (.f64 eps #s(literal 1/8 binary64)) (.f64 x (*.f64 x x))) (/.f64 #s(literal 1/2 binary64) x))
(* 1/8 (/ eps (* x (* x x))))
(/.f64 (.f64 eps #s(literal 1/8 binary64)) (.f64 x (*.f64 x x)))
1/8
#s(literal 1/8 binary64)
(/ eps (* x (* x x)))
(/.f64 (/.f64 eps x) (*.f64 x x))
(* x (* x x))
(.f64 x (.f64 x x))
x
(* x x)
(*.f64 x x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
(- x (/ (* (- 1 (* 1/4 (* (/ eps (* x x)) (/ eps (* x x))))) x) (- 1 (* eps (/ -1/2 (* x x))))))
(-.f64 x (/.f64 (+.f64 x (/.f64 (.f64 eps (/.f64 (/.f64 (.f64 eps #s(literal -1/4 binary64)) x) x)) x)) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x))))
x
(/ (* (- 1 (* 1/4 (* (/ eps (* x x)) (/ eps (* x x))))) x) (- 1 (* eps (/ -1/2 (* x x)))))
(/.f64 (+.f64 x (/.f64 (.f64 eps (/.f64 (/.f64 (.f64 eps #s(literal -1/4 binary64)) x) x)) x)) (+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x)))
(* (- 1 (* 1/4 (* (/ eps (* x x)) (/ eps (* x x))))) x)
(+.f64 x (/.f64 (.f64 eps (/.f64 (/.f64 (.f64 eps #s(literal -1/4 binary64)) x) x)) x))
(- 1 (* 1/4 (* (/ eps (* x x)) (/ eps (* x x)))))
(+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps (/.f64 (/.f64 (.f64 eps #s(literal -1/4 binary64)) x) x)) (*.f64 x x)))
1
#s(literal 1 binary64)
(* 1/4 (* (/ eps (* x x)) (/ eps (* x x))))
(.f64 (/.f64 (/.f64 eps x) (.f64 x x)) (*.f64 #s(literal 1/4 binary64) (/.f64 eps x)))
1/4
#s(literal 1/4 binary64)
(* (/ eps (* x x)) (/ eps (* x x)))
(.f64 (/.f64 (/.f64 eps x) (.f64 x x)) (/.f64 eps x))
(/ eps (* x x))
(/.f64 eps (*.f64 x x))
eps
(* x x)
(*.f64 x x)
(- 1 (* eps (/ -1/2 (* x x))))
(+.f64 #s(literal 1 binary64) (/.f64 (*.f64 eps (/.f64 #s(literal 1/2 binary64) x)) x))
(* eps (/ -1/2 (* x x)))
(/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x))
(/ -1/2 (* x x))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
-1/2
#s(literal -1/2 binary64)
(- x (sqrt (neg eps)))
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
x
(sqrt (neg eps))
(sqrt.f64 (-.f64 #s(literal 0 binary64) eps))
(neg eps)
(-.f64 #s(literal 0 binary64) eps)
eps

localize326.0ms (3.4%)

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (neg.f64 eps))
✓	accuracy	100.0%	(neg.f64 eps)
✓	accuracy	100.0%	(-.f64 x (sqrt.f64 (neg.f64 eps)))
✓	accuracy	83.6%	(/.f64 eps (*.f64 x x))
✓	accuracy	82.6%	(.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
✓	accuracy	82.0%	(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
✓	accuracy	75.6%	(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))
✓	accuracy	100.0%	(+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	90.0%	(/.f64 eps (.f64 x (.f64 x x)))
✓	accuracy	88.1%	(.f64 eps (+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
✓	accuracy	100.0%	(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
✓	accuracy	99.6%	(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
✓	accuracy	90.8%	(/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))

Results

112.0ms	95×	1	valid
54.0ms	32×	2	valid
51.0ms	55×	0	invalid
38.0ms	74×	0	valid

Compiler

Compiled 338 to 35 computations (89.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 128.0ms

ival-mult: 47.0ms (36.7% of total)

ival-pow: 21.0ms (16.4% of total)

ival-div: 20.0ms (15.6% of total)

backward-pass: 15.0ms (11.7% of total)

ival-sub: 13.0ms (10.1% of total)

ival-add: 6.0ms (4.7% of total)

ival-sqrt: 3.0ms (2.3% of total)

ival-neg: 2.0ms (1.6% of total)

const: 1.0ms (0.8% of total)

series40.0ms (0.4%)

Counts

20 → 444

Calls

Call 1

Inputs
#<alt (+ (- (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))) (/ (* x x) (+ x (pow (- (* x x) eps) 1/2)))) (/ eps (+ x (pow (- (* x x) eps) 1/2))))>
#<alt (- (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))) (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))))>
#<alt (/ (* x x) (+ x (pow (- (* x x) eps) 1/2)))>
#<alt (+ x (pow (- (* x x) eps) 1/2))>
#<alt (* eps (+ (* 1/8 (/ eps (* x (* x x)))) (/ 1/2 x)))>
#<alt (+ (* 1/8 (/ eps (* x (* x x)))) (/ 1/2 x))>
#<alt (* 1/8 (/ eps (* x (* x x))))>
#<alt (/ eps (* x (* x x)))>
#<alt (- x (/ (* (- 1 (* 1/4 (* (/ eps (* x x)) (/ eps (* x x))))) x) (- 1 (* eps (/ -1/2 (* x x))))))>
#<alt (/ (* (- 1 (* 1/4 (* (/ eps (* x x)) (/ eps (* x x))))) x) (- 1 (* eps (/ -1/2 (* x x)))))>
#<alt (* (- 1 (* 1/4 (* (/ eps (* x x)) (/ eps (* x x))))) x)>
#<alt (- 1 (* 1/4 (* (/ eps (* x x)) (/ eps (* x x)))))>
#<alt (- x (sqrt (neg eps)))>
#<alt (sqrt (neg eps))>
#<alt (neg eps)>
#<alt (/ eps (+ x (pow (- (* x x) eps) 1/2)))>
#<alt (pow (- (* x x) eps) 1/2)>
#<alt (* x (* x x))>
#<alt (* eps (/ -1/2 (* x x)))>
#<alt (/ eps (* x x))>

Outputs
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)>
#<alt (/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))>
#<alt (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))>
#<alt (- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))))))) (* -1/2 (* (pow eps 2) (pow x 3)))) eps)) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))>
#<alt (* (pow x 2) (+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))>
#<alt (* (pow x 2) (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))>
#<alt (* (pow x 2) (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* 1/8 (/ eps (pow x 2)))))>
#<alt (* x (- (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2)))))>
#<alt (* x (- (+ 1/2 (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4))))))>
#<alt (* 2 (/ (pow x 3) eps))>
#<alt (* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))>
#<alt (* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2)))) (pow x 6))) (* 1/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))))>
#<alt (* 1/2 x)>
#<alt (+ (* 1/8 (/ eps x)) (* 1/2 x))>
#<alt (+ (* 1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 1/8 (/ 1 x)))))>
#<alt (+ (* 1/2 x) (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x)))))>
#<alt (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))>
#<alt (/ (+ (* -1 (/ (pow x 3) (pow (sqrt -1) 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) eps)>
#<alt (/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (/ (pow x 3) (pow (sqrt -1) 2))) eps)>
#<alt (/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 5)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (pow (sqrt -1) 2))))) eps)>
#<alt (* -1 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))>
#<alt (* -1 (/ (+ (* -1 (pow x 3)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))>
#<alt (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1))))))))) (* -1/2 (* eps (pow x 5)))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))>
#<alt (* 2 x)>
#<alt (+ (* -1/2 (/ eps x)) (* 2 x))>
#<alt (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))>
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 3)))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))>
#<alt (/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (/ 1/2 x)>
#<alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))>
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))>
#<alt (* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))>
#<alt (/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))>
#<alt (/ 1/2 x)>
#<alt (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)>
#<alt (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)>
#<alt (/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))>
#<alt (* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (* 1/8 (/ eps (pow x 3)))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (/ eps (pow x 3))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)>
#<alt (/ (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* -1/8 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))) x)>
#<alt (/ (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* -1/8 (/ (pow eps 3) (pow x 4))) (+ (* -1/16 (/ (pow eps 4) (pow x 6))) (+ (* 1/16 (/ (pow eps 4) (pow x 6))) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))))) x)>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* -1 (/ x eps)) (+ (* 1/2 (/ 1 x)) (/ x eps))))>
#<alt (* eps (+ (* -1 (/ x eps)) (+ (* 1/2 (/ 1 x)) (/ x eps))))>
#<alt (* eps (+ (* -1 (/ x eps)) (+ (* 1/2 (/ 1 x)) (/ x eps))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1 x)) eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1 x)) eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (- (* -1 (/ (+ x (* -1 x)) eps)) (* 1/2 (/ 1 x)))))>
#<alt x>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (* -1/2 (/ eps x))>
#<alt (* eps (- (/ x eps) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (/ x eps) (* 1/2 (/ 1 x))))>
#<alt (* eps (- (/ x eps) (* 1/2 (/ 1 x))))>
#<alt (* -1/2 (/ eps x))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))>
#<alt (* -1/2 (/ eps x))>
#<alt (/ (+ (* -1/2 eps) (pow x 2)) x)>
#<alt (/ (+ (* -1/2 eps) (pow x 2)) x)>
#<alt (/ (+ (* -1/2 eps) (pow x 2)) x)>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))>
#<alt x>
#<alt (+ x (* -1/4 (/ (pow eps 2) (pow x 3))))>
#<alt (+ x (* -1/4 (/ (pow eps 2) (pow x 3))))>
#<alt (+ x (* -1/4 (/ (pow eps 2) (pow x 3))))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 3)))>
#<alt (* (pow eps 2) (- (/ x (pow eps 2)) (* 1/4 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (- (/ x (pow eps 2)) (* 1/4 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (- (/ x (pow eps 2)) (* 1/4 (/ 1 (pow x 3)))))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 3)))>
#<alt (* (pow eps 2) (- (/ x (pow eps 2)) (* 1/4 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (- (/ x (pow eps 2)) (* 1/4 (/ 1 (pow x 3)))))>
#<alt (* (pow eps 2) (- (/ x (pow eps 2)) (* 1/4 (/ 1 (pow x 3)))))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 3)))>
#<alt (/ (+ (* -1/4 (pow eps 2)) (pow x 4)) (pow x 3))>
#<alt (/ (+ (* -1/4 (pow eps 2)) (pow x 4)) (pow x 3))>
#<alt (/ (+ (* -1/4 (pow eps 2)) (pow x 4)) (pow x 3))>
#<alt x>
#<alt (* x (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4)))))>
#<alt (* x (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4)))))>
#<alt (* x (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4)))))>
#<alt x>
#<alt (* -1 (* x (- (* 1/4 (/ (pow eps 2) (pow x 4))) 1)))>
#<alt (* -1 (* x (- (* 1/4 (/ (pow eps 2) (pow x 4))) 1)))>
#<alt (* -1 (* x (- (* 1/4 (/ (pow eps 2) (pow x 4))) 1)))>
#<alt 1>
#<alt (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4))))>
#<alt (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4))))>
#<alt (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4))))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 4)))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) (* 1/4 (/ 1 (pow x 4)))))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) (* 1/4 (/ 1 (pow x 4)))))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) (* 1/4 (/ 1 (pow x 4)))))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 4)))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) (* 1/4 (/ 1 (pow x 4)))))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) (* 1/4 (/ 1 (pow x 4)))))>
#<alt (* (pow eps 2) (- (/ 1 (pow eps 2)) (* 1/4 (/ 1 (pow x 4)))))>
#<alt (* -1/4 (/ (pow eps 2) (pow x 4)))>
#<alt (/ (- (pow x 4) (* 1/4 (pow eps 2))) (pow x 4))>
#<alt (/ (- (pow x 4) (* 1/4 (pow eps 2))) (pow x 4))>
#<alt (/ (- (pow x 4) (* 1/4 (pow eps 2))) (pow x 4))>
#<alt 1>
#<alt (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4))))>
#<alt (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4))))>
#<alt (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4))))>
#<alt 1>
#<alt (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4))))>
#<alt (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4))))>
#<alt (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt x>
#<alt (* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))>
#<alt (* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))>
#<alt (* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))>
#<alt x>
#<alt (* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))>
#<alt (* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))>
#<alt (* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (- x (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* -1 eps)>
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))>
#<alt (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (+ x (* -1 (* (sqrt eps) (sqrt -1))))>
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))>
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))>
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)>
#<alt (/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))>
#<alt (+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))>
#<alt x>
#<alt (* x (+ 1 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))>
#<alt (* -1 x)>
#<alt (* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))>
#<alt (* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))>
#<alt x>
#<alt (+ x (* -1/2 (/ eps x)))>
#<alt (+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))>
#<alt (* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (* -1/2 (/ eps (pow x 2)))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>
#<alt (/ eps (pow x 2))>

Calls

111 calls:

Time	Variable		Point	Expression
9.0ms	x	@	0	(- x (/ (* (- 1 (* 1/4 (* (/ eps (* x x)) (/ eps (* x x))))) x) (- 1 (* eps (/ -1/2 (* x x))))))
2.0ms	eps	@	-inf	(/ eps (+ x (pow (- (* x x) eps) 1/2)))
2.0ms	eps	@	0	(- x (/ (* (- 1 (* 1/4 (* (/ eps (* x x)) (/ eps (* x x))))) x) (- 1 (* eps (/ -1/2 (* x x))))))
1.0ms	x	@	-inf	(- x (/ (* (- 1 (* 1/4 (* (/ eps (* x x)) (/ eps (* x x))))) x) (- 1 (* eps (/ -1/2 (* x x))))))
1.0ms	eps	@	0	(* eps (+ (* 1/8 (/ eps (* x (* x x)))) (/ 1/2 x)))

rewrite322.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

2862×	`-lowering-.f32`
2862×	`-lowering-.f64`
2640×	`fma-lowering-fma.f32`
2640×	`fma-lowering-fma.f64`
2088×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	164
1	261	160
2	2590	135
0	8989	135

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 475

Calls

Call 1

Inputs
(+ (- (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))) (/ (* x x) (+ x (pow (- (* x x) eps) 1/2)))) (/ eps (+ x (pow (- (* x x) eps) 1/2))))
(- (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))) (/ (* x x) (+ x (pow (- (* x x) eps) 1/2))))
(/ (* x x) (+ x (pow (- (* x x) eps) 1/2)))
(+ x (pow (- (* x x) eps) 1/2))
(* eps (+ (* 1/8 (/ eps (* x (* x x)))) (/ 1/2 x)))
(+ (* 1/8 (/ eps (* x (* x x)))) (/ 1/2 x))
(* 1/8 (/ eps (* x (* x x))))
(/ eps (* x (* x x)))
(- x (/ (* (- 1 (* 1/4 (* (/ eps (* x x)) (/ eps (* x x))))) x) (- 1 (* eps (/ -1/2 (* x x))))))
(/ (* (- 1 (* 1/4 (* (/ eps (* x x)) (/ eps (* x x))))) x) (- 1 (* eps (/ -1/2 (* x x)))))
(* (- 1 (* 1/4 (* (/ eps (* x x)) (/ eps (* x x))))) x)
(- 1 (* 1/4 (* (/ eps (* x x)) (/ eps (* x x)))))
(- x (sqrt (neg eps)))
(sqrt (neg eps))
(neg eps)
(/ eps (+ x (pow (- (* x x) eps) 1/2)))
(pow (- (* x x) eps) 1/2)
(* x (* x x))
(* eps (/ -1/2 (* x x)))
(/ eps (* x x))

Outputs
(+.f64 (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (neg.f64 (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))))
(+.f64 #s(literal 0 binary64) (/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(+.f64 (/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 0 binary64))
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(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 eps (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))))
(.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (/.f64 eps (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))))
(.f64 (/.f64 eps (+.f64 (.f64 x (.f64 x x)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (+.f64 (.f64 x x) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))))
(.f64 (/.f64 eps (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))) (-.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 (.f64 x x) eps))))
(exp.f64 (.f64 (log.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (-.f64 (*.f64 x x) eps)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log.f64 (-.f64 (.f64 x x) eps)) #s(literal 1/4 binary64)) (.f64 (log.f64 (-.f64 (.f64 x x) eps)) #s(literal 1/4 binary64))))
(hypot.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
(hypot.f64 (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)) x)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 eps (.f64 eps eps)))) (sqrt.f64 (+.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 eps (+.f64 (.f64 x x) eps)))))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 eps eps))) (pow.f64 (+.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (*.f64 x x) eps)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (-.f64 (*.f64 x x) eps)))
(.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (-.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (.f64 eps (.f64 eps eps)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 eps (+.f64 (*.f64 x x) eps)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 eps eps))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) eps)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/4 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 3/2 binary64)))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 x)) #s(literal 3 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(/.f64 eps (/.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 eps #s(literal -1/2 binary64))))
(/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 x x))
(/.f64 (.f64 eps #s(literal 1 binary64)) (/.f64 (.f64 x x) #s(literal -1/2 binary64)))
(/.f64 (.f64 #s(literal 1 binary64) eps) (/.f64 (.f64 x x) #s(literal -1/2 binary64)))
(/.f64 (neg.f64 (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (.f64 eps #s(literal 1/2 binary64)) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (.f64 #s(literal 1 binary64) (.f64 eps #s(literal -1/2 binary64))) (*.f64 x x))
(/.f64 (*.f64 eps (/.f64 #s(literal -1/2 binary64) x)) x)
(/.f64 (.f64 #s(literal 1/2 binary64) eps) (-.f64 #s(literal 0 binary64) (.f64 x x)))
(/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) eps) x)
(/.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x)
(pow.f64 (/.f64 (.f64 x x) (.f64 eps #s(literal -1/2 binary64))) #s(literal -1 binary64))
(.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))
(.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x)))
(.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) eps)
(.f64 (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))) #s(literal 1 binary64))
(.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (*.f64 x x)))
(*.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x))
(.f64 (.f64 #s(literal 1 binary64) eps) (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))
(exp.f64 (.f64 (log.f64 (/.f64 eps (.f64 x x))) #s(literal 1 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) eps)) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) (/.f64 eps (-.f64 #s(literal 0 binary64) (.f64 x x))))
(neg.f64 (/.f64 eps (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 x x)))
(/.f64 eps (*.f64 x x))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 eps x)))
(/.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) eps)))
(/.f64 (/.f64 eps x) x)
(/.f64 (.f64 eps #s(literal 1 binary64)) (.f64 x x))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) eps)) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (/.f64 eps x)) (-.f64 #s(literal 0 binary64) x))
(pow.f64 (/.f64 eps (*.f64 x x)) #s(literal 1 binary64))
(pow.f64 (/.f64 (*.f64 x x) eps) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (*.f64 x x) eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 x (/.f64 eps x)) #s(literal -1 binary64))
(.f64 eps (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 #s(literal 1 binary64) (/.f64 eps (.f64 x x)))
(.f64 (-.f64 #s(literal 0 binary64) eps) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 (-.f64 #s(literal 0 binary64) eps) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))) #s(literal 1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) eps)
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 eps x))
(.f64 #s(literal -1 binary64) (/.f64 eps (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 #s(literal -1 binary64) (pow.f64 (/.f64 eps (-.f64 #s(literal 0 binary64) (.f64 x x))) #s(literal 1 binary64)))
(*.f64 (/.f64 eps x) (/.f64 #s(literal 1 binary64) x))
(.f64 (pow.f64 eps #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1 binary64)) (pow.f64 eps #s(literal 1 binary64)))
(*.f64 (pow.f64 (/.f64 eps x) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))

simplify320.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

6462×	`-lowering-.f32`
6462×	`-lowering-.f64`
3348×	`+-lowering-+.f64`
3348×	`+-lowering-+.f32`
1604×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	651	5194
1	2242	4591
0	8395	4591

Stop Event

1×	iter limit
1×	node limit

Counts

444 → 444

Calls

Call 1

Inputs
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))
(- (* -1 (/ (+ (* -1 (* eps x)) (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))))))) (* -1/2 (* (pow eps 2) (pow x 3)))) eps)) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))) eps))) eps)) (* (sqrt eps) (sqrt -1)))
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
0
(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))
(* (pow x 2) (+ (* -1 (/ x (* eps (pow (sqrt -1) 2)))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(* (pow x 2) (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(* (pow x 2) (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* (pow eps 2) (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (* eps (pow (sqrt -1) 2))))) (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))
(* 1/2 x)
(* x (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))) (* -1/8 (/ eps (pow x 2)))))
(* x (- (+ 1/2 (* -1 (/ (+ (* -1/32 (pow eps 3)) (* -1/128 (pow eps 3))) (pow x 6)))) (+ (* -1/8 (/ eps (pow x 2))) (* -1/16 (/ (pow eps 2) (pow x 4))))))
(* 2 (/ (pow x 3) eps))
(* -1 (* (pow x 3) (- (* 1/2 (/ 1 (pow x 2))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -1/4 eps) (* 1/8 eps)) (pow x 4))) (* 1/2 (/ 1 (pow x 2)))) (* 2 (/ 1 eps)))))
(* -1 (* (pow x 3) (- (+ (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow eps 2))) (+ (* -1/4 (* eps (+ (* -1/4 eps) (* 1/8 eps)))) (* 1/16 (pow eps 2)))) (pow x 6))) (* 1/2 (/ 1 (pow x 2)))) (+ (* -1/4 (/ eps (pow x 4))) (+ (* 1/8 (/ eps (pow x 4))) (* 2 (/ 1 eps)))))))
(* 1/2 x)
(+ (* 1/8 (/ eps x)) (* 1/2 x))
(+ (* 1/2 x) (* eps (+ (* 1/16 (/ eps (pow x 3))) (* 1/8 (/ 1 x)))))
(+ (* 1/2 x) (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 5))) (* 1/16 (/ 1 (pow x 3))))) (* 1/8 (/ 1 x)))))
(* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))
(/ (+ (* -1 (/ (pow x 3) (pow (sqrt -1) 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (/ (pow x 3) (pow (sqrt -1) 2))) eps)
(/ (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 4) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 5)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ (pow x 2) (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 4) (pow (sqrt -1) 3)))) (/ (pow x 3) (pow (sqrt -1) 2))))) eps)
(* -1 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))
(* -1 (/ (+ (* -1 (pow x 3)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(* -1 (/ (+ (* -1 (/ (- (+ (* -1 (* (sqrt eps) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 4) (sqrt -1))))) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1))))))))) (* -1/2 (* eps (pow x 5)))) (+ (* -1 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt (pow eps 3)) (* (pow x 4) (sqrt -1)))))) eps)) (* -1 (* eps (pow x 3)))) eps)) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) eps))
(* (sqrt eps) (sqrt -1))
(+ x (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(* 2 x)
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(/ 1/2 x)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(* 1/8 (/ eps (pow x 3)))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ eps (pow x 3)))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ 1/2 x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(/ eps (pow x 3))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(/ (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(/ (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* -1/8 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))) x)
(/ (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* -1/8 (/ (pow eps 3) (pow x 4))) (+ (* -1/16 (/ (pow eps 4) (pow x 6))) (+ (* 1/16 (/ (pow eps 4) (pow x 6))) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))))) x)
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* eps (+ (* -1 (/ x eps)) (+ (* 1/2 (/ 1 x)) (/ x eps))))
(* eps (+ (* -1 (/ x eps)) (+ (* 1/2 (/ 1 x)) (/ x eps))))
(* eps (+ (* -1 (/ x eps)) (+ (* 1/2 (/ 1 x)) (/ x eps))))
(* 1/2 (/ eps x))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 x)) eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 x)) eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (- (* -1 (/ (+ x (* -1 x)) eps)) (* 1/2 (/ 1 x)))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* -1/2 (/ eps x)))
(+ x (* -1/2 (/ eps x)))
(* -1/2 (/ eps x))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* -1/2 (/ eps x))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
x
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
x
(+ x (* -1/4 (/ (pow eps 2) (pow x 3))))
(+ x (* -1/4 (/ (pow eps 2) (pow x 3))))
(+ x (* -1/4 (/ (pow eps 2) (pow x 3))))
(* -1/4 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (- (/ x (pow eps 2)) (* 1/4 (/ 1 (pow x 3)))))
(* (pow eps 2) (- (/ x (pow eps 2)) (* 1/4 (/ 1 (pow x 3)))))
(* (pow eps 2) (- (/ x (pow eps 2)) (* 1/4 (/ 1 (pow x 3)))))
(* -1/4 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (- (/ x (pow eps 2)) (* 1/4 (/ 1 (pow x 3)))))
(* (pow eps 2) (- (/ x (pow eps 2)) (* 1/4 (/ 1 (pow x 3)))))
(* (pow eps 2) (- (/ x (pow eps 2)) (* 1/4 (/ 1 (pow x 3)))))
(* -1/4 (/ (pow eps 2) (pow x 3)))
(/ (+ (* -1/4 (pow eps 2)) (pow x 4)) (pow x 3))
(/ (+ (* -1/4 (pow eps 2)) (pow x 4)) (pow x 3))
(/ (+ (* -1/4 (pow eps 2)) (pow x 4)) (pow x 3))
x
(* x (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4)))))
(* x (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4)))))
(* x (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4)))))
x
(* -1 (* x (- (* 1/4 (/ (pow eps 2) (pow x 4))) 1)))
(* -1 (* x (- (* 1/4 (/ (pow eps 2) (pow x 4))) 1)))
(* -1 (* x (- (* 1/4 (/ (pow eps 2) (pow x 4))) 1)))
1
(+ 1 (* -1/4 (/ (pow eps 2) (pow x 4))))
(+ 1 (* -1/4 (/ (pow eps 2) (pow x 4))))
(+ 1 (* -1/4 (/ (pow eps 2) (pow x 4))))
(* -1/4 (/ (pow eps 2) (pow x 4)))
(* (pow eps 2) (- (/ 1 (pow eps 2)) (* 1/4 (/ 1 (pow x 4)))))
(* (pow eps 2) (- (/ 1 (pow eps 2)) (* 1/4 (/ 1 (pow x 4)))))
(* (pow eps 2) (- (/ 1 (pow eps 2)) (* 1/4 (/ 1 (pow x 4)))))
(* -1/4 (/ (pow eps 2) (pow x 4)))
(* (pow eps 2) (- (/ 1 (pow eps 2)) (* 1/4 (/ 1 (pow x 4)))))
(* (pow eps 2) (- (/ 1 (pow eps 2)) (* 1/4 (/ 1 (pow x 4)))))
(* (pow eps 2) (- (/ 1 (pow eps 2)) (* 1/4 (/ 1 (pow x 4)))))
(* -1/4 (/ (pow eps 2) (pow x 4)))
(/ (- (pow x 4) (* 1/4 (pow eps 2))) (pow x 4))
(/ (- (pow x 4) (* 1/4 (pow eps 2))) (pow x 4))
(/ (- (pow x 4) (* 1/4 (pow eps 2))) (pow x 4))
1
(+ 1 (* -1/4 (/ (pow eps 2) (pow x 4))))
(+ 1 (* -1/4 (/ (pow eps 2) (pow x 4))))
(+ 1 (* -1/4 (/ (pow eps 2) (pow x 4))))
1
(+ 1 (* -1/4 (/ (pow eps 2) (pow x 4))))
(+ 1 (* -1/4 (/ (pow eps 2) (pow x 4))))
(+ 1 (* -1/4 (/ (pow eps 2) (pow x 4))))
(* -1 (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
x
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
(* x (+ 1 (* -1 (* (sqrt eps) (/ (sqrt -1) x)))))
x
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(* -1 (* x (- (* (sqrt eps) (/ (sqrt -1) x)) 1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(- x (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* (sqrt eps) (sqrt -1))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* (sqrt eps) (sqrt -1))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* -1 eps)
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(* -1/2 (/ eps (pow x 2)))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))
(/ eps (pow x 2))

Outputs
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x)
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (.f64 x (+.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
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(.f64 eps (-.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (-.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* eps (- (/ x eps) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (-.f64 (/.f64 x eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 x eps)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 x eps)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (- (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 x eps)) (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (-.f64 #s(literal 0 binary64) eps))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* -1 (* (sqrt eps) (sqrt -1)))
(.f64 (sqrt.f64 eps) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (sqrt eps) (sqrt -1)))
(.f64 (sqrt.f64 eps) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (sqrt eps) (sqrt -1)))
(.f64 (sqrt.f64 eps) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* (sqrt eps) (sqrt -1)))
(.f64 (sqrt.f64 eps) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (.f64 x x))))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (*.f64 #s(literal 1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64))))))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 eps (+.f64 (/.f64 (.f64 #s(literal 5/128 binary64) eps) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x)
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(+.f64 (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (.f64 (/.f64 (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (.f64 x x)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))) x)
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(+.f64 (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (-.f64 (/.f64 (.f64 (.f64 eps eps) (.f64 (.f64 x (.f64 x x)) #s(literal -1/2 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (/.f64 (.f64 (.f64 (/.f64 (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (.f64 x x)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal -1/2 binary64) x)) (sqrt.f64 eps)) (sqrt.f64 #s(literal -1 binary64)))) (.f64 eps (.f64 eps eps)))) (+.f64 (neg.f64 (.f64 (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 x x)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64))) x))
(* -1 (* (sqrt eps) (sqrt -1)))
(.f64 (sqrt.f64 eps) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(-.f64 (.f64 (sqrt.f64 eps) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (.f64 (sqrt.f64 eps) (.f64 (sqrt.f64 #s(literal -1 binary64)) (.f64 x x)))) (*.f64 eps x)) eps))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(-.f64 (/.f64 (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (-.f64 (.f64 eps (.f64 (.f64 x (.f64 x x)) #s(literal 1/2 binary64))) (.f64 (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (.f64 x x)) #s(literal -1 binary64))) (.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))))) (.f64 (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (.f64 x x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64)))) eps)) (.f64 eps x)) (-.f64 #s(literal 0 binary64) eps)) (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) x)
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (.f64 x (+.f64 (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 x #s(literal 1/2 binary64))) #s(literal 1 binary64))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/2 binary64))) (sqrt.f64 #s(literal -1 binary64)))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))))) #s(literal 1 binary64))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 eps #s(literal 1/2 binary64)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 x x))) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/.f64 (+.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (/.f64 (.f64 eps (.f64 (.f64 eps eps) #s(literal 1/16 binary64))) (pow.f64 x #s(literal 4 binary64)))) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (*.f64 x x))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(/.f64 (-.f64 (-.f64 (.f64 eps #s(literal 1/2 binary64)) (/.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -5/128 binary64)) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (/.f64 (.f64 eps (.f64 eps #s(literal -1/8 binary64))) (.f64 x x)) (/.f64 (.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps eps)) eps) (pow.f64 x #s(literal 4 binary64))))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(.f64 x (.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 eps (.f64 x x))) #s(literal -2 binary64)) #s(literal -1 binary64)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 (/.f64 (.f64 eps (.f64 eps #s(literal -1/8 binary64))) (neg.f64 (pow.f64 x #s(literal 4 binary64)))) (+.f64 #s(literal 2 binary64) (.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(.f64 (-.f64 (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (/.f64 (.f64 #s(literal -2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) eps) (+.f64 (.f64 (.f64 eps (.f64 eps #s(literal -1/8 binary64))) (.f64 eps #s(literal -1/4 binary64))) (.f64 eps (.f64 (.f64 eps eps) #s(literal 1/16 binary64))))) (pow.f64 x #s(literal 6 binary64)))) (+.f64 (+.f64 #s(literal 2 binary64) (.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))) (/.f64 (.f64 eps (.f64 eps #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+.f64 (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (.f64 x (.f64 (.f64 x #s(literal 1/2 binary64)) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+.f64 (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (/.f64 (.f64 x x) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(+.f64 (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (.f64 x (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64))) (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64)))))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(.f64 x (+.f64 (/.f64 (.f64 eps (.f64 eps #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(.f64 x (+.f64 (+.f64 (/.f64 (.f64 eps (.f64 eps #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64)))) (/.f64 (.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps eps)) eps) (pow.f64 x #s(literal 6 binary64)))))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(-.f64 #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (/.f64 (.f64 eps (.f64 eps #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 eps (*.f64 x x)) #s(literal -1/2 binary64)))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (+.f64 (/.f64 (.f64 eps (.f64 eps #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64)))) (/.f64 (.f64 (.f64 #s(literal -1/16 binary64) (.f64 eps eps)) eps) (pow.f64 x #s(literal 6 binary64)))))
x
(+ x (* -1/2 (/ eps x)))
(+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+.f64 x (.f64 eps (/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x))) #s(literal -1/2 binary64)) x)))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+.f64 x (.f64 eps (+.f64 (.f64 eps (+.f64 (.f64 #s(literal -1/16 binary64) (/.f64 eps (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -1/8 binary64) (.f64 x (*.f64 x x))))) (/.f64 #s(literal -1/2 binary64) x))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (*.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64))) (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64)))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 eps (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (.f64 (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/8 binary64))) (+.f64 (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 #s(literal 1/2 binary64) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x x)) (sqrt.f64 #s(literal -1 binary64))))) (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(.f64 (sqrt.f64 eps) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(-.f64 #s(literal 0 binary64) (.f64 eps (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 (-.f64 #s(literal 0 binary64) eps) (+.f64 (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)))) (.f64 #s(literal -1/8 binary64) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64))))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(-.f64 #s(literal 0 binary64) (.f64 eps (+.f64 (.f64 #s(literal -1/8 binary64) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))))) (+.f64 (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 x x)) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)))) (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64)))) (.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 6 binary64)))))))))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(* -1/2 (/ eps (pow x 2)))
(.f64 (/.f64 eps (.f64 x x)) #s(literal -1/2 binary64))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))
(/ eps (pow x 2))
(/.f64 eps (*.f64 x x))

eval191.0ms (2%)

Compiler: Compiled 40858 to 2997 computations (92.7% saved)

prune167.0ms (1.7%)

Pruning

46 alts after pruning (42 fresh and 4 done)

	Pruned	Kept	Total
New	1167	20	1187
Fresh	10	22	32
Picked	3	2	5
Done	1	2	3
Total	1181	46	1227

Accuracy

100.0%

Counts

1227 → 46

Alt Table

Click to see full alt table

Status	Accuracy	Program
	5.7%	(/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))) (+.f64 (.f64 x x) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
▶	35.0%	(/.f64 (+.f64 (+.f64 (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x))) (.f64 eps #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 x x))) x)
▶	99.6%	(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
	42.9%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
	5.7%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)))) (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))))
	4.4%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (+.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))))) (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))))))
	6.7%	(-.f64 (/.f64 (.f64 x x) (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
	3.6%	(-.f64 x (/.f64 (/.f64 (.f64 (.f64 eps (/.f64 eps (.f64 x x))) #s(literal -1/4 binary64)) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
▶	6.8%	(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
	3.6%	(-.f64 x (/.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
	2.7%	(-.f64 x (/.f64 (.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/64 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 x x) eps)) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 x x) eps)))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))
	4.8%	(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (/.f64 eps x) x) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))
	5.3%	(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) x))))
	5.3%	(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) eps) x))))
	4.8%	(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 eps x)))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))
	4.4%	(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/16 binary64) (.f64 (/.f64 (/.f64 eps (.f64 x x)) (/.f64 (.f64 x x) eps)) (/.f64 (/.f64 eps (.f64 x x)) (/.f64 (.f64 x x) eps))))) x) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 x x) eps))) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))))
	3.5%	(-.f64 x (/.f64 (.f64 (+.f64 (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))
	2.5%	(-.f64 x (/.f64 (.f64 (.f64 eps eps) (+.f64 (/.f64 x (.f64 eps eps)) (/.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x x))))) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
	5.5%	(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
	5.8%	(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))))
	6.8%	(-.f64 x (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))
	2.7%	(-.f64 x (.f64 (/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))))
	5.9%	(-.f64 x (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) x))
	4.7%	(-.f64 x (.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
	4.8%	(-.f64 x (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (*.f64 x x)))))))))
	4.8%	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 (.f64 x (.f64 x eps)) eps)))))
	6.0%	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (/.f64 (.f64 x x) eps) eps)))))
	4.8%	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x (*.f64 x eps)) (/.f64 #s(literal 1 binary64) eps))))))
	5.2%	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 eps x) (/.f64 x eps))))))
	6.0%	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) eps) #s(literal -1/2 binary64))))))
	6.6%	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))))
	6.6%	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
	6.7%	(-.f64 x (*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))))
✓	62.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	62.8%	(-.f64 x (sqrt.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps)))))
✓	58.3%	(-.f64 x (sqrt.f64 (neg.f64 eps)))
▶	4.3%	(-.f64 x x)
	42.5%	(+.f64 (-.f64 (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 eps (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 eps (/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 eps (.f64 x x))) #s(literal -1/2 binary64)) x)))))
	4.4%	(.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (+.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))))))
	43.2%	(.f64 (.f64 (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
	15.0%	(.f64 (.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
	40.8%	(.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))) x))
	43.3%	(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
▶	40.8%	(.f64 eps (+.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (/.f64 eps x)) (/.f64 #s(literal 1/2 binary64) x)))
	43.4%	(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
✓	3.5%	x

Compiler

Compiled 2566 to 1178 computations (54.1% saved)

simplify242.0ms (2.5%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x)))
✓	cost-diff	128	(+.f64 (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x))) (*.f64 eps #s(literal 1/2 binary64)))
✓	cost-diff	512	(+.f64 (+.f64 (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x))) (.f64 eps #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 x x)))
✓	cost-diff	512	(/.f64 (+.f64 (+.f64 (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x))) (.f64 eps #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 x x))) x)
✓	cost-diff	128	(.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
✓	cost-diff	128	(-.f64 (.f64 x x) (.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)))
✓	cost-diff	1024	(/.f64 (-.f64 (.f64 x x) (.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
✓	cost-diff	1024	(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
✓	cost-diff	0	(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
✓	cost-diff	0	(.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 eps x))
✓	cost-diff	0	(+.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 eps x)) (/.f64 #s(literal 1/2 binary64) x))
✓	cost-diff	128	(.f64 eps (+.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (/.f64 eps x)) (/.f64 #s(literal 1/2 binary64) x)))
✓	cost-diff	128	(-.f64 x x)
✓	cost-diff	0	(-.f64 (*.f64 x x) eps)
✓	cost-diff	64	(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
✓	cost-diff	64	(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
✓	cost-diff	64	(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))

Rules

4188×	`-lowering-.f32`
4188×	`-lowering-.f64`
1486×	`+-lowering-+.f64`
1486×	`+-lowering-+.f32`
1230×	`distribute-lft-neg-in`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	36	249
1	119	246
2	345	220
3	1128	211
4	3782	210
0	8186	210

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ eps (+ x (pow (- (* x x) eps) 1/2)))
eps
(+ x (pow (- (* x x) eps) 1/2))
x
(pow (- (* x x) eps) 1/2)
(- (* x x) eps)
(* x x)
1/2
(- x x)
x
(* eps (+ (* (/ 1/8 (* x x)) (/ eps x)) (/ 1/2 x)))
eps
(+ (* (/ 1/8 (* x x)) (/ eps x)) (/ 1/2 x))
(* (/ 1/8 (* x x)) (/ eps x))
(/ 1/8 (* x x))
1/8
(* x x)
x
(/ eps x)
(/ 1/2 x)
1/2
(- x (/ (- (* x x) (* (/ (* eps -1/2) x) (/ (* eps -1/2) x))) (- x (/ (* eps -1/2) x))))
x
(/ (- (* x x) (* (/ (* eps -1/2) x) (/ (* eps -1/2) x))) (- x (/ (* eps -1/2) x)))
(- (* x x) (* (/ (* eps -1/2) x) (/ (* eps -1/2) x)))
(* x x)
(* (/ (* eps -1/2) x) (/ (* eps -1/2) x))
(/ (* eps -1/2) x)
(* eps -1/2)
eps
-1/2
(- x (/ (* eps -1/2) x))
(/ (+ (+ (/ (* (* eps (* eps eps)) 1/16) (* (* x x) (* x x))) (* eps 1/2)) (/ (* 1/8 (* eps eps)) (* x x))) x)
(+ (+ (/ (* (* eps (* eps eps)) 1/16) (* (* x x) (* x x))) (* eps 1/2)) (/ (* 1/8 (* eps eps)) (* x x)))
(+ (/ (* (* eps (* eps eps)) 1/16) (* (* x x) (* x x))) (* eps 1/2))
(/ (* (* eps (* eps eps)) 1/16) (* (* x x) (* x x)))
(* (* eps (* eps eps)) 1/16)
(* eps (* eps eps))
eps
(* eps eps)
1/16
(* (* x x) (* x x))
(* x x)
x
(* eps 1/2)
1/2
(/ (* 1/8 (* eps eps)) (* x x))
(* 1/8 (* eps eps))
1/8

Outputs
(/ eps (+ x (pow (- (* x x) eps) 1/2)))
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
eps
(+ x (pow (- (* x x) eps) 1/2))
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
x
(pow (- (* x x) eps) 1/2)
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(- (* x x) eps)
(-.f64 (*.f64 x x) eps)
(* x x)
(*.f64 x x)
1/2
#s(literal 1/2 binary64)
(- x x)
#s(literal 0 binary64)
x
(* eps (+ (* (/ 1/8 (* x x)) (/ eps x)) (/ 1/2 x)))
(.f64 (/.f64 eps x) (+.f64 #s(literal 1/2 binary64) (.f64 #s(literal 1/8 binary64) (/.f64 (/.f64 eps x) x))))
eps
(+ (* (/ 1/8 (* x x)) (/ eps x)) (/ 1/2 x))
(+.f64 (/.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (/.f64 eps x) x)) x) (/.f64 #s(literal 1/2 binary64) x))
(* (/ 1/8 (* x x)) (/ eps x))
(/.f64 (*.f64 #s(literal 1/8 binary64) (/.f64 (/.f64 eps x) x)) x)
(/ 1/8 (* x x))
(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
1/8
#s(literal 1/8 binary64)
(* x x)
(*.f64 x x)
x
(/ eps x)
(/.f64 eps x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
(- x (/ (- (* x x) (* (/ (* eps -1/2) x) (/ (* eps -1/2) x))) (- x (/ (* eps -1/2) x))))
(+.f64 x (-.f64 (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x) x))
x
(/ (- (* x x) (* (/ (* eps -1/2) x) (/ (* eps -1/2) x))) (- x (/ (* eps -1/2) x)))
(+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(- (* x x) (* (/ (* eps -1/2) x) (/ (* eps -1/2) x)))
(+.f64 (.f64 x x) (/.f64 (.f64 eps (*.f64 eps (/.f64 #s(literal -1/4 binary64) x))) x))
(* x x)
(*.f64 x x)
(* (/ (* eps -1/2) x) (/ (* eps -1/2) x))
(/.f64 (.f64 eps (/.f64 (.f64 eps #s(literal 1/4 binary64)) x)) x)
(/ (* eps -1/2) x)
(/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)
(* eps -1/2)
(*.f64 eps #s(literal -1/2 binary64))
eps
-1/2
#s(literal -1/2 binary64)
(- x (/ (* eps -1/2) x))
(+.f64 x (/.f64 (*.f64 eps #s(literal 1/2 binary64)) x))
(/ (+ (+ (/ (* (* eps (* eps eps)) 1/16) (* (* x x) (* x x))) (* eps 1/2)) (/ (* 1/8 (* eps eps)) (* x x))) x)
(/.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 (/.f64 (/.f64 (.f64 eps eps) x) x) (+.f64 (/.f64 (.f64 eps #s(literal 1/16 binary64)) (*.f64 x x)) #s(literal 1/8 binary64)))) x)
(+ (+ (/ (* (* eps (* eps eps)) 1/16) (* (* x x) (* x x))) (* eps 1/2)) (/ (* 1/8 (* eps eps)) (* x x)))
(+.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 (/.f64 (/.f64 (.f64 eps eps) x) x) (+.f64 (/.f64 (.f64 eps #s(literal 1/16 binary64)) (*.f64 x x)) #s(literal 1/8 binary64))))
(+ (/ (* (* eps (* eps eps)) 1/16) (* (* x x) (* x x))) (* eps 1/2))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/16 binary64) (/.f64 (/.f64 (.f64 eps eps) x) x)) (.f64 x x))))
(/ (* (* eps (* eps eps)) 1/16) (* (* x x) (* x x)))
(/.f64 (/.f64 (.f64 eps (/.f64 (.f64 (.f64 eps eps) #s(literal 1/16 binary64)) x)) x) (.f64 x x))
(* (* eps (* eps eps)) 1/16)
(.f64 eps (.f64 (*.f64 eps eps) #s(literal 1/16 binary64)))
(* eps (* eps eps))
(.f64 eps (.f64 eps eps))
eps
(* eps eps)
(*.f64 eps eps)
1/16
#s(literal 1/16 binary64)
(* (* x x) (* x x))
(.f64 (.f64 x x) (*.f64 x x))
(* x x)
(*.f64 x x)
x
(* eps 1/2)
(*.f64 eps #s(literal 1/2 binary64))
1/2
#s(literal 1/2 binary64)
(/ (* 1/8 (* eps eps)) (* x x))
(.f64 eps (.f64 #s(literal 1/8 binary64) (/.f64 (/.f64 eps x) x)))
(* 1/8 (* eps eps))
(.f64 eps (.f64 eps #s(literal 1/8 binary64)))
1/8
#s(literal 1/8 binary64)

localize333.0ms (3.4%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.7%	(.f64 (.f64 x x) (*.f64 x x))
✓	accuracy	89.0%	(+.f64 (+.f64 (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x))) (.f64 eps #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 x x)))
✓	accuracy	61.4%	(/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (*.f64 x x))
✓	accuracy	55.5%	(/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x)))
✓	accuracy	100.0%	(-.f64 (.f64 x x) (.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)))
✓	accuracy	99.5%	(.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
✓	accuracy	89.3%	(/.f64 (-.f64 (.f64 x x) (.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))
✓	accuracy	62.9%	(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
✓	accuracy	100.0%	(+.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 eps x)) (/.f64 #s(literal 1/2 binary64) x))
✓	accuracy	99.8%	(/.f64 #s(literal 1/8 binary64) (*.f64 x x))
✓	accuracy	96.8%	(.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x x)) (/.f64 eps x))
✓	accuracy	88.0%	(.f64 eps (+.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (/.f64 eps x)) (/.f64 #s(literal 1/2 binary64) x)))
✓	accuracy	100.0%	(-.f64 x x)
✓	accuracy	100.0%	(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(-.f64 (*.f64 x x) eps)
✓	accuracy	100.0%	(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
✓	accuracy	99.6%	(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))

Results

123.0ms	82×	1	valid
89.0ms	155×	0	valid
62.0ms	19×	2	valid

Compiler

Compiled 336 to 37 computations (89% saved)

Precisions

Click to see histograms. Total time spent on operations: 99.0ms

ival-mult: 26.0ms (26.3% of total)

ival-div: 21.0ms (21.2% of total)

backward-pass: 17.0ms (17.2% of total)

ival-pow: 13.0ms (13.1% of total)

ival-add: 12.0ms (12.1% of total)

ival-sub: 8.0ms (8.1% of total)

const: 1.0ms (1% of total)

series35.0ms (0.4%)

Counts

19 → 420

Calls

Call 1

Inputs
#<alt (/ eps (+ x (pow (- (* x x) eps) 1/2)))>
#<alt (+ x (pow (- (* x x) eps) 1/2))>
#<alt (pow (- (* x x) eps) 1/2)>
#<alt (- (* x x) eps)>
#<alt (- x x)>
#<alt (* eps (+ (* (/ 1/8 (* x x)) (/ eps x)) (/ 1/2 x)))>
#<alt (+ (* (/ 1/8 (* x x)) (/ eps x)) (/ 1/2 x))>
#<alt (* (/ 1/8 (* x x)) (/ eps x))>
#<alt (/ 1/8 (* x x))>
#<alt (- x (/ (- (* x x) (* (/ (* eps -1/2) x) (/ (* eps -1/2) x))) (- x (/ (* eps -1/2) x))))>
#<alt (/ (- (* x x) (* (/ (* eps -1/2) x) (/ (* eps -1/2) x))) (- x (/ (* eps -1/2) x)))>
#<alt (- (* x x) (* (/ (* eps -1/2) x) (/ (* eps -1/2) x)))>
#<alt (* (/ (* eps -1/2) x) (/ (* eps -1/2) x))>
#<alt (/ (+ (+ (/ (* (* eps (* eps eps)) 1/16) (* (* x x) (* x x))) (* eps 1/2)) (/ (* 1/8 (* eps eps)) (* x x))) x)>
#<alt (+ (+ (/ (* (* eps (* eps eps)) 1/16) (* (* x x) (* x x))) (* eps 1/2)) (/ (* 1/8 (* eps eps)) (* x x)))>
#<alt (+ (/ (* (* eps (* eps eps)) 1/16) (* (* x x) (* x x))) (* eps 1/2))>
#<alt (/ (* (* eps (* eps eps)) 1/16) (* (* x x) (* x x)))>
#<alt (/ (* 1/8 (* eps eps)) (* x x))>
#<alt (* (* x x) (* x x))>

Outputs
#<alt (* 1/2 (/ eps x))>
#<alt (* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))>
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))>
#<alt (- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))>
#<alt (* -1 (* (sqrt eps) (sqrt -1)))>
#<alt (+ x (* -1 (* (sqrt eps) (sqrt -1))))>
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))>
#<alt (+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))>
#<alt (* (sqrt eps) (/ 1 (sqrt -1)))>
#<alt (+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))>
#<alt (* 1/2 (/ eps x))>
#<alt (/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)>
#<alt (/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)>
#<alt (/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)>
#<alt (* 2 x)>
#<alt (* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))>
#<alt (* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))>
#<alt (* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (+ x (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))>
#<alt (+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* -1/2 (/ eps (pow x 2)))))>
#<alt (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))>
#<alt (* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))>
#<alt (* 1/2 (/ eps x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))>
#<alt (* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))>
#<alt (* 2 x)>
#<alt (+ (* -1/2 (/ eps x)) (* 2 x))>
#<alt (+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))>
#<alt (+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))>
#<alt (* (sqrt eps) (sqrt -1))>
#<alt (* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))>
#<alt (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))>
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#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))>
#<alt (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))>
#<alt (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))>
#<alt (* 1/2 eps)>
#<alt (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))>
#<alt (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))>
#<alt (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))>
#<alt (* 1/2 eps)>
#<alt (* eps (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))))>
#<alt (* eps (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))))>
#<alt (* eps (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* (pow eps 3) (+ (* 1/2 (/ 1 (pow eps 2))) (* 1/16 (/ 1 (pow x 4)))))>
#<alt (* (pow eps 3) (+ (* 1/2 (/ 1 (pow eps 2))) (* 1/16 (/ 1 (pow x 4)))))>
#<alt (* (pow eps 3) (+ (* 1/2 (/ 1 (pow eps 2))) (* 1/16 (/ 1 (pow x 4)))))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* (pow eps 3) (+ (* 1/16 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 3) (+ (* 1/16 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* (pow eps 3) (+ (* 1/16 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow eps 2)))))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (/ (+ (* 1/16 (pow eps 3)) (* 1/2 (* eps (pow x 4)))) (pow x 4))>
#<alt (/ (+ (* 1/16 (pow eps 3)) (* 1/2 (* eps (pow x 4)))) (pow x 4))>
#<alt (/ (+ (* 1/16 (pow eps 3)) (* 1/2 (* eps (pow x 4)))) (pow x 4))>
#<alt (* 1/2 eps)>
#<alt (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))>
#<alt (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))>
#<alt (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))>
#<alt (* 1/2 eps)>
#<alt (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))>
#<alt (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))>
#<alt (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/16 (/ (pow eps 3) (pow x 4)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (* 1/8 (/ (pow eps 2) (pow x 2)))>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>
#<alt (pow x 4)>

Calls

105 calls:

Time	Variable		Point	Expression
4.0ms	eps	@	0	(- x (/ (- (* x x) (* (/ (* eps -1/2) x) (/ (* eps -1/2) x))) (- x (/ (* eps -1/2) x))))
3.0ms	x	@	0	(- x (/ (- (* x x) (* (/ (* eps -1/2) x) (/ (* eps -1/2) x))) (- x (/ (* eps -1/2) x))))
2.0ms	eps	@	inf	(- x (/ (- (* x x) (* (/ (* eps -1/2) x) (/ (* eps -1/2) x))) (- x (/ (* eps -1/2) x))))
2.0ms	eps	@	0	(/ (+ (+ (/ (* (* eps (* eps eps)) 1/16) (* (* x x) (* x x))) (* eps 1/2)) (/ (* 1/8 (* eps eps)) (* x x))) x)
2.0ms	eps	@	-inf	(- x (/ (- (* x x) (* (/ (* eps -1/2) x) (/ (* eps -1/2) x))) (- x (/ (* eps -1/2) x))))

rewrite369.0ms (3.8%)

Algorithm

1×	batch-egg-rewrite

Rules

3716×	`-lowering-.f32`
3716×	`-lowering-.f64`
2696×	`/-lowering-/.f32`
2696×	`/-lowering-/.f64`
2652×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	187
1	281	163
2	3203	158
0	8628	158

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 538

Calls

Call 1

Inputs
(/ eps (+ x (pow (- (* x x) eps) 1/2)))
(+ x (pow (- (* x x) eps) 1/2))
(pow (- (* x x) eps) 1/2)
(- (* x x) eps)
(- x x)
(* eps (+ (* (/ 1/8 (* x x)) (/ eps x)) (/ 1/2 x)))
(+ (* (/ 1/8 (* x x)) (/ eps x)) (/ 1/2 x))
(* (/ 1/8 (* x x)) (/ eps x))
(/ 1/8 (* x x))
(- x (/ (- (* x x) (* (/ (* eps -1/2) x) (/ (* eps -1/2) x))) (- x (/ (* eps -1/2) x))))
(/ (- (* x x) (* (/ (* eps -1/2) x) (/ (* eps -1/2) x))) (- x (/ (* eps -1/2) x)))
(- (* x x) (* (/ (* eps -1/2) x) (/ (* eps -1/2) x)))
(* (/ (* eps -1/2) x) (/ (* eps -1/2) x))
(/ (+ (+ (/ (* (* eps (* eps eps)) 1/16) (* (* x x) (* x x))) (* eps 1/2)) (/ (* 1/8 (* eps eps)) (* x x))) x)
(+ (+ (/ (* (* eps (* eps eps)) 1/16) (* (* x x) (* x x))) (* eps 1/2)) (/ (* 1/8 (* eps eps)) (* x x)))
(+ (/ (* (* eps (* eps eps)) 1/16) (* (* x x) (* x x))) (* eps 1/2))
(/ (* (* eps (* eps eps)) 1/16) (* (* x x) (* x x)))
(/ (* 1/8 (* eps eps)) (* x x))
(* (* x x) (* x x))

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) eps)) #s(literal -1 binary64)))
(neg.f64 (/.f64 eps (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) eps) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps) #s(literal 1 binary64)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps)))
(/.f64 (.f64 eps #s(literal 1 binary64)) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) eps)) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(pow.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))) eps) #s(literal 1 binary64)) #s(literal -1 binary64))
(.f64 eps (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))))
(.f64 (-.f64 #s(literal 0 binary64) eps) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))))
(.f64 #s(literal 1 binary64) (/.f64 eps (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) eps)
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) eps) #s(literal -1 binary64)))
(.f64 (/.f64 eps (+.f64 (.f64 x (.f64 x x)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (+.f64 (.f64 x x) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))))
(.f64 (/.f64 eps (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))) (-.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))
(+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))
(+.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) x)
(-.f64 (/.f64 (.f64 x x) (-.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (-.f64 (.f64 x x) eps) (-.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))))
(fma.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) x)
(/.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (+.f64 (.f64 x x) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (+.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) (.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (.f64 x x) (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (.f64 x x) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps))) (neg.f64 (-.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))
(/.f64 (-.f64 (-.f64 (.f64 x x) eps) (.f64 x x)) (-.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) x))
(pow.f64 (/.f64 (+.f64 (.f64 x x) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (+.f64 (.f64 x (.f64 x x)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (.f64 x x) (-.f64 (*.f64 x x) eps))) #s(literal -1 binary64))
(.f64 (+.f64 (.f64 x (.f64 x x)) (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (-.f64 (-.f64 (.f64 x x) eps) (.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))))))
(.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (/.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 (.f64 x x) eps))))
(exp.f64 (.f64 (log.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (-.f64 (*.f64 x x) eps)) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log.f64 (-.f64 (.f64 x x) eps)) #s(literal 1/4 binary64)) (.f64 (log.f64 (-.f64 (.f64 x x) eps)) #s(literal 1/4 binary64))))
(sqrt.f64 (-.f64 (*.f64 x x) eps))
(/.f64 (sqrt.f64 (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps)))) (sqrt.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 eps (.f64 x x))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps eps))) (pow.f64 (+.f64 eps (*.f64 x x)) #s(literal 1/2 binary64)))
(pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (*.f64 x x) eps)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log.f64 (-.f64 (*.f64 x x) eps)))
(.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)))
(.f64 (sqrt.f64 (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 eps (*.f64 x x))))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps eps))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 eps (.f64 x x))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 3/4 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 3/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/4 binary64)) #s(literal 1/2 binary64)))
(+.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) eps))
(+.f64 (-.f64 #s(literal 0 binary64) eps) (*.f64 x x))
(exp.f64 (log.f64 (-.f64 (*.f64 x x) eps)))
(exp.f64 (.f64 (log.f64 (-.f64 (.f64 x x) eps)) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (-.f64 (*.f64 x x) eps))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps))) #s(literal 1/2 binary64)))
(-.f64 (*.f64 x x) eps)
(-.f64 (/.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 eps (.f64 x x))))) (/.f64 (.f64 eps (.f64 eps eps)) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 eps (*.f64 x x))))))
(-.f64 (/.f64 (.f64 x (.f64 x (.f64 x x))) (+.f64 eps (.f64 x x))) (/.f64 (.f64 eps eps) (+.f64 eps (.f64 x x))))
(sqrt.f64 (.f64 (-.f64 (.f64 x x) eps) (-.f64 (*.f64 x x) eps)))
(fma.f64 x x (-.f64 #s(literal 0 binary64) eps))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 eps (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 eps (.f64 x x)))) (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 eps (.f64 x x)) (-.f64 (.f64 x (.f64 x (.f64 x x))) (*.f64 eps eps))))
(/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps eps)) (+.f64 eps (*.f64 x x)))
(/.f64 (neg.f64 (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps)))) (neg.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 eps (.f64 x x))))))
(/.f64 (neg.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps eps))) (neg.f64 (+.f64 eps (*.f64 x x))))
(/.f64 (+.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 #s(literal -1 binary64) (.f64 eps (.f64 eps eps)))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (-.f64 (.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) eps)) (.f64 (.f64 x x) (-.f64 #s(literal 0 binary64) eps)))))
(/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (-.f64 #s(literal 0 binary64) eps) (-.f64 #s(literal 0 binary64) eps))) (-.f64 (*.f64 x x) (-.f64 #s(literal 0 binary64) eps)))
(/.f64 (exp.f64 (log.f64 (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 eps (.f64 eps eps))))) (exp.f64 (log.f64 (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 eps (+.f64 eps (.f64 x x)))))))
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(.f64 (pow.f64 (/.f64 x #s(literal 1/16 binary64)) #s(literal -1 binary64)) (pow.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 eps (*.f64 eps eps))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 x (.f64 x x)) (.f64 eps (*.f64 eps eps))) #s(literal -1 binary64)) (pow.f64 (/.f64 x #s(literal 1/16 binary64)) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 x x) eps) #s(literal -1 binary64)) (pow.f64 (/.f64 (.f64 x x) (.f64 (*.f64 eps eps) #s(literal 1/16 binary64))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (.f64 x (.f64 x x)) eps) #s(literal -1 binary64)) (pow.f64 (/.f64 x (.f64 (*.f64 eps eps) #s(literal 1/16 binary64))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (.f64 eps (.f64 eps #s(literal 1/8 binary64))))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (.f64 eps (.f64 eps #s(literal 1/8 binary64))) (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(neg.f64 (/.f64 (.f64 (.f64 eps eps) #s(literal -1/8 binary64)) (*.f64 x x)))
(/.f64 (.f64 eps (.f64 eps #s(literal 1/8 binary64))) (*.f64 x x))
(/.f64 (.f64 (.f64 eps eps) #s(literal -1/8 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (.f64 eps (*.f64 eps #s(literal 1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) (.f64 eps (*.f64 eps #s(literal 1/8 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (.f64 eps (.f64 eps #s(literal 1/8 binary64))) x)))
(/.f64 (/.f64 (.f64 eps (.f64 eps #s(literal 1/8 binary64))) x) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 x x) (.f64 eps (*.f64 eps #s(literal 1/8 binary64))))))
(/.f64 (.f64 (.f64 eps (.f64 eps #s(literal 1/8 binary64))) #s(literal 1 binary64)) (.f64 x x))
(/.f64 (neg.f64 (.f64 (.f64 eps eps) #s(literal -1/8 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (/.f64 (.f64 eps (.f64 eps #s(literal 1/8 binary64))) x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 (/.f64 #s(literal 1/8 binary64) x) (.f64 eps eps)) x)
(pow.f64 (/.f64 (.f64 x x) (.f64 eps (*.f64 eps #s(literal 1/8 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (.f64 x x) (.f64 eps (*.f64 eps #s(literal 1/8 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 x (/.f64 (.f64 eps (.f64 eps #s(literal 1/8 binary64))) x)) #s(literal -1 binary64))
(.f64 #s(literal 1/8 binary64) (/.f64 (/.f64 (.f64 eps eps) x) x))
(.f64 (.f64 eps eps) (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))
(.f64 (.f64 eps (.f64 eps #s(literal 1/8 binary64))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (.f64 eps #s(literal 1/8 binary64)) (/.f64 eps (*.f64 x x)))
(.f64 (.f64 eps #s(literal 1/8 binary64)) (.f64 eps (/.f64 #s(literal 1 binary64) (.f64 x x))))
(.f64 (.f64 (.f64 eps eps) #s(literal -1/8 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 (/.f64 #s(literal 1/8 binary64) x) (/.f64 (.f64 eps eps) x))
(.f64 (/.f64 (.f64 eps eps) x) (/.f64 #s(literal 1/8 binary64) x))
(.f64 #s(literal 1 binary64) (/.f64 (.f64 eps (.f64 eps #s(literal 1/8 binary64))) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (.f64 eps (*.f64 eps #s(literal 1/8 binary64))) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (.f64 eps (.f64 eps #s(literal 1/8 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (pow.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps #s(literal 1/8 binary64)))) #s(literal -1 binary64)))
(.f64 (/.f64 (.f64 eps #s(literal 1/8 binary64)) x) (/.f64 eps x))
(.f64 (/.f64 (.f64 eps (*.f64 eps #s(literal 1/8 binary64))) x) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (/.f64 (.f64 eps eps) x) x) #s(literal 1/8 binary64))
(.f64 (pow.f64 (/.f64 x (.f64 eps #s(literal 1/8 binary64))) #s(literal -1 binary64)) (/.f64 eps x))
(exp.f64 (.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 4 binary64)))
(exp.f64 (+.f64 (.f64 #s(literal 2 binary64) (log.f64 x)) (.f64 #s(literal 2 binary64) (log.f64 x))))
(pow.f64 x #s(literal 4 binary64))
(pow.f64 (*.f64 x x) #s(literal 2 binary64))
(pow.f64 (.f64 x (.f64 x (*.f64 x x))) #s(literal 1 binary64))
(.f64 x (.f64 x (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 x x))
(.f64 (.f64 x (*.f64 x x)) x)

simplify365.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

4766×	`-lowering-.f32`
4766×	`-lowering-.f64`
2324×	`+-lowering-+.f64`
2324×	`+-lowering-+.f32`
1902×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	522	5014
1	1746	4415
2	6466	4338
0	8035	4338

Stop Event

1×	iter limit
1×	node limit

Counts

420 → 420

Calls

Call 1

Inputs
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(* (sqrt eps) (/ 1 (sqrt -1)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(* 2 x)
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(* (sqrt eps) (sqrt -1))
(+ x (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(* 2 x)
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(* 2 x)
(+ (* -1/2 (/ eps x)) (* 2 x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* (sqrt eps) (sqrt -1))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(* -1 x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(* (sqrt eps) (sqrt -1))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(* -1 eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(- (pow x 2) eps)
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(pow x 2)
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(+ (* -1 eps) (pow x 2))
(* -1 eps)
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* eps (- (/ (pow x 2) eps) 1))
(* -1 eps)
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
(* -1 (* eps (+ 1 (* -1 (/ (pow x 2) eps)))))
0
0
0
0
0
0
0
0
0
0
0
0
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* (pow eps 2) (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ (pow eps 2) (pow x 3)))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(/ (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))) (pow x 3))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* 1/8 (/ eps (pow x 3)))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ (+ (* 1/8 eps) (* 1/2 (pow x 2))) (pow x 3))
(/ 1/2 x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ (+ 1/2 (* 1/8 (/ eps (pow x 2)))) x)
(/ 1/2 x)
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(* -1 (/ (- (* -1/8 (/ eps (pow x 2))) 1/2) x))
(/ 1/2 x)
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))
(* 1/8 (/ eps (pow x 3)))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* eps (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))))
(* 1/8 (/ eps (pow x 3)))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(* eps (+ (* 1/8 (/ 1 (pow x 3))) (* 1/2 (/ 1 (* eps x)))))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(* 1/8 (/ eps (pow x 3)))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(/ 1/8 (pow x 2))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(/ (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(/ (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* -1/8 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))) x)
(/ (+ (* -1/4 (/ (pow eps 2) (pow x 2))) (+ (* -1/8 (/ (pow eps 3) (pow x 4))) (+ (* -1/16 (/ (pow eps 4) (pow x 6))) (+ (* 1/16 (/ (pow eps 4) (pow x 6))) (+ (* 1/8 (/ (pow eps 3) (pow x 4))) (+ (* 1/4 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))))))) x)
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* 1/2 (/ eps x))
(* eps (+ (* -1 (/ (+ (* -2 (pow x 3)) (* 2 (pow x 3))) (pow eps 2))) (* 1/2 (/ 1 x))))
(* eps (+ (* -1 (/ (+ (* -2 (pow x 3)) (* 2 (pow x 3))) (pow eps 2))) (* 1/2 (/ 1 x))))
(* eps (+ (* -1 (/ (+ (* -2 (pow x 3)) (* 2 (pow x 3))) (pow eps 2))) (* 1/2 (/ 1 x))))
(* 1/2 (/ eps x))
(* -1 (* eps (- (* -1 (/ (+ (* -2 (pow x 3)) (* 2 (pow x 3))) (pow eps 2))) (* 1/2 (/ 1 x)))))
(* -1 (* eps (- (* -1 (/ (+ (* -2 (pow x 3)) (* 2 (pow x 3))) (pow eps 2))) (* 1/2 (/ 1 x)))))
(* -1 (* eps (- (* -1 (/ (+ (* -2 (pow x 3)) (* 2 (pow x 3))) (pow eps 2))) (* 1/2 (/ 1 x)))))
(* -1/2 (/ eps x))
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
(/ (+ (* -1/2 eps) (pow x 2)) x)
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
x
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 1)))
x
(+ x (* -1/2 (/ eps x)))
(+ x (* -1/2 (/ eps x)))
(+ x (* -1/2 (/ eps x)))
(* -1/2 (/ eps x))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* eps (- (/ x eps) (* 1/2 (/ 1 x))))
(* -1/2 (/ eps x))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* 1/2 (/ 1 x)))))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(/ (- (pow x 4) (* 1/4 (pow eps 2))) (pow x 2))
(/ (- (pow x 4) (* 1/4 (pow eps 2))) (pow x 2))
(/ (- (pow x 4) (* 1/4 (pow eps 2))) (pow x 2))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4)))))
(* (pow x 2) (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4)))))
(* (pow x 2) (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4)))))
(pow x 2)
(* (pow x 2) (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4)))))
(* (pow x 2) (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4)))))
(* (pow x 2) (+ 1 (* -1/4 (/ (pow eps 2) (pow x 4)))))
(pow x 2)
(+ (* -1/4 (/ (pow eps 2) (pow x 2))) (pow x 2))
(+ (* -1/4 (/ (pow eps 2) (pow x 2))) (pow x 2))
(+ (* -1/4 (/ (pow eps 2) (pow x 2))) (pow x 2))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* (pow eps 2) (- (/ (pow x 2) (pow eps 2)) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (- (/ (pow x 2) (pow eps 2)) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (- (/ (pow x 2) (pow eps 2)) (* 1/4 (/ 1 (pow x 2)))))
(* -1/4 (/ (pow eps 2) (pow x 2)))
(* (pow eps 2) (- (/ (pow x 2) (pow eps 2)) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (- (/ (pow x 2) (pow eps 2)) (* 1/4 (/ 1 (pow x 2)))))
(* (pow eps 2) (- (/ (pow x 2) (pow eps 2)) (* 1/4 (/ 1 (pow x 2)))))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/4 (/ (pow eps 2) (pow x 2)))
(* 1/2 (/ eps x))
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(* 1/16 (/ (pow eps 3) (pow x 5)))
(* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(* (pow eps 3) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))
(* (pow eps 3) (+ (/ 1/8 (* eps (pow x 3))) (+ (/ 1/2 (* (pow eps 2) x)) (* 1/16 (/ 1 (pow x 5))))))
(* 1/16 (/ (pow eps 3) (pow x 5)))
(* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 3)))) (* 1/16 (/ 1 (pow x 5)))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))) eps)) (* 1/16 (/ 1 (pow x 5))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 (* eps x))) (* 1/8 (/ 1 (pow x 3)))) eps)) (* 1/16 (/ 1 (pow x 5))))))
(* 1/16 (/ (pow eps 3) (pow x 5)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))) (pow x 5))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 5))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 5))
(* 1/2 (/ eps x))
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(/ (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))) x)
(* 1/2 (/ eps x))
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(* 1/2 eps)
(* eps (+ 1/2 (* 1/8 (/ eps (pow x 2)))))
(* eps (+ 1/2 (* eps (+ (* 1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2)))))))
(* eps (+ 1/2 (* eps (+ (* 1/16 (/ eps (pow x 4))) (* 1/8 (/ 1 (pow x 2)))))))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* (pow eps 3) (+ (* 1/8 (/ 1 (* eps (pow x 2)))) (* 1/16 (/ 1 (pow x 4)))))
(* (pow eps 3) (+ (/ 1/8 (* eps (pow x 2))) (+ (/ 1/2 (pow eps 2)) (* 1/16 (/ 1 (pow x 4))))))
(* (pow eps 3) (+ (/ 1/8 (* eps (pow x 2))) (+ (/ 1/2 (pow eps 2)) (* 1/16 (/ 1 (pow x 4))))))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* (pow eps 3) (+ (* 1/16 (/ 1 (pow x 4))) (* 1/8 (/ 1 (* eps (pow x 2))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))) eps)) (* 1/16 (/ 1 (pow x 4))))))
(* -1 (* (pow eps 3) (- (* -1 (/ (+ (* 1/2 (/ 1 eps)) (* 1/8 (/ 1 (pow x 2)))) eps)) (* 1/16 (/ 1 (pow x 4))))))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/8 (* (pow eps 2) (pow x 2)))) (pow x 4))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 4))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 4))
(* 1/2 eps)
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))
(* 1/2 eps)
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))
(* 1/2 eps)
(* eps (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))))
(* eps (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))))
(* eps (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* (pow eps 3) (+ (* 1/2 (/ 1 (pow eps 2))) (* 1/16 (/ 1 (pow x 4)))))
(* (pow eps 3) (+ (* 1/2 (/ 1 (pow eps 2))) (* 1/16 (/ 1 (pow x 4)))))
(* (pow eps 3) (+ (* 1/2 (/ 1 (pow eps 2))) (* 1/16 (/ 1 (pow x 4)))))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* (pow eps 3) (+ (* 1/16 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 3) (+ (* 1/16 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow eps 2)))))
(* (pow eps 3) (+ (* 1/16 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow eps 2)))))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/2 (* eps (pow x 4)))) (pow x 4))
(/ (+ (* 1/16 (pow eps 3)) (* 1/2 (* eps (pow x 4)))) (pow x 4))
(/ (+ (* 1/16 (pow eps 3)) (* 1/2 (* eps (pow x 4)))) (pow x 4))
(* 1/2 eps)
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))
(* 1/2 eps)
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)
(pow x 4)

Outputs
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* eps (+ (* 1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x))))
(.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 (.f64 eps #s(literal 1/8 binary64)) (.f64 x (.f64 x x)))))
(* eps (+ (* eps (+ (* 1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (/.f64 (*.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 5 binary64)))))))
(* eps (+ (* eps (+ (* eps (+ (* 5/128 (/ eps (pow x 7))) (* 1/16 (/ 1 (pow x 5))))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x))))
(.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 eps (+.f64 (/.f64 (.f64 eps #s(literal 5/128 binary64)) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3))))) (pow eps 2))) (* (sqrt eps) (/ 1 (sqrt -1)))) (/ x (pow (sqrt -1) 2)))
(+.f64 x (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (/.f64 (.f64 x x) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (/.f64 #s(literal -1/2 binary64) (*.f64 eps eps)))))
(- (+ (* -1 (/ (+ (* -1 (* (sqrt eps) (/ (* x (+ (* -1 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (pow eps 3)) (/ (pow x 2) (pow (sqrt -1) 3)))))) (sqrt -1)))) (* -1/2 (/ (* (pow eps 2) (pow x 3)) (pow (sqrt -1) 4)))) (pow eps 3))) (* (sqrt eps) (/ 1 (sqrt -1)))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (pow (sqrt -1) 3)))) (/ x (pow (sqrt -1) 2)))))
(+.f64 (-.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (/.f64 (-.f64 (.f64 (.f64 #s(literal -1/2 binary64) (.f64 eps eps)) (/.f64 (.f64 x (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (.f64 (.f64 (sqrt.f64 eps) x) (.f64 (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (/.f64 (.f64 x x) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (.f64 eps (.f64 eps eps)))) (+.f64 (neg.f64 (.f64 (/.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) #s(literal -1/2 binary64))) x))
(* -1 (* (sqrt eps) (sqrt -1)))
(.f64 (sqrt.f64 eps) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(+ x (* -1 (* (sqrt eps) (sqrt -1))))
(-.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (+ (* -1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* (sqrt eps) (* (pow x 2) (sqrt -1)))) (* eps x)) eps)))
(-.f64 (.f64 (sqrt.f64 eps) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (-.f64 (.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 eps))) (*.f64 eps x)) eps))
(+ (* -1 (* (sqrt eps) (sqrt -1))) (* -1 (/ (- (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 eps)) (* x (* (sqrt -1) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))))))) (* 1/2 (* eps (pow x 3)))) (+ (* -1/2 (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1)))) (* (sqrt (pow eps 3)) (* (pow x 2) (sqrt -1))))) eps)) (* eps x)) eps)))
(-.f64 (.f64 (sqrt.f64 eps) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 (-.f64 (/.f64 (+.f64 (.f64 (neg.f64 (.f64 x (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))) (.f64 #s(literal 1/2 binary64) (.f64 (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (.f64 x x)) #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) (-.f64 (.f64 eps (.f64 x (.f64 x x))) (.f64 (sqrt.f64 (.f64 eps (.f64 eps eps))) (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))))))) (-.f64 #s(literal 0 binary64) eps)) (.f64 eps x)) eps))
(* (sqrt eps) (/ 1 (sqrt -1)))
(/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* -1 (/ x (pow (sqrt -1) 2))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 x (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) x)))))
(+ (* x (- (* x (- (* x (- (* 1/2 (/ 1 (* eps (pow (sqrt -1) 4)))) (* -1 (* (sqrt (/ 1 eps)) (/ (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))) (sqrt -1)))))) (+ (* -1 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (pow (sqrt -1) 3))))))) (/ 1 (pow (sqrt -1) 2)))) (* (sqrt eps) (/ 1 (sqrt -1))))
(+.f64 (/.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))) (.f64 x (+.f64 (/.f64 #s(literal 1/2 binary64) (.f64 eps (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (*.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (/.f64 #s(literal -1/2 binary64) (sqrt.f64 #s(literal -1 binary64))))))))))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(/ (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)) x)
(/.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x))))) x)
(/ (- (+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps)) (* -1/8 (/ (pow eps 2) (pow x 2)))) x)
(/.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (+.f64 (/.f64 (.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))))) x)
(/ (- (+ (* -1 (/ (+ (* -1/32 (pow eps 4)) (* -1/128 (pow eps 4))) (pow x 6))) (* 1/2 eps)) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x)
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -1 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal -5/128 binary64))) (pow.f64 x #s(literal 6 binary64))) (-.f64 (.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (/.f64 #s(literal 1/8 binary64) (.f64 x x))))) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 4 binary64))))) x)
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* -1 (* x (- (* 1/2 (/ eps (pow x 2))) 2)))
(.f64 x (.f64 #s(literal -1 binary64) (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 eps (.f64 x x))) #s(literal -2 binary64))))
(* -1 (* x (- (* -1 (/ (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))) (pow x 4))) (+ 2 (* -1/2 (/ eps (pow x 2)))))))
(.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 (/.f64 (.f64 (.f64 #s(literal -1 binary64) (.f64 eps eps)) #s(literal -1/8 binary64)) (pow.f64 x #s(literal 4 binary64))) (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x))))))
(* -1 (* x (- (* -1 (/ (+ (* -2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) eps)) (+ (* -1/4 (* eps (+ (* -1/4 (pow eps 2)) (* 1/8 (pow eps 2))))) (* 1/16 (pow eps 3)))) (pow x 6))) (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/4 (/ (pow eps 2) (pow x 4))) (* 1/8 (/ (pow eps 2) (pow x 4)))))))))
(.f64 (-.f64 (/.f64 (+.f64 (/.f64 (.f64 #s(literal -2 binary64) (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64))) eps) (+.f64 (.f64 #s(literal -1/4 binary64) (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64))) (.f64 #s(literal 1/16 binary64) (.f64 eps (.f64 eps eps))))) (neg.f64 (pow.f64 x #s(literal 6 binary64)))) (+.f64 #s(literal 2 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 eps (.f64 eps #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ x (* (sqrt eps) (sqrt -1)))
(+.f64 x (*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))))
(+ (* x (+ 1 (* 1/2 (* (sqrt (/ 1 eps)) (/ x (sqrt -1)))))) (* (sqrt eps) (sqrt -1)))
(+.f64 (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (/.f64 x (sqrt.f64 #s(literal -1 binary64))) #s(literal 1/2 binary64))))))
(+ (* x (+ 1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))) (* (sqrt eps) (sqrt -1)))
(+.f64 (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 (/.f64 (.f64 x x) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* -1/2 (/ eps (pow x 2)))))
(.f64 x (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(.f64 x (+.f64 #s(literal 2 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(* x (+ 2 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(.f64 x (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 (.f64 eps (.f64 eps #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64)))))))
(* 1/2 (/ eps x))
(/.f64 (*.f64 #s(literal 1/2 binary64) eps) x)
(* -1 (/ (+ (* -1/2 eps) (* -1/8 (/ (pow eps 2) (pow x 2)))) x))
(/.f64 (+.f64 (/.f64 (.f64 eps (.f64 eps #s(literal -1/8 binary64))) (.f64 x x)) (.f64 eps #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4))))) x))
(/.f64 (+.f64 (/.f64 (.f64 eps (.f64 eps #s(literal -1/8 binary64))) (.f64 x x)) (+.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 (.f64 (.f64 eps (*.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1/2 eps) (+ (* -1/2 (/ (+ (* 1/64 (pow eps 4)) (* 1/16 (pow eps 4))) (pow x 6))) (+ (* -1/8 (/ (pow eps 2) (pow x 2))) (* -1/16 (/ (pow eps 3) (pow x 4)))))) x))
(/.f64 (+.f64 (+.f64 (/.f64 (.f64 eps (.f64 eps #s(literal -1/8 binary64))) (.f64 x x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 4 binary64)))) (.f64 #s(literal -1/2 binary64) (+.f64 eps (/.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(+ (* -1/2 (/ eps x)) (* 2 x))
(+.f64 (.f64 x #s(literal 2 binary64)) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))
(+ (* 2 x) (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 eps (.f64 x x)))) x)))
(+ (* 2 x) (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+.f64 (.f64 x #s(literal 2 binary64)) (.f64 eps (+.f64 (.f64 eps (+.f64 (.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal -1/16 binary64)) (/.f64 #s(literal -1/8 binary64) (.f64 x (.f64 x x))))) (/.f64 #s(literal -1/2 binary64) x))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))
(.f64 eps (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 x eps)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps))))
(.f64 eps (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))) (/.f64 x eps))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (+ (* (sqrt (/ 1 eps)) (sqrt -1)) (/ x eps)))))
(.f64 eps (+.f64 (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))) (/.f64 x eps))) (.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(.f64 (sqrt.f64 eps) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* -1 (/ x eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (-.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 x eps)) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1/2 (* (sqrt (/ 1 eps)) (* (pow x 2) (sqrt -1))))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 (-.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (+.f64 x (.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal -1/2 binary64)))) eps)) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (+ (* -1 (/ (+ x (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 eps)) (* (pow x 4) (sqrt -1)))) (* 1/2 (* (sqrt eps) (* (pow x 2) (sqrt -1))))) eps))) eps)) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(-.f64 #s(literal 0 binary64) (.f64 eps (-.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (/.f64 (-.f64 x (/.f64 (+.f64 (.f64 (.f64 x (.f64 x (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 eps))) (.f64 #s(literal -1/8 binary64) (.f64 (pow.f64 x #s(literal 4 binary64)) (*.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)))))) eps)) eps))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(+ (* 1/2 (* (sqrt (/ 1 eps)) (/ (pow x 2) (sqrt -1)))) (* (sqrt eps) (sqrt -1)))
(+.f64 (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (.f64 (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (pow (sqrt -1) 3)))) (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))))))
(+.f64 (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 (/.f64 (.f64 x x) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))))) (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))))))
(+ (* (sqrt eps) (sqrt -1)) (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 eps)) (/ 1 (sqrt -1)))) (* (pow x 2) (+ (* -1/8 (* (sqrt (/ 1 (pow eps 3))) (/ 1 (pow (sqrt -1) 3)))) (* 1/16 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 2) (pow (sqrt -1) 5)))))))))
(+.f64 (.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) eps)) (sqrt.f64 #s(literal -1 binary64)))) (.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))) #s(literal -1/8 binary64))) (.f64 #s(literal 1/16 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (*.f64 x x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))))))))))
x
(* x (+ 1 (* -1/2 (/ eps (pow x 2)))))
(.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4))))))
(.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64))))))
(* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6)))))))
(.f64 x (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 eps (.f64 eps #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64)))))))
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (+ 1 (* -1/2 (/ eps (pow x 2))))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (* -1/8 (/ (pow eps 2) (pow x 4)))))))
(.f64 (+.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 eps (*.f64 eps #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1 (+ (* -1/2 (/ eps (pow x 2))) (+ (* -1/8 (/ (pow eps 2) (pow x 4))) (* -1/16 (/ (pow eps 3) (pow x 6))))))))
(.f64 (+.f64 #s(literal 1 binary64) (+.f64 (/.f64 (.f64 eps (.f64 eps #s(literal -1/8 binary64))) (pow.f64 x #s(literal 4 binary64))) (+.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/16 binary64)) (pow.f64 x #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) x))
x
(+ x (* -1/2 (/ eps x)))
(+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(+ x (* eps (- (* -1/8 (/ eps (pow x 3))) (* 1/2 (/ 1 x)))))
(+.f64 x (.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x)))
(+ x (* eps (- (* eps (- (* -1/16 (/ eps (pow x 5))) (* 1/8 (/ 1 (pow x 3))))) (* 1/2 (/ 1 x)))))
(+.f64 x (.f64 eps (+.f64 (.f64 eps (+.f64 (.f64 (/.f64 eps (pow.f64 x #s(literal 5 binary64))) #s(literal -1/16 binary64)) (/.f64 #s(literal -1/8 binary64) (.f64 x (*.f64 x x))))) (/.f64 #s(literal -1/2 binary64) x))))
(* (sqrt eps) (sqrt -1))
(*.f64 (sqrt.f64 eps) (sqrt.f64 #s(literal -1 binary64)))
(* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))
(.f64 eps (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (*.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64)))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(.f64 eps (+.f64 (.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))))))
(* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (/ (pow x 4) (pow (sqrt -1) 3)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (/ (pow x 6) (pow (sqrt -1) 5)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (/ (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 eps (+.f64 (.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (/.f64 (pow.f64 x #s(literal 4 binary64)) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64)))))) (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps)))) (.f64 (.f64 x (/.f64 x (sqrt.f64 #s(literal -1 binary64)))) #s(literal 1/2 binary64))) (.f64 (/.f64 (pow.f64 x #s(literal 6 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 5 binary64))) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))))))))
(* -1 (* (sqrt eps) (sqrt -1)))
(.f64 (sqrt.f64 eps) (.f64 #s(literal -1 binary64) (sqrt.f64 #s(literal -1 binary64))))
(* -1 (* eps (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))
(-.f64 #s(literal 0 binary64) (.f64 eps (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))))))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1))))))
(.f64 (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (+.f64 (.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (.f64 (*.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64))))) (-.f64 #s(literal 0 binary64) eps))
(* -1 (* eps (+ (* -1/8 (* (sqrt (/ 1 (pow eps 5))) (* (pow x 4) (sqrt -1)))) (+ (* 1/16 (* (sqrt (/ 1 (pow eps 7))) (* (pow x 6) (sqrt -1)))) (+ (* 1/2 (* (sqrt (/ 1 (pow eps 3))) (* (pow x 2) (sqrt -1)))) (* (sqrt (/ 1 eps)) (sqrt -1)))))))
(.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) eps))) (.f64 (.f64 (.f64 x x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 eps (.f64 eps eps))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/2 binary64)))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 5 binary64)))) (.f64 (.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 x #s(literal 4 binary64))) #s(literal -1/8 binary64))) (.f64 (.f64 (pow.f64 x #s(literal 6 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 eps #s(literal 7 binary64))))) (.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 1/16 binary64))))) (-.f64 #s(literal 0 binary64) eps))
(* -1 eps)
(-.f64 #s(literal 0 binary64) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(- (pow x 2) eps)
(-.f64 (*.f64 x x) eps)
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(* (pow x 2) (+ 1 (* -1 (/ eps (pow x 2)))))
(.f64 (.f64 x x) (-.f64 #s(literal 1 binary64) (/.f64 eps (*.f64 x x))))
(pow x 2)
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(/.f64 (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (.f64 eps eps))) (.f64 x (.f64 x (+.f64 (.f64 eps (.f64 eps #s(literal 1/8 binary64))) (.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 x x))))))) (pow.f64 x #s(literal 4 binary64)))
(/ (+ (* 1/16 (pow eps 3)) (* (pow x 2) (+ (* 1/8 (pow eps 2)) (* 1/2 (* eps (pow x 2)))))) (pow x 4))
(/.f64 (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (.f64 eps eps))) (.f64 x (.f64 x (+.f64 (.f64 eps (.f64 eps #s(literal 1/8 binary64))) (.f64 #s(literal 1/2 binary64) (.f64 eps (.f64 x x))))))) (pow.f64 x #s(literal 4 binary64)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (+.f64 (/.f64 (.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (+.f64 (/.f64 (.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (/.f64 #s(literal 1/8 binary64) (*.f64 x x)))))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (+.f64 (/.f64 (.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (+ (* 1/8 (/ (pow eps 2) (pow x 2))) (* 1/2 eps)))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (.f64 eps (+.f64 (/.f64 (.f64 eps #s(literal 1/16 binary64)) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/8 binary64) (.f64 x x))))))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(* eps (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/16 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))))
(* eps (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/16 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))))
(* eps (+ 1/2 (* 1/16 (/ (pow eps 2) (pow x 4)))))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/16 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* (pow eps 3) (+ (* 1/2 (/ 1 (pow eps 2))) (* 1/16 (/ 1 (pow x 4)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))))
(* (pow eps 3) (+ (* 1/2 (/ 1 (pow eps 2))) (* 1/16 (/ 1 (pow x 4)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))))
(* (pow eps 3) (+ (* 1/2 (/ 1 (pow eps 2))) (* 1/16 (/ 1 (pow x 4)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* (pow eps 3) (+ (* 1/16 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))))
(* (pow eps 3) (+ (* 1/16 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))))
(* (pow eps 3) (+ (* 1/16 (/ 1 (pow x 4))) (* 1/2 (/ 1 (pow eps 2)))))
(.f64 (.f64 eps (.f64 eps eps)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 4 binary64))) (/.f64 #s(literal 1/2 binary64) (.f64 eps eps))))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/2 (* eps (pow x 4)))) (pow x 4))
(/.f64 (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (.f64 eps eps))) (.f64 #s(literal 1/2 binary64) (*.f64 eps (pow.f64 x #s(literal 4 binary64))))) (pow.f64 x #s(literal 4 binary64)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/2 (* eps (pow x 4)))) (pow x 4))
(/.f64 (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (.f64 eps eps))) (.f64 #s(literal 1/2 binary64) (*.f64 eps (pow.f64 x #s(literal 4 binary64))))) (pow.f64 x #s(literal 4 binary64)))
(/ (+ (* 1/16 (pow eps 3)) (* 1/2 (* eps (pow x 4)))) (pow x 4))
(/.f64 (+.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (.f64 eps eps))) (.f64 #s(literal 1/2 binary64) (*.f64 eps (pow.f64 x #s(literal 4 binary64))))) (pow.f64 x #s(literal 4 binary64)))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/16 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/16 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/16 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))))
(* 1/2 eps)
(*.f64 #s(literal 1/2 binary64) eps)
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/16 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/16 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))))
(+ (* 1/16 (/ (pow eps 3) (pow x 4))) (* 1/2 eps))
(.f64 eps (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 #s(literal 1/16 binary64) (*.f64 eps eps)) (pow.f64 x #s(literal 4 binary64)))))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/16 (/ (pow eps 3) (pow x 4)))
(/.f64 (.f64 #s(literal 1/16 binary64) (.f64 eps (*.f64 eps eps))) (pow.f64 x #s(literal 4 binary64)))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(* 1/8 (/ (pow eps 2) (pow x 2)))
(.f64 #s(literal 1/8 binary64) (.f64 eps (/.f64 eps (*.f64 x x))))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))
(pow x 4)
(pow.f64 x #s(literal 4 binary64))

eval124.0ms (1.3%)

Compiler: Compiled 29419 to 2730 computations (90.7% saved)

prune258.0ms (2.7%)

Pruning

38 alts after pruning (34 fresh and 4 done)

	Pruned	Kept	Total
New	940	18	958
Fresh	21	16	37
Picked	5	0	5
Done	0	4	4
Total	966	38	1004

Accuracy

100.0%

Counts

1004 → 38

Alt Table

Click to see full alt table

Status	Accuracy	Program
	5.7%	(/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))) (+.f64 (.f64 x x) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
	44.0%	(/.f64 eps (+.f64 (.f64 x #s(literal 2 binary64)) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)))
	42.5%	(/.f64 eps (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 eps (.f64 x x)))) x))))
	44.0%	(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
	42.5%	(/.f64 eps (+.f64 x (+.f64 x (.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x)))))
	99.6%	(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
	43.4%	(/.f64 eps (+.f64 x x))
	43.6%	(/.f64 eps (.f64 x (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x))))))
	42.9%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
	4.4%	(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (+.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))))) (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))))))
	6.7%	(-.f64 (/.f64 (.f64 x x) (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
	3.6%	(-.f64 x (/.f64 (/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) x)) (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 x x)))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
	6.3%	(-.f64 x (/.f64 (-.f64 (.f64 x x) (/.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (-.f64 #s(literal 0 binary64) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
	6.8%	(-.f64 x (/.f64 (-.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
	6.3%	(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps x)) eps) (/.f64 #s(literal -1/2 binary64) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
	6.6%	(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps x)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
	6.6%	(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 eps (.f64 (/.f64 #s(literal -1/2 binary64) x) (.f64 #s(literal -1/2 binary64) (/.f64 eps x))))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
	6.0%	(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (.f64 eps eps) x) x))) (-.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
	3.6%	(-.f64 x (/.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
	5.3%	(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) eps) x))))
	4.4%	(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/16 binary64) (.f64 (/.f64 (/.f64 eps (.f64 x x)) (/.f64 (.f64 x x) eps)) (/.f64 (/.f64 eps (.f64 x x)) (/.f64 (.f64 x x) eps))))) x) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 x x) eps))) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))))
	5.5%	(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
	6.7%	(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
	6.8%	(-.f64 x (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))
	2.7%	(-.f64 x (.f64 (/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))))
	5.1%	(-.f64 x (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 eps (/.f64 x #s(literal 1/2 binary64))))) (-.f64 (.f64 x x) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 x x)))))
	6.8%	(-.f64 x (.f64 (+.f64 x (.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 eps (/.f64 x #s(literal 1/2 binary64))))))))
	4.7%	(-.f64 x (.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
	4.8%	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 (.f64 x (.f64 x eps)) eps)))))
	5.2%	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 eps x) (/.f64 x eps))))))
	6.6%	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))))
	6.6%	(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
✓	62.9%	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
✓	62.8%	(-.f64 x (sqrt.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps)))))
✓	58.3%	(-.f64 x (sqrt.f64 (neg.f64 eps)))
	43.3%	(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
✓	3.5%	x
	4.3%	#s(literal 0 binary64)

Compiler

Compiled 2947 to 869 computations (70.5% saved)

regimes90.0ms (0.9%)

Counts

84 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
x
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 eps (+.f64 x x))
(-.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))
(-.f64 x (*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 x (.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 eps (+.f64 (.f64 x #s(literal 2 binary64)) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)))
(.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))) x))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(-.f64 x (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) x))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
(/.f64 eps (.f64 x (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x))))))
(.f64 eps (+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(.f64 eps (+.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (/.f64 eps x)) (/.f64 #s(literal 1/2 binary64) x)))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) eps) #s(literal -1/2 binary64))))))
(/.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 x x))) x)
(.f64 (.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 eps x) (/.f64 x eps))))))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (/.f64 (.f64 x x) eps) eps)))))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 (.f64 x (.f64 x eps)) eps)))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x (*.f64 x eps)) (/.f64 #s(literal 1 binary64) eps))))))
(-.f64 x (+.f64 x (.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 x (.f64 x x)))))))
(/.f64 eps (+.f64 x (+.f64 x (.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x)))))
(/.f64 eps (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 eps (.f64 x x)))) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (.f64 eps eps) x) x))) (-.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (/.f64 (.f64 (.f64 eps (/.f64 eps (.f64 x x))) #s(literal -1/4 binary64)) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 eps (/.f64 x #s(literal 1/2 binary64))))) (-.f64 (.f64 x x) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 x x)))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 eps (.f64 (/.f64 #s(literal -1/2 binary64) x) (.f64 #s(literal -1/2 binary64) (/.f64 eps x))))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps x)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps x)) eps) (/.f64 #s(literal -1/2 binary64) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (.f64 (+.f64 x (.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 eps (/.f64 x #s(literal 1/2 binary64))))))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (/.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (-.f64 #s(literal 0 binary64) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (.f64 (.f64 eps eps) (+.f64 (/.f64 x (.f64 eps eps)) (/.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x x))))) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (/.f64 (.f64 (+.f64 (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) eps) x))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) x))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (/.f64 eps x) x) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))
(.f64 (.f64 (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (*.f64 x x)))))))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 eps x)))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 (+.f64 (+.f64 (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x))) (.f64 eps #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 x x))) x)
(-.f64 (/.f64 (.f64 x x) (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(-.f64 x (/.f64 (/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) x)) (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 x x)))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))) (+.f64 (.f64 x x) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)))) (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/16 binary64) (.f64 (/.f64 (/.f64 eps (.f64 x x)) (/.f64 (.f64 x x) eps)) (/.f64 (/.f64 eps (.f64 x x)) (/.f64 (.f64 x x) eps))))) x) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 x x) eps))) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))))
(-.f64 x (.f64 (/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))))
(.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (+.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (+.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))))) (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))))))
(-.f64 x (/.f64 (.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/64 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 x x) eps)) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 x x) eps)))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64))))
(-.f64 x (sqrt.f64 (.f64 eps (+.f64 #s(literal -1 binary64) (/.f64 (.f64 x x) eps)))))
(-.f64 x (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) eps)))))
(/.f64 (-.f64 (.f64 x x) (-.f64 (.f64 x x) eps)) (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))) (-.f64 (.f64 x x) (-.f64 (*.f64 x x) eps))))
(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x (.f64 x (.f64 x x)))) (.f64 (-.f64 (.f64 x x) eps) (.f64 (-.f64 (.f64 x x) eps) (-.f64 (.f64 x x) eps)))) (.f64 (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (+.f64 (.f64 x (.f64 x (.f64 x x))) (.f64 (-.f64 (.f64 x x) eps) (+.f64 (.f64 x x) (-.f64 (*.f64 x x) eps))))))
(-.f64 (/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (/.f64 (-.f64 (.f64 x x) eps) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))))
(-.f64 (/.f64 (.f64 x x) (+.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps)))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (-.f64 (*.f64 x x) eps)))
(.f64 eps (+.f64 (/.f64 #s(literal 1/2 binary64) x) (.f64 eps (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (.f64 eps (+.f64 (/.f64 (.f64 eps #s(literal 5/128 binary64)) (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (.f64 (pow.f64 eps #s(literal 4 binary64)) #s(literal 5/64 binary64)) (pow.f64 x #s(literal 6 binary64))) eps)) (+.f64 (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (*.f64 x x)))) x)
(+.f64 (-.f64 (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 eps (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 eps (/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (/.f64 eps (.f64 x x))) #s(literal -1/2 binary64)) x)))))
(fma.f64 (sqrt.f64 eps) (neg.f64 (sqrt.f64 (+.f64 #s(literal -1 binary64) (/.f64 (*.f64 x x) eps)))) x)
(fma.f64 (-.f64 (.f64 x x) eps) (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))))
(+.f64 (-.f64 (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64)))) (/.f64 (.f64 x x) (+.f64 x (pow.f64 (-.f64 (.f64 x x) eps) #s(literal 1/2 binary64))))) (/.f64 eps (+.f64 x (pow.f64 (-.f64 (*.f64 x x) eps) #s(literal 1/2 binary64)))))

Outputs
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))

Calls

3 calls:

26.0ms	x
26.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
24.0ms	eps

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`eps`
99.6%	1	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes74.0ms (0.8%)

Counts

69 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
x
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 eps (+.f64 x x))
(-.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))
(-.f64 x (*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 x (.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 eps (+.f64 (.f64 x #s(literal 2 binary64)) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)))
(.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))) x))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(-.f64 x (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) x))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
(/.f64 eps (.f64 x (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x))))))
(.f64 eps (+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(.f64 eps (+.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (/.f64 eps x)) (/.f64 #s(literal 1/2 binary64) x)))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) eps) #s(literal -1/2 binary64))))))
(/.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 x x))) x)
(.f64 (.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 eps x) (/.f64 x eps))))))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (/.f64 (.f64 x x) eps) eps)))))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 (.f64 x (.f64 x eps)) eps)))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x (*.f64 x eps)) (/.f64 #s(literal 1 binary64) eps))))))
(-.f64 x (+.f64 x (.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 x (.f64 x x)))))))
(/.f64 eps (+.f64 x (+.f64 x (.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x)))))
(/.f64 eps (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 eps (.f64 x x)))) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (.f64 eps eps) x) x))) (-.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (/.f64 (.f64 (.f64 eps (/.f64 eps (.f64 x x))) #s(literal -1/4 binary64)) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 eps (/.f64 x #s(literal 1/2 binary64))))) (-.f64 (.f64 x x) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 x x)))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 eps (.f64 (/.f64 #s(literal -1/2 binary64) x) (.f64 #s(literal -1/2 binary64) (/.f64 eps x))))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps x)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps x)) eps) (/.f64 #s(literal -1/2 binary64) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (.f64 (+.f64 x (.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 eps (/.f64 x #s(literal 1/2 binary64))))))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (/.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (-.f64 #s(literal 0 binary64) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (.f64 (.f64 eps eps) (+.f64 (/.f64 x (.f64 eps eps)) (/.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x x))))) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (/.f64 (.f64 (+.f64 (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) eps) x))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) x))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (/.f64 eps x) x) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))
(.f64 (.f64 (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (*.f64 x x)))))))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 eps x)))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 (+.f64 (+.f64 (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x))) (.f64 eps #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 x x))) x)
(-.f64 (/.f64 (.f64 x x) (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(-.f64 x (/.f64 (/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) x)) (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 x x)))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))) (+.f64 (.f64 x x) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)))) (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/16 binary64) (.f64 (/.f64 (/.f64 eps (.f64 x x)) (/.f64 (.f64 x x) eps)) (/.f64 (/.f64 eps (.f64 x x)) (/.f64 (.f64 x x) eps))))) x) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 x x) eps))) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))))
(-.f64 x (.f64 (/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))))
(.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (+.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (+.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))))) (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))))))
(-.f64 x (/.f64 (.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/64 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 x x) eps)) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 x x) eps)))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))
(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

Outputs

(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))

(/.f64 eps (+.f64 (*.f64 x #s(literal 2 binary64)) (*.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (*.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x))))

Calls

3 calls:

23.0ms	eps
19.0ms	(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))
19.0ms	x

Results

Accuracy	Segments	Branch
88.1%	2	`x`
82.8%	2	`eps`
99.5%	2	`(-.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps)))`

Compiler

Compiled 16 to 10 computations (37.5% saved)

regimes35.0ms (0.4%)

Counts

68 → 2

Calls

Call 1

Inputs
#s(literal 0 binary64)
x
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 eps (+.f64 x x))
(-.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))
(-.f64 x (*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 x (.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 eps (+.f64 (.f64 x #s(literal 2 binary64)) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)))
(.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))) x))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(-.f64 x (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) x))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
(/.f64 eps (.f64 x (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x))))))
(.f64 eps (+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(.f64 eps (+.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (/.f64 eps x)) (/.f64 #s(literal 1/2 binary64) x)))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) eps) #s(literal -1/2 binary64))))))
(/.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 x x))) x)
(.f64 (.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 eps x) (/.f64 x eps))))))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (/.f64 (.f64 x x) eps) eps)))))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 (.f64 x (.f64 x eps)) eps)))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x (*.f64 x eps)) (/.f64 #s(literal 1 binary64) eps))))))
(-.f64 x (+.f64 x (.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 x (.f64 x x)))))))
(/.f64 eps (+.f64 x (+.f64 x (.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x)))))
(/.f64 eps (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 eps (.f64 x x)))) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (.f64 eps eps) x) x))) (-.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (/.f64 (.f64 (.f64 eps (/.f64 eps (.f64 x x))) #s(literal -1/4 binary64)) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 eps (/.f64 x #s(literal 1/2 binary64))))) (-.f64 (.f64 x x) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 x x)))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 eps (.f64 (/.f64 #s(literal -1/2 binary64) x) (.f64 #s(literal -1/2 binary64) (/.f64 eps x))))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps x)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps x)) eps) (/.f64 #s(literal -1/2 binary64) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (.f64 (+.f64 x (.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 eps (/.f64 x #s(literal 1/2 binary64))))))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (/.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (-.f64 #s(literal 0 binary64) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (.f64 (.f64 eps eps) (+.f64 (/.f64 x (.f64 eps eps)) (/.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x x))))) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (/.f64 (.f64 (+.f64 (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) eps) x))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) x))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (/.f64 eps x) x) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))
(.f64 (.f64 (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (*.f64 x x)))))))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 eps x)))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 (+.f64 (+.f64 (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x))) (.f64 eps #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 x x))) x)
(-.f64 (/.f64 (.f64 x x) (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(-.f64 x (/.f64 (/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) x)) (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 x x)))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))) (+.f64 (.f64 x x) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)))) (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/16 binary64) (.f64 (/.f64 (/.f64 eps (.f64 x x)) (/.f64 (.f64 x x) eps)) (/.f64 (/.f64 eps (.f64 x x)) (/.f64 (.f64 x x) eps))))) x) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 x x) eps))) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))))
(-.f64 x (.f64 (/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))))
(.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (+.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (+.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))))) (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))))))
(-.f64 x (/.f64 (.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/64 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 x x) eps)) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 x x) eps)))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps)))

Outputs
(-.f64 x (sqrt.f64 (neg.f64 eps)))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))

Calls

1 calls:

24.0ms

Results

Accuracy	Segments	Branch
86.6%	2	`x`

Compiler

Compiled 3 to 2 computations (33.3% saved)

regimes83.0ms (0.9%)

Counts

66 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
x
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 eps (+.f64 x x))
(-.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))
(-.f64 x (*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 x (.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 eps (+.f64 (.f64 x #s(literal 2 binary64)) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)))
(.f64 eps (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (.f64 eps #s(literal 1/8 binary64)) (*.f64 x x))) x))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 (/.f64 eps x) (/.f64 #s(literal -1/2 binary64) x)))))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x)))))
(-.f64 x (.f64 (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))) x))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))))
(/.f64 eps (.f64 x (+.f64 #s(literal 2 binary64) (.f64 #s(literal -1/2 binary64) (/.f64 eps (*.f64 x x))))))
(.f64 eps (+.f64 (.f64 #s(literal 1/8 binary64) (/.f64 eps (.f64 x (.f64 x x)))) (/.f64 #s(literal 1/2 binary64) x)))
(.f64 eps (+.f64 (.f64 (/.f64 #s(literal 1/8 binary64) (*.f64 x x)) (/.f64 eps x)) (/.f64 #s(literal 1/2 binary64) x)))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) eps) #s(literal -1/2 binary64))))))
(/.f64 (+.f64 (.f64 eps #s(literal 1/2 binary64)) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 x x))) x)
(.f64 (.f64 eps eps) (+.f64 (/.f64 #s(literal 1/8 binary64) (.f64 x (.f64 x x))) (/.f64 (/.f64 #s(literal 1/2 binary64) x) eps)))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 eps x) (/.f64 x eps))))))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (/.f64 (.f64 x x) eps) eps)))))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 (.f64 x (.f64 x eps)) eps)))))
(-.f64 x (/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))))
(-.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 eps #s(literal -1/2 binary64)) (.f64 (.f64 x (*.f64 x eps)) (/.f64 #s(literal 1 binary64) eps))))))
(-.f64 x (+.f64 x (.f64 eps (+.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 (.f64 eps #s(literal -1/8 binary64)) (.f64 x (.f64 x x)))))))
(/.f64 eps (+.f64 x (+.f64 x (.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 eps (*.f64 x x)))) x)))))
(/.f64 eps (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 eps (.f64 x x)))) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 #s(literal 1/4 binary64) (/.f64 (/.f64 (.f64 eps eps) x) x))) (-.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (/.f64 (.f64 (.f64 eps (/.f64 eps (.f64 x x))) #s(literal -1/4 binary64)) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 eps (/.f64 x #s(literal 1/2 binary64))))) (-.f64 (.f64 x x) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (*.f64 x x)))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 eps (.f64 (/.f64 #s(literal -1/2 binary64) x) (.f64 #s(literal -1/2 binary64) (/.f64 eps x))))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 eps #s(literal -1/2 binary64)) (/.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps x)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 (.f64 (.f64 #s(literal -1/2 binary64) (/.f64 eps x)) eps) (/.f64 #s(literal -1/2 binary64) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (.f64 (+.f64 x (.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (*.f64 (+.f64 x (/.f64 eps (/.f64 x #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 x (/.f64 eps (/.f64 x #s(literal 1/2 binary64))))))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 (/.f64 x eps) #s(literal -1/2 binary64)) (/.f64 (/.f64 x eps) #s(literal -1/2 binary64))))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (-.f64 (.f64 x x) (/.f64 (.f64 (.f64 eps #s(literal 1/2 binary64)) (.f64 #s(literal -1/2 binary64) (/.f64 eps x))) (-.f64 #s(literal 0 binary64) x))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (.f64 (.f64 eps eps) (+.f64 (/.f64 x (.f64 eps eps)) (/.f64 #s(literal -1/4 binary64) (.f64 x (.f64 x x))))) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (/.f64 (.f64 (+.f64 (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))) #s(literal 1 binary64)) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) eps) x))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) x))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 (/.f64 eps x) x) (/.f64 eps (.f64 x x))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))
(.f64 (.f64 (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (.f64 x (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)))) (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 eps (*.f64 x x)))))))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/4 binary64) (.f64 (/.f64 eps (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 eps x)))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (-.f64 (-.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 (+.f64 (+.f64 (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal 1/16 binary64)) (.f64 (.f64 x x) (.f64 x x))) (.f64 eps #s(literal 1/2 binary64))) (/.f64 (.f64 #s(literal 1/8 binary64) (.f64 eps eps)) (.f64 x x))) x)
(-.f64 (/.f64 (.f64 x x) (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (/.f64 (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))) (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))
(-.f64 x (/.f64 (+.f64 (.f64 x (.f64 x x)) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (-.f64 (.f64 (/.f64 (.f64 eps #s(literal -1/2 binary64)) x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))))
(-.f64 x (/.f64 (/.f64 (-.f64 (.f64 x (.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) x)) (.f64 x (.f64 x x)))) (+.f64 (.f64 x x) (/.f64 (.f64 (.f64 eps eps) #s(literal 1/4 binary64)) (.f64 x x)))) (-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(/.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x))))) (+.f64 (.f64 x x) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 (+.f64 x x) (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)))) (-.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (.f64 (+.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) x)) (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))))
(-.f64 x (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 #s(literal 1/16 binary64) (.f64 (/.f64 (/.f64 eps (.f64 x x)) (/.f64 (.f64 x x) eps)) (/.f64 (/.f64 eps (.f64 x x)) (/.f64 (.f64 x x) eps))))) x) (.f64 (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 x x) eps))) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x)))))))
(-.f64 x (.f64 (/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal -1/4 binary64) (.f64 eps eps)) (.f64 (.f64 x x) (.f64 x x))))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 eps (.f64 eps eps)) #s(literal -1/8 binary64)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))))
(.f64 (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))))) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (+.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 x x) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (+.f64 x (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x)))))))) (-.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (*.f64 x x))))))))))
(-.f64 x (/.f64 (.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 #s(literal 1/64 binary64) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (/.f64 (.f64 eps (.f64 eps eps)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))))) (+.f64 #s(literal 1 binary64) (.f64 (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 x x) eps)) (+.f64 #s(literal 1 binary64) (/.f64 (.f64 #s(literal 1/4 binary64) (/.f64 eps (.f64 x x))) (/.f64 (.f64 x x) eps)))))) x) (-.f64 #s(literal 1 binary64) (.f64 eps (/.f64 #s(literal -1/2 binary64) (.f64 x x))))))

Outputs
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))

Calls

2 calls:

59.0ms	eps
20.0ms	x

Results

Accuracy	Segments	Branch
44.0%	1	`eps`
44.0%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes11.0ms (0.1%)

Counts

13 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
x
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
(*.f64 eps (/.f64 #s(literal 1/2 binary64) x))
(/.f64 eps (+.f64 x x))
(-.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x)))
(-.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))
(-.f64 x (+.f64 x (*.f64 #s(literal -1/2 binary64) (/.f64 eps x))))
(-.f64 x (+.f64 (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x) x))
(-.f64 x (*.f64 eps (+.f64 (/.f64 x eps) (/.f64 #s(literal -1/2 binary64) x))))
(-.f64 x (.f64 x (/.f64 (.f64 eps #s(literal -1/2 binary64)) (*.f64 x x))))

Outputs
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))

Calls

2 calls:

6.0ms	eps
4.0ms	x

Results

Accuracy	Segments	Branch
43.4%	1	`eps`
43.4%	1	`x`

Compiler

Compiled 6 to 4 computations (33.3% saved)

regimes5.0ms (0%)

Accuracy

Total -0.8b remaining (-1.3%)

Threshold costs -0.8b (-1.3%)

Counts

4 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
x
(*.f64 x #s(literal 2 binary64))
(-.f64 x x)

Outputs
#s(literal 0 binary64)

Calls

2 calls:

2.0ms	eps
2.0ms	x

Results

Accuracy	Segments	Branch
4.3%	1	`x`
4.3%	1	`eps`

Compiler

Compiled 6 to 4 computations (33.3% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-6.017913732657772e-154	0.0

Compiler

Compiled 15 to 10 computations (33.3% saved)

bsearch16.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	6.432524868148161e-95	4.655363714235024e-94

Results

6.0ms	42×	1	valid
3.0ms	54×	0	valid
1.0ms	18×	0	invalid

Compiler

Compiled 147 to 100 computations (32% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-sub: 3.0ms (50.7% of total)

ival-mult: 1.0ms (16.9% of total)

ival-sqrt: 1.0ms (16.9% of total)

backward-pass: 1.0ms (16.9% of total)

const: 0.0ms (0% of total)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

22×	`+-commutative_binary64`
16×	`*-commutative_binary64`
12×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	85
1	55	85
2	64	85
3	69	85
4	71	85

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 eps (.f64 x x)))) x)))))
(if (<=.f64 x #s(literal 211368832449645/587135645693458306972370149197334256843920637227079967676822742883052256278652110865924749596192175757983744 binary64)) (-.f64 x (sqrt.f64 (neg.f64 eps))) (/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
#s(literal 0 binary64)

Outputs
(/.f64 eps (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) eps))))
(if (<=.f64 (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) #s(literal -7547924849643083/15095849699286165408966218323953075563667684881665761713504825200982496649568595408344506900710635070165873500123055379599082338519699170530245737005730784174597581307904 binary64)) (-.f64 x (sqrt.f64 (-.f64 (.f64 x x) eps))) (/.f64 eps (+.f64 (.f64 x #s(literal 2 binary64)) (.f64 eps (/.f64 (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1/8 binary64) (/.f64 eps (.f64 x x)))) x)))))
(if (<=.f64 x #s(literal 211368832449645/587135645693458306972370149197334256843920637227079967676822742883052256278652110865924749596192175757983744 binary64)) (-.f64 x (sqrt.f64 (neg.f64 eps))) (/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(if (<=.f64 x #s(literal 211368832449645/587135645693458306972370149197334256843920637227079967676822742883052256278652110865924749596192175757983744 binary64)) (-.f64 x (sqrt.f64 (-.f64 #s(literal 0 binary64) eps))) (/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x)))))
(/.f64 eps (+.f64 x (+.f64 x (/.f64 (*.f64 eps #s(literal -1/2 binary64)) x))))
(*.f64 #s(literal 1/2 binary64) (/.f64 eps x))
#s(literal 0 binary64)

soundness1.8s (18.1%)

Rules

4906×	`-lowering-.f32`
4906×	`-lowering-.f64`
4766×	`-lowering-.f32`
4766×	`-lowering-.f64`
3716×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	164
1	261	160
2	2590	135
0	8989	135
0	36	187
1	281	163
2	3203	158
0	8628	158
0	522	5014
1	1746	4415
2	6466	4338
0	8035	4338
0	28	129
1	218	126
2	2304	106
0	8482	106
0	257	1162
1	856	1066
2	3033	1031
0	8035	1031

Stop Event

1×	fuel
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit

Compiler

Compiled 266 to 152 computations (42.9% saved)

preprocess76.0ms (0.8%)

Compiler: Compiled 220 to 100 computations (54.5% saved)

analyze26.0ms (0.3%)

sample1.6s (16.5%)

preprocess60.0ms (0.6%)

explain140.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify28.0ms (0.3%)

localize50.0ms (0.5%)

series8.0ms (0.1%)

rewrite318.0ms (3.3%)

simplify274.0ms (2.8%)

eval44.0ms (0.5%)

prune51.0ms (0.5%)

simplify181.0ms (1.9%)

localize295.0ms (3%)

series51.0ms (0.5%)

rewrite400.0ms (4.1%)

simplify337.0ms (3.5%)

eval197.0ms (2%)

prune184.0ms (1.9%)

simplify206.0ms (2.1%)

localize326.0ms (3.4%)

series40.0ms (0.4%)

rewrite322.0ms (3.3%)

simplify320.0ms (3.3%)

eval191.0ms (2%)

prune167.0ms (1.7%)

simplify242.0ms (2.5%)

localize333.0ms (3.4%)

series35.0ms (0.4%)

rewrite369.0ms (3.8%)

simplify365.0ms (3.8%)

eval124.0ms (1.3%)

prune258.0ms (2.7%)

regimes90.0ms (0.9%)

regimes74.0ms (0.8%)

regimes35.0ms (0.4%)

regimes83.0ms (0.9%)

regimes11.0ms (0.1%)

regimes5.0ms (0%)

bsearch1.0ms (0%)

bsearch16.0ms (0.2%)

simplify11.0ms (0.1%)

soundness1.8s (18.1%)

preprocess76.0ms (0.8%)

end0.0ms (0%)

Profiling