Metrics for 2isqrt (example 3.6)

analyze3.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	25%	75%	0%	0%	0%	0
0%	0%	25%	75%	0%	0%	0%	1
50%	12.5%	12.5%	75%	0%	0%	0%	2
75%	18.7%	6.2%	75%	0%	0%	0%	3
87.5%	21.9%	3.1%	75%	0%	0%	0%	4
93.8%	23.4%	1.6%	75%	0%	0%	0%	5
96.9%	24.2%	0.8%	75%	0%	0%	0%	6
98.4%	24.6%	0.4%	75%	0%	0%	0%	7
99.2%	24.8%	0.2%	75%	0%	0%	0%	8
99.6%	24.9%	0.1%	75%	0%	0%	0%	9
99.8%	24.9%	0%	75%	0%	0%	0%	10
99.9%	25%	0%	75%	0%	0%	0%	11
100%	25%	0%	75%	0%	0%	0%	12

Compiler

Compiled 19 to 12 computations (36.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 2.0ms

ival-div: 0.0ms (0% of total)

ival-add: 0.0ms (0% of total)

ival-sub: 0.0ms (0% of total)

ival-and: 0.0ms (0% of total)

ival-sqrt: 0.0ms (0% of total)

...c/correct-round.rkt:119:19: 0.0ms (0% of total)

const: 0.0ms (0% of total)

ival->: 0.0ms (0% of total)

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

ival-<: 0.0ms (0% of total)

sample2.1s (22.2%)

Results

1.3s	6521×	1	valid
419.0ms	1565×	2	valid
15.0ms	170×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.3s

ival-sqrt: 340.0ms (25.7% of total)

ival-div: 280.0ms (21.2% of total)

...c/correct-round.rkt:119:19: 154.0ms (11.7% of total)

backward-pass: 129.0ms (9.8% of total)

ival-add: 122.0ms (9.2% of total)

ival->: 117.0ms (8.9% of total)

ival-sub: 90.0ms (6.8% of total)

ival-<: 50.0ms (3.8% of total)

ival-and: 24.0ms (1.8% of total)

const: 16.0ms (1.2% of total)

Bogosity

preprocess51.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

308×	`fnmadd-define`
302×	`sum3-define`
248×	`fmsub-define`
232×	`fnmsub-define`
194×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	26
1	37	24
2	71	23
3	131	23
4	233	23
5	447	23
6	673	23
7	897	23
8	1037	23
9	1183	23
10	1293	23
11	1329	23
12	1337	23
0	8	7
1	17	7
2	25	7
3	36	7
4	50	7
5	87	7
6	157	7
7	252	7
8	351	7
9	483	7
10	594	7
11	630	7
12	638	7
0	638	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

Inputs
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

Outputs
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
(+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))

Call 2

Inputs
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
(- (/ 1 (sqrt (neg x))) (/ 1 (sqrt (+ (neg x) 1))))
(neg (- (/ 1 (sqrt (neg x))) (/ 1 (sqrt (+ (neg x) 1)))))

Outputs
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
(- (rsqrt x) (rsqrt (+ 1 x)))
(- (/ 1 (sqrt (neg x))) (/ 1 (sqrt (+ (neg x) 1))))
(- (rsqrt (neg x)) (rsqrt (- 1 x)))
(neg (- (/ 1 (sqrt (neg x))) (/ 1 (sqrt (+ (neg x) 1)))))
(- (rsqrt (- 1 x)) (rsqrt (neg x)))

explain158.0ms (1.7%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
175	1	(53.35527988154909)	-	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
0	0	-	-	`x`
0	0	-	-	`(sqrt.f64 (+.f64 x #s(literal 1 binary64)))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 x))`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))`
0	0	-	-	`(sqrt.f64 x)`
0	0	-	-	`(+.f64 x #s(literal 1 binary64))`

Results

90.0ms	414×	1	valid
24.0ms	86×	2	valid
1.0ms	12×	0	valid

Compiler

Compiled 80 to 26 computations (67.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 60.0ms

ival-sqrt: 20.0ms (33.4% of total)

ival-div: 18.0ms (30.1% of total)

backward-pass: 10.0ms (16.7% of total)

ival-add: 6.0ms (10% of total)

ival-sub: 5.0ms (8.4% of total)

const: 1.0ms (1.7% of total)

eval0.0ms (0%)

Compiler: Compiled 12 to 9 computations (25% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	38.3%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify20.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	cost-diff	(sqrt.f64 x)
✓	cost-diff	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	cost-diff	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Rules

156×	`fnmadd-define`
138×	`sum3-define`
112×	`fma-lowering-fma.f32`
112×	`fnmsub-define`
112×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	17	24
2	25	24
3	36	24
4	50	24
5	87	24
6	157	24
7	252	24
8	351	24
9	483	24
10	594	24
11	630	24
12	638	24
0	638	24

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
(/ 1 (sqrt x))
1
(sqrt x)
x
(/ 1 (sqrt (+ x 1)))
(sqrt (+ x 1))
(+ x 1)

Outputs
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
(+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/ 1 (sqrt x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
1
#s(literal 1 binary64)
(sqrt x)
(sqrt.f64 x)
x
(/ 1 (sqrt (+ x 1)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(sqrt (+ x 1))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(+ x 1)
(+.f64 #s(literal 1 binary64) x)

localize65.0ms (0.7%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	38.3%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

37.0ms	207×	1	valid
12.0ms	43×	2	valid
0.0ms	6×	0	valid

Compiler

Compiled 34 to 9 computations (73.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 29.0ms

ival-sqrt: 10.0ms (34.7% of total)

ival-div: 8.0ms (27.8% of total)

backward-pass: 5.0ms (17.4% of total)

ival-add: 3.0ms (10.4% of total)

ival-sub: 3.0ms (10.4% of total)

const: 1.0ms (3.5% of total)

series5.0ms (0.1%)

Counts

4 → 48

Calls

Call 1

Inputs
#<alt (- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))>
#<alt (/ 1 (sqrt x))>
#<alt (sqrt x)>
#<alt (/ 1 (sqrt (+ x 1)))>

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

Calls

12 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
1.0ms	x	@	inf	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
1.0ms	x	@	-inf	(/ 1 (sqrt x))
1.0ms	x	@	-inf	(/ 1 (sqrt (+ x 1)))
0.0ms	x	@	0	(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))

rewrite241.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

2958×	`-lowering-.f32`
2958×	`-lowering-.f64`
2750×	`/-lowering-/.f32`
2750×	`/-lowering-/.f64`
1418×	`sum5-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	64	15
2	598	15
3	7261	15
0	8224	15

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 220

Calls

Call 1

Inputs
(- (/ 1 (sqrt x)) (/ 1 (sqrt (+ x 1))))
(/ 1 (sqrt x))
(sqrt x)
(/ 1 (sqrt (+ x 1)))

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

simplify209.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

3318×	`-lowering-.f32`
3318×	`-lowering-.f64`
1694×	`sum4-define`
1580×	`sum3-define`
1304×	`times-frac`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	114	458
1	334	397
2	1139	374
3	4889	373
0	8236	373

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval30.0ms (0.3%)

Compiler: Compiled 6483 to 723 computations (88.8% saved)

prune56.0ms (0.6%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	255	13	268
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	256	13	269

Accuracy

83.1%

Counts

269 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	40.2%	(/.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
	40.2%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
▶	40.2%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
▶	81.8%	(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (*.f64 x x))
	40.2%	(/.f64 (.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
▶	38.3%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	32.9%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	27.1%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
	30.3%	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	40.3%	(.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
▶	80.7%	(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
	66.3%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
▶	5.7%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 430 to 256 computations (40.5% saved)

simplify158.0ms (1.7%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Rules

1808×	`-lowering-.f32`
1808×	`-lowering-.f64`
1628×	`fma-define`
1552×	`fnmsub-define`
1476×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	245
1	90	232
2	202	222
3	503	222
4	1054	222
5	2377	222
6	7292	222
0	8066	222

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize359.0ms (3.8%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
✓	accuracy	99.0%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
✓	accuracy	53.9%	(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))
✓	accuracy	8.4%	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
✓	accuracy	100.0%	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.1%	(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
✓	accuracy	83.8%	(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
✓	accuracy	100.0%	(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(pow.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) x)
✓	accuracy	38.3%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.2%	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
✓	accuracy	82.9%	(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (*.f64 x x))
✓	accuracy	70.1%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64)))))
✓	accuracy	69.7%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))

Results

206.0ms	207×	1	valid
68.0ms	43×	2	valid
2.0ms	6×	0	valid

Compiler

Compiled 282 to 34 computations (87.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 185.0ms

ival-pow: 49.0ms (26.4% of total)

ival-mult: 37.0ms (20% of total)

ival-div: 27.0ms (14.6% of total)

ival-sqrt: 25.0ms (13.5% of total)

backward-pass: 20.0ms (10.8% of total)

ival-add: 18.0ms (9.7% of total)

ival-sub: 8.0ms (4.3% of total)

const: 1.0ms (0.5% of total)

series25.0ms (0.3%)

Counts

19 → 228

Calls

Call 1

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

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

Calls

57 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	(* (- (sqrt (/ 1 x)) (sqrt x)) (/ -1/2 (* x x)))
2.0ms	x	@	-inf	(sqrt (* x (+ 1 x)))
2.0ms	x	@	0	(/ (- (+ 1 x) x) (* (sqrt (* x (+ 1 x))) (+ (sqrt (+ 1 x)) (sqrt x))))
1.0ms	x	@	-inf	(/ (- (+ 1 x) x) (* (sqrt (* x (+ 1 x))) (+ (sqrt (+ 1 x)) (sqrt x))))
1.0ms	x	@	inf	(* 1/2 (+ 1 (* x 1/4)))

rewrite327.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

3282×	`-lowering-.f32`
3282×	`-lowering-.f64`
2090×	`/-lowering-/.f32`
2090×	`/-lowering-/.f64`
2036×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	33	168
1	221	133
2	1990	124
0	8663	124

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 618

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))))) #s(literal -1 binary64)))
(neg.f64 (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))) (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))))) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 x x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (.f64 x x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))) x)))
(/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))) (*.f64 x x))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 x x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))))) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 (+.f64 (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))))) (pow.f64 x #s(literal 9/2 binary64))) (pow.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) #s(literal 3 binary64))) (.f64 (.f64 x x) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))))) (.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) (-.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))))))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))))) (pow.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) #s(literal 2 binary64))) (.f64 (.f64 x x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal 1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))))))
(/.f64 (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))) x) x)
(/.f64 (.f64 (+.f64 (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))))) (pow.f64 x #s(literal 9/2 binary64))) (pow.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))))) (.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) (-.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64)))))) (*.f64 x x)))
(/.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))))) (pow.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) #s(literal 2 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (.f64 #s(literal 1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))) (.f64 x x)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))))) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(/.f64 (neg.f64 (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))) x)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))) #s(literal 1 binary64)) (.f64 x x))
(/.f64 (.f64 (+.f64 (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))))) (pow.f64 x #s(literal 9/2 binary64))) (pow.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))))) (.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) (-.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64)))))))
(/.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))))) (pow.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) #s(literal 2 binary64))) (/.f64 #s(literal 1 binary64) (.f64 x x))) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal 1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))))
(pow.f64 (/.f64 (.f64 x x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (.f64 x x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 x (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))) x)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))) x))
(.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))) (/.f64 #s(literal 1 binary64) (.f64 x x)))
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(exp.f64 (.f64 (.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal 3 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -3/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 3 binary64)) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 3/2 binary64))) #s(literal -1 binary64)))
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) #s(literal 3/2 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 3 binary64)) #s(literal -1 binary64)))
(exp.f64 (+.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) (*.f64 #s(literal -1/2 binary64) (log.f64 x))))
(exp.f64 (+.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x)) (-.f64 #s(literal 0 binary64) (log.f64 x))))
(exp.f64 (neg.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 3 binary64))))
(fabs.f64 (pow.f64 x #s(literal -3/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 x))
(/.f64 (pow.f64 x #s(literal -1/2 binary64)) x)
(/.f64 #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3/2 binary64))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64)) #s(literal 3 binary64)))
(/.f64 (sqrt.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(pow.f64 x #s(literal -3/2 binary64))
(pow.f64 (*.f64 x x) #s(literal -3/4 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 3 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -3 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 3/4 binary64))
(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 6 binary64))
(pow.f64 (pow.f64 x #s(literal -3/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal 1/4 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -3/2 binary64)))
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 #s(literal 1 binary64) #s(literal -3/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (/.f64 (.f64 x x) #s(literal 1 binary64)) #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x)))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x))))))
(*.f64 (pow.f64 x #s(literal -3/4 binary64)) (pow.f64 x #s(literal -3/4 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 x #s(literal -3/4 binary64)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 #s(literal 1 binary64) #s(literal -3/2 binary64)) (pow.f64 x #s(literal -3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 #s(literal -1 binary64) #s(literal 3/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -3/4 binary64)) #s(literal 3/2 binary64)) (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 3/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal -3/2 binary64))) (sqrt.f64 (pow.f64 x #s(literal -3/2 binary64))))
(exp.f64 (*.f64 #s(literal -3 binary64) (log.f64 x)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -3 binary64)))
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) #s(literal 3 binary64)))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal 3 binary64))))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal 3 binary64)) (.f64 (.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal 3 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) (log.f64 x)) #s(literal 3 binary64))))
(exp.f64 (-.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))
(neg.f64 (pow.f64 (/.f64 #s(literal -1 binary64) x) #s(literal 3 binary64)))
(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))))
(/.f64 #s(literal 1 binary64) (pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x)) #s(literal 3 binary64)))
(/.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 x x))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(pow.f64 x #s(literal -3 binary64))
(pow.f64 (*.f64 x x) #s(literal -3/2 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 6 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -6 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 3/2 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) #s(literal -1 binary64))
(pow.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x))) #s(literal -1/2 binary64))
(pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 x #s(literal -3/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (*.f64 x x)))))
(*.f64 #s(literal -1 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal 3 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (pow.f64 x #s(literal -3/4 binary64)) (pow.f64 (pow.f64 x #s(literal -3/4 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -3/4 binary64)) #s(literal 3 binary64)) (pow.f64 x #s(literal -3/4 binary64)))
(exp.f64 (.f64 (log.f64 (/.f64 (.f64 x x) #s(literal -1/2 binary64))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))
(/.f64 #s(literal 1 binary64) (/.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal -1/2 binary64) x)))
(/.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 0 binary64) (*.f64 x x)))
(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
(/.f64 #s(literal -1/2 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (*.f64 x x) #s(literal -1/2 binary64))))
(/.f64 (/.f64 #s(literal -1/2 binary64) x) x)
(/.f64 (neg.f64 (/.f64 #s(literal -1/2 binary64) x)) (-.f64 #s(literal 0 binary64) x))
(pow.f64 (/.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (*.f64 x x) #s(literal -1/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 x (/.f64 #s(literal -1/2 binary64) x)) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x x))))
(.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1/2 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal -1/2 binary64))
(*.f64 (/.f64 #s(literal -1/2 binary64) x) (/.f64 #s(literal 1 binary64) x))
(exp.f64 (.f64 (log.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)))
(exp.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) (.f64 #s(literal 1/2 binary64) (log1p.f64 x))))
(exp.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (log1p.f64 x)) (.f64 #s(literal 1/2 binary64) (log.f64 x))))
(hypot.f64 x (sqrt.f64 x))
(hypot.f64 (sqrt.f64 x) x)
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (sqrt.f64 (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x))))))
(/.f64 (sqrt.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (sqrt.f64 (-.f64 x (*.f64 x x))))
(/.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 x #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) x)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 x #s(literal 1 binary64))))))
(/.f64 (sqrt.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(pow.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) (*.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 (log.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) #s(literal 1/2 binary64))
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))
(.f64 (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)))

simplify257.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

2916×	`-lowering-.f32`
2916×	`-lowering-.f64`
2134×	`+-lowering-+.f64`
2134×	`+-lowering-+.f32`
1770×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	422	2754
1	1364	2252
2	5270	2227
0	8075	2227

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

Calls

Call 1

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

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

eval179.0ms (1.9%)

Compiler: Compiled 32077 to 3326 computations (89.6% saved)

prune164.0ms (1.7%)

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	1205	21	1226
Fresh	6	2	8
Picked	3	2	5
Done	0	0	0
Total	1214	25	1239

Accuracy

100.0%

Counts

1239 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
	36.4%	(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
	36.4%	(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
▶	5.7%	(pow.f64 x #s(literal -1/2 binary64))
	40.2%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	97.4%	(/.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) x) x)
	80.7%	(/.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)) (/.f64 (*.f64 x x) #s(literal -1/2 binary64)))
	39.2%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (*.f64 (+.f64 #s(literal 1/2 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
	39.5%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
	32.7%	(/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (.f64 x (.f64 x x)))
	98.5%	(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64))) x)
▶	80.7%	(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64))) (*.f64 x x))
	97.3%	(/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) x)
	80.6%	(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
	98.9%	(/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) x))))
	5.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	38.3%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	32.6%	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
▶	99.3%	(.f64 (pow.f64 (.f64 (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (sqrt.f64 x)) #s(literal -1 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
▶	97.4%	(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)) x) (/.f64 #s(literal -1/2 binary64) x))
	80.7%	(.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))
	81.5%	(*.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 (/.f64 #s(literal -1/2 binary64) x) x))
	80.6%	(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
	67.4%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)))
▶	66.3%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
✓	5.7%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 643 to 421 computations (34.5% saved)

simplify178.0ms (1.9%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	cost-diff	0	(+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64)))
✓	cost-diff	0	(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64))) (*.f64 x x))
✓	cost-diff	0	(pow.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))
✓	cost-diff	0	(/.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)) x)
✓	cost-diff	0	(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)) x) (/.f64 #s(literal -1/2 binary64) x))
✓	cost-diff	0	(.f64 x (.f64 x x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
✓	cost-diff	0	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
✓	cost-diff	0	(pow.f64 x #s(literal -1/2 binary64))
✓	cost-diff	64	(+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
✓	cost-diff	6464	(*.f64 (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (sqrt.f64 x))
✓	cost-diff	12800	(pow.f64 (*.f64 (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (sqrt.f64 x)) #s(literal -1 binary64))
✓	cost-diff	12928	(.f64 (pow.f64 (.f64 (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (sqrt.f64 x)) #s(literal -1 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))

Rules

2130×	`sum5-define`
2000×	`fnmadd-define`
1920×	`-lowering-.f32`
1920×	`-lowering-.f64`
1730×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	177
1	61	175
2	97	168
3	169	168
4	366	168
5	977	168
6	2439	168
7	5397	168
0	8437	168

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize167.0ms (1.8%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	82.9%	(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64))) (*.f64 x x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))
✓	accuracy	99.7%	(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)) x) (/.f64 #s(literal -1/2 binary64) x))
✓	accuracy	99.6%	(/.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)) x)
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.2%	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
✓	accuracy	69.7%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
✓	accuracy	100.0%	(pow.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(pow.f64 (*.f64 (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (sqrt.f64 x)) #s(literal -1 binary64))
✓	accuracy	100.0%	(+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
✓	accuracy	99.6%	(.f64 (pow.f64 (.f64 (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (sqrt.f64 x)) #s(literal -1 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	accuracy	99.2%	(*.f64 (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (sqrt.f64 x))

Results

125.0ms

256×

valid

Compiler

Compiled 202 to 31 computations (84.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 72.0ms

ival-mult: 26.0ms (36.3% of total)

ival-pow: 25.0ms (34.9% of total)

ival-div: 9.0ms (12.6% of total)

ival-sqrt: 6.0ms (8.4% of total)

ival-add: 4.0ms (5.6% of total)

ival-sub: 1.0ms (1.4% of total)

const: 1.0ms (1.4% of total)

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

series15.0ms (0.2%)

Counts

17 → 204

Calls

Call 1

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

Outputs
#<alt (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))>
#<alt (/ (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)>
#<alt (/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)>
#<alt (/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (+ (* x (+ (* -1 (* (sqrt x) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))) (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))))))) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x)))))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2))>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (pow x 2))>
#<alt (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))>
#<alt (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* 1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 4))))) x)) (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))>
#<alt (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))>
#<alt (/ (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)>
#<alt (/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* (sqrt (pow x 3)) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)>
#<alt (/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1 (* (sqrt (pow x 3)) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))) (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)>
#<alt (/ 1/2 x)>
#<alt (/ (- 1/2 (* 1/8 (/ 1 x))) x)>
#<alt (/ (- (+ 1/2 (* 1/16 (/ 1 (pow x 2)))) (/ 1/8 x)) x)>
#<alt (/ (- (+ 1/2 (+ (* -1 (* (sqrt (/ 1 (pow x 13))) (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))))) (* 1/16 (/ 1 (pow x 2))))) (/ 1/8 x)) x)>
#<alt (/ -1/2 (* x (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (+ (* 1/8 (/ 1 (* x (pow (sqrt -1) 4)))) (* 1/2 (/ 1 (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (- (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 6))) (* 1/2 (/ 1 (pow (sqrt -1) 2)))) (/ -1/8 (* x (pow (sqrt -1) 4)))) x))>
#<alt (* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 (pow x 13))) (* (sqrt -1) (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 7)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 7)))))))) (+ (* 1/16 (/ 1 (* (pow x 2) (pow (sqrt -1) 6)))) (* 1/2 (/ 1 (pow (sqrt -1) 2))))) (/ -1/8 (* x (pow (sqrt -1) 4)))) x))>
#<alt (* (sqrt x) (+ 1 (sqrt x)))>
#<alt (+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (+ 1 (sqrt x))))>
#<alt (+ (* x (+ (* -1/8 (sqrt (pow x 3))) (* 1/2 (sqrt x)))) (* (sqrt x) (+ 1 (sqrt x))))>
#<alt (+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/16 (sqrt (pow x 3))))))) (* (sqrt x) (+ 1 (sqrt x))))>
#<alt (* 2 x)>
#<alt (* (pow x 2) (+ (* 2 (/ 1 x)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (- (+ (* 2 (/ 1 x)) (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 3))))>
#<alt (* (pow x 2) (- (+ (/ 1/16 (pow x 4)) (+ (* 2 (/ 1 x)) (* 1/2 (/ 1 (pow x 2))))) (* 1/8 (/ 1 (pow x 3)))))>
#<alt (* -2 (* x (pow (sqrt -1) 2)))>
#<alt (* (pow x 2) (+ (* -2 (/ (pow (sqrt -1) 2) x)) (* 1/2 (/ 1 (pow x 2)))))>
#<alt (* (pow x 2) (+ (* -2 (/ (pow (sqrt -1) 2) x)) (+ (/ 1/8 (* (pow x 3) (pow (sqrt -1) 2))) (* 1/2 (/ 1 (pow x 2))))))>
#<alt (* (pow x 2) (+ (* -2 (/ (pow (sqrt -1) 2) x)) (+ (* 1/8 (/ 1 (* (pow x 3) (pow (sqrt -1) 2)))) (+ (* 1/16 (/ 1 (* (pow x 4) (pow (sqrt -1) 4)))) (* 1/2 (/ 1 (pow x 2)))))))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (+ (sqrt x) (* 1/2 x)))>
#<alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))>
#<alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))>
#<alt (* 2 (sqrt x))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))>
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (pow x 3))>
#<alt (/ 1 (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 (pow x 3)>
#<alt (* -1/2 (sqrt (/ 1 (pow x 5))))>
#<alt (/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) (pow x 2))>
#<alt (* -1 (sqrt (/ 1 x)))>
#<alt (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x))))>
#<alt (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x))))>
#<alt (+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x))))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ 1 x))>
#<alt (/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)>
#<alt (* -1 (sqrt x))>
#<alt (* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))>
#<alt (* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))>
#<alt (* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))>
#<alt (* (sqrt x) (pow (sqrt -1) 2))>
#<alt (* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1/4 (sqrt (/ 1 (pow x 5))))>
#<alt (/ (+ (* -1/4 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (/ (+ (* -1/4 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (/ (+ (* -1/4 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1/4 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/4 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (* -1/4 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (* -1/4 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (* 1/2 (sqrt x))>
#<alt (* x (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>

Calls

51 calls:

Time	Variable		Point	Expression
4.0ms	x	@	-inf	(pow (* (+ (sqrt x) (pow (+ 1 x) 1/2)) (sqrt x)) -1)
1.0ms	x	@	inf	(pow (* (+ (sqrt x) (pow (+ 1 x) 1/2)) (sqrt x)) -1)
0.0ms	x	@	-inf	(* (+ (sqrt x) (pow (+ 1 x) 1/2)) (sqrt x))
0.0ms	x	@	-inf	(/ (+ (* 1/2 (sqrt x)) (* (sqrt (/ 1 x)) -1/4)) (* x x))
0.0ms	x	@	0	(/ (+ (* 1/2 (sqrt x)) (* (sqrt (/ 1 x)) -1/4)) (* x x))

rewrite315.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

3430×	`/-lowering-/.f32`
3430×	`/-lowering-/.f64`
3128×	`-lowering-.f32`
3128×	`-lowering-.f64`
1772×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	126
1	172	105
2	1320	103
0	8371	103

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 811

Calls

Call 1

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

Outputs
(exp.f64 (+.f64 (.f64 #s(literal -1 binary64) (log.f64 (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))))) (*.f64 #s(literal -1/2 binary64) (log1p.f64 x))))
(exp.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (log1p.f64 x)) (.f64 #s(literal -1 binary64) (log.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))) (.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))) (.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)))))
(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))))
(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))) #s(literal 1 binary64)))
(/.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 x))
(/.f64 (.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))))
(/.f64 (.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64))) (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))))
(/.f64 (neg.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64))) (neg.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64))) (neg.f64 (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)))) (neg.f64 (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64)))))))
(pow.f64 (.f64 (pow.f64 (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))) #s(literal 2 binary64))
(pow.f64 (.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (pow.f64 (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))) #s(literal -1/2 binary64))) #s(literal 2 binary64))
(pow.f64 (.f64 (pow.f64 (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal -1/2 binary64))
(pow.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (pow.f64 (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))) #s(literal -1/2 binary64))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64)))))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64)))))))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (pow.f64 (.f64 x (+.f64 x #s(literal 1 binary64))) #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 x)))
(.f64 (pow.f64 (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))) #s(literal -1/2 binary64)) (pow.f64 (.f64 (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))) (+.f64 x #s(literal 1 binary64))) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64)))))))
(.f64 (.f64 (pow.f64 (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))) (.f64 (pow.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))))
(.f64 (.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (pow.f64 (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))) #s(literal -1/2 binary64))) (.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (pow.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))) #s(literal -1/2 binary64))))
(.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)))
(*.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (pow.f64 x #s(literal -1/2 binary64)))
(.f64 (pow.f64 (.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64)))))) #s(literal -1/2 binary64)) (pow.f64 (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))) #s(literal -1/2 binary64)))
(.f64 (.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))))
(.f64 (.f64 #s(literal 1 binary64) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))))
(*.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 x)) (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(*.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/4 binary64)) (sqrt.f64 x)))
(*.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))))
(exp.f64 (.f64 #s(literal -1 binary64) (log.f64 (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))))))
(exp.f64 (.f64 (log.f64 (pow.f64 (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))) #s(literal -1/2 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (pow.f64 (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))) #s(literal 2 binary64))) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))) #s(literal -1/2 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (log.f64 x)) (.f64 (log.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal -1 binary64))))
(exp.f64 (+.f64 (.f64 (log.f64 (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))) #s(literal -1 binary64)) (.f64 #s(literal -1/2 binary64) (log.f64 x))))
(exp.f64 (+.f64 (.f64 (log.f64 (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64)))))) #s(literal -1/2 binary64)) (.f64 (log.f64 (+.f64 x (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64)))))) #s(literal -1/2 binary64))))
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(*.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) x))
(*.f64 (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 x)) (/.f64 (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 x)))

simplify238.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

4190×	`-lowering-.f32`
4190×	`-lowering-.f64`
3174×	`+-lowering-+.f64`
3174×	`+-lowering-+.f32`
1450×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	350	2397
1	1102	2051
2	4203	2017
0	8353	2017

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
(* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))
(/ (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
(/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
(/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))) (+ (* x (+ (* -1 (* (sqrt x) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))) (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))))))) (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* 1/2 (* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x)))))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) (pow x 2))
(/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -5/32 (sqrt (/ 1 (pow x 5)))) (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))))) (pow x 2))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* 1/4 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/2 (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* 1/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 4))))) x)) (+ (* -1/4 (* (sqrt x) (/ (+ 1 (* 1/4 (/ 1 (pow (sqrt -1) 2)))) (pow (sqrt -1) 2)))) (* -1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))))) x)) (* -1/4 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) x)) (* 1/2 (sqrt x))) (pow x 2))
(* (sqrt (/ 1 x)) (/ 1 (+ 1 (sqrt x))))
(/ (+ (* -1/2 (* (sqrt (pow x 3)) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
(/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* (sqrt (pow x 3)) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
(/ (+ (* x (+ (* -1/2 (* (sqrt x) (/ 1 (pow (+ 1 (sqrt x)) 2)))) (* x (+ (* -1 (* (sqrt (pow x 3)) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))) (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))))))) (* (sqrt x) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))))))) (* (sqrt x) (/ 1 (+ 1 (sqrt x))))) x)
(/ 1/2 x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (* 1/16 (/ 1 (pow x 2)))) (/ 1/8 x)) x)
(/ (- (+ 1/2 (+ (* -1 (* (sqrt (/ 1 (pow x 13))) (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))))) (* 1/16 (/ 1 (pow x 2))))) (/ 1/8 x)) x)
(/ -1/2 (* x (pow (sqrt -1) 2)))
(* -1 (/ (+ (* 1/8 (/ 1 (* x (pow (sqrt -1) 4)))) (* 1/2 (/ 1 (pow (sqrt -1) 2)))) x))
(* -1 (/ (- (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 6))) (* 1/2 (/ 1 (pow (sqrt -1) 2)))) (/ -1/8 (* x (pow (sqrt -1) 4)))) x))
(* -1 (/ (- (+ (* -1 (* (sqrt (/ 1 (pow x 13))) (* (sqrt -1) (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 7)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 7)))))))) (+ (* 1/16 (/ 1 (* (pow x 2) (pow (sqrt -1) 6)))) (* 1/2 (/ 1 (pow (sqrt -1) 2))))) (/ -1/8 (* x (pow (sqrt -1) 4)))) x))
(* (sqrt x) (+ 1 (sqrt x)))
(+ (* 1/2 (sqrt (pow x 3))) (* (sqrt x) (+ 1 (sqrt x))))
(+ (* x (+ (* -1/8 (sqrt (pow x 3))) (* 1/2 (sqrt x)))) (* (sqrt x) (+ 1 (sqrt x))))
(+ (* x (+ (* 1/2 (sqrt x)) (* x (+ (* -1/8 (sqrt x)) (* 1/16 (sqrt (pow x 3))))))) (* (sqrt x) (+ 1 (sqrt x))))
(* 2 x)
(* (pow x 2) (+ (* 2 (/ 1 x)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (- (+ (* 2 (/ 1 x)) (* 1/2 (/ 1 (pow x 2)))) (/ 1/8 (pow x 3))))
(* (pow x 2) (- (+ (/ 1/16 (pow x 4)) (+ (* 2 (/ 1 x)) (* 1/2 (/ 1 (pow x 2))))) (* 1/8 (/ 1 (pow x 3)))))
(* -2 (* x (pow (sqrt -1) 2)))
(* (pow x 2) (+ (* -2 (/ (pow (sqrt -1) 2) x)) (* 1/2 (/ 1 (pow x 2)))))
(* (pow x 2) (+ (* -2 (/ (pow (sqrt -1) 2) x)) (+ (/ 1/8 (* (pow x 3) (pow (sqrt -1) 2))) (* 1/2 (/ 1 (pow x 2))))))
(* (pow x 2) (+ (* -2 (/ (pow (sqrt -1) 2) x)) (+ (* 1/8 (/ 1 (* (pow x 3) (pow (sqrt -1) 2)))) (+ (* 1/16 (/ 1 (* (pow x 4) (pow (sqrt -1) 4)))) (* 1/2 (/ 1 (pow x 2)))))))
(+ 1 (sqrt x))
(+ 1 (+ (sqrt x) (* 1/2 x)))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))
(* 2 (sqrt x))
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 1 (pow x 3))
(/ 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)
(pow x 3)
(* -1/2 (sqrt (/ 1 (pow x 5))))
(/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(sqrt (/ 1 (pow x 3)))
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) (pow x 2))
(* -1 (sqrt (/ 1 x)))
(+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x))))
(+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x))))
(+ (sqrt (/ 1 (pow x 3))) (* -1 (sqrt (/ 1 x))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)
(/ (+ (sqrt x) (* -1 (sqrt (pow x 3)))) x)
(* -1 (sqrt x))
(* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))
(* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))
(* x (- (sqrt (/ 1 (pow x 3))) (sqrt (/ 1 x))))
(* (sqrt x) (pow (sqrt -1) 2))
(* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (- (* -1 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1/4 (sqrt (/ 1 (pow x 5))))
(/ (+ (* -1/4 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(/ (+ (* -1/4 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(/ (+ (* -1/4 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1/4 (sqrt (/ 1 x)))
(/ (+ (* -1/4 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/4 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/4 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(* 1/2 (sqrt x))
(* x (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* 1/4 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* 1/2 (sqrt x))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))

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

eval171.0ms (1.8%)

Compiler: Compiled 21889 to 3152 computations (85.6% saved)

prune180.0ms (1.9%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	1179	11	1190
Fresh	16	2	18
Picked	4	1	5
Done	1	1	2
Total	1200	15	1215

Accuracy

100.0%

Counts

1215 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	5.7%	(pow.f64 x #s(literal -1/2 binary64))
	83.0%	(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))))
	96.7%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 x #s(literal -1/2 binary64)))
	5.7%	(/.f64 (sqrt.f64 x) x)
▶	5.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
▶	96.7%	(/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3/2 binary64)))
✓	38.3%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	32.6%	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	97.6%	(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
▶	98.8%	(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
▶	98.5%	(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	97.4%	(*.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	97.2%	(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))
	97.4%	(*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) x))
▶	97.2%	(*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))

Compiler

Compiled 272 to 204 computations (25% saved)

simplify48.0ms (0.5%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal -1/8 binary64) x)
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
✓	cost-diff	0	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
✓	cost-diff	0	(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 x))
✓	cost-diff	128	(*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))
✓	cost-diff	0	(pow.f64 x #s(literal 3/2 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3/2 binary64)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	cost-diff	0	(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
✓	cost-diff	128	(+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))
✓	cost-diff	128	(/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) x)
✓	cost-diff	128	(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))

Rules

996×	`fma-define`
692×	`fma-lowering-fma.f32`
692×	`fma-lowering-fma.f64`
500×	`-lowering-.f32`
500×	`-lowering-.f64`

Iterations

Useful iterations: 9 (0.0ms)

Iter	Nodes	Cost
0	25	150
1	48	145
2	74	145
3	117	145
4	220	145
5	330	145
6	405	145
7	495	144
8	601	144
9	866	142
10	1490	142
11	1690	142
12	1720	142
0	1720	142

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* (/ (+ (/ 1/16 (* x x)) (+ 1/2 (/ -1/8 x))) x) (pow (+ 1 x) -1/2))
(/ (+ (/ 1/16 (* x x)) (+ 1/2 (/ -1/8 x))) x)
(+ (/ 1/16 (* x x)) (+ 1/2 (/ -1/8 x)))
(/ 1/16 (* x x))
1/16
(* x x)
x
(+ 1/2 (/ -1/8 x))
1/2
(/ -1/8 x)
-1/8
(pow (+ 1 x) -1/2)
(+ 1 x)
1
-1/2
(/ 1 (sqrt x))
1
(sqrt x)
x
(/ 1/2 (pow x 3/2))
1/2
(pow x 3/2)
x
3/2
(* 1/2 (/ (/ 1 x) (sqrt x)))
1/2
(/ (/ 1 x) (sqrt x))
(/ 1 x)
1
x
(sqrt x)
(* (/ (+ 1/2 (/ -1/8 x)) x) (pow (+ 1 x) -1/2))
(/ (+ 1/2 (/ -1/8 x)) x)
(+ 1/2 (/ -1/8 x))
1/2
(/ -1/8 x)
-1/8
x
(pow (+ 1 x) -1/2)
(+ 1 x)
1
-1/2

Outputs
(* (/ (+ (/ 1/16 (* x x)) (+ 1/2 (/ -1/8 x))) x) (pow (+ 1 x) -1/2))
(*.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) x) (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)))
(/ (+ (/ 1/16 (* x x)) (+ 1/2 (/ -1/8 x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) x)
(+ (/ 1/16 (* x x)) (+ 1/2 (/ -1/8 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x))
(/ 1/16 (* x x))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
1/16
#s(literal 1/16 binary64)
(* x x)
(*.f64 x x)
x
(+ 1/2 (/ -1/8 x))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
1/2
#s(literal 1/2 binary64)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
-1/8
#s(literal -1/8 binary64)
(pow (+ 1 x) -1/2)
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
1
#s(literal 1 binary64)
-1/2
#s(literal -1/2 binary64)
(/ 1 (sqrt x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
1
#s(literal 1 binary64)
(sqrt x)
(sqrt.f64 x)
x
(/ 1/2 (pow x 3/2))
(/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3/2 binary64)))
1/2
#s(literal 1/2 binary64)
(pow x 3/2)
(pow.f64 x #s(literal 3/2 binary64))
x
3/2
#s(literal 3/2 binary64)
(* 1/2 (/ (/ 1 x) (sqrt x)))
(/.f64 #s(literal 1/2 binary64) (*.f64 x (sqrt.f64 x)))
1/2
#s(literal 1/2 binary64)
(/ (/ 1 x) (sqrt x))
(/.f64 #s(literal 1 binary64) (*.f64 x (sqrt.f64 x)))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
1
#s(literal 1 binary64)
x
(sqrt x)
(sqrt.f64 x)
(* (/ (+ 1/2 (/ -1/8 x)) x) (pow (+ 1 x) -1/2))
(*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))
(/ (+ 1/2 (/ -1/8 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(+ 1/2 (/ -1/8 x))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
1/2
#s(literal 1/2 binary64)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
-1/8
#s(literal -1/8 binary64)
x
(pow (+ 1 x) -1/2)
(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
1
#s(literal 1 binary64)
-1/2
#s(literal -1/2 binary64)

localize120.0ms (1.3%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
✓	accuracy	100.0%	(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
✓	accuracy	99.6%	(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 x))
✓	accuracy	100.0%	(pow.f64 x #s(literal 3/2 binary64))
✓	accuracy	99.0%	(/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3/2 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) x)
✓	accuracy	99.6%	(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	accuracy	99.1%	(/.f64 #s(literal 1/16 binary64) (*.f64 x x))

Results

81.0ms

256×

valid

Compiler

Compiled 157 to 26 computations (83.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 45.0ms

ival-pow: 17.0ms (38.1% of total)

ival-div: 14.0ms (31.4% of total)

ival-mult: 8.0ms (17.9% of total)

ival-add: 4.0ms (9% of total)

ival-sqrt: 2.0ms (4.5% of total)

const: 1.0ms (2.2% of total)

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

series10.0ms (0.1%)

Counts

17 → 204

Calls

Call 1

Inputs
#<alt (* (/ (+ (/ 1/16 (* x x)) (+ 1/2 (/ -1/8 x))) x) (pow (+ 1 x) -1/2))>
#<alt (/ (+ (/ 1/16 (* x x)) (+ 1/2 (/ -1/8 x))) x)>
#<alt (+ (/ 1/16 (* x x)) (+ 1/2 (/ -1/8 x)))>
#<alt (/ 1/16 (* x x))>
#<alt (/ 1 (sqrt x))>
#<alt (sqrt x)>
#<alt (/ 1/2 (pow x 3/2))>
#<alt (pow x 3/2)>
#<alt (* 1/2 (/ (/ 1 x) (sqrt x)))>
#<alt (/ (/ 1 x) (sqrt x))>
#<alt (/ 1 x)>
#<alt (* (/ (+ 1/2 (/ -1/8 x)) x) (pow (+ 1 x) -1/2))>
#<alt (/ (+ 1/2 (/ -1/8 x)) x)>
#<alt (+ 1/2 (/ -1/8 x))>
#<alt (/ -1/8 x)>
#<alt (* x x)>
#<alt (+ 1 x)>

Outputs
#<alt (/ 1/16 (pow x 3))>
#<alt (/ (+ 1/16 (* -5/32 x)) (pow x 3))>
#<alt (/ (+ 1/16 (* x (- (* 75/128 x) 5/32))) (pow x 3))>
#<alt (/ (+ 1/16 (* x (- (* x (+ 75/128 (* -81/256 x))) 5/32))) (pow x 3))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))) x)>
#<alt (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/4 (sqrt (/ 1 x))) (* -1/16 (sqrt (/ 1 x))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ (+ 1/16 (* -1/8 x)) (pow x 3))>
#<alt (/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 3))>
#<alt (/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 3))>
#<alt (/ 1/2 x)>
#<alt (/ (- 1/2 (* 1/8 (/ 1 x))) x)>
#<alt (/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)>
#<alt (/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))>
#<alt (/ 1/16 (pow x 2))>
#<alt (/ (+ 1/16 (* -1/8 x)) (pow x 2))>
#<alt (/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 2))>
#<alt (/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 2))>
#<alt 1/2>
#<alt (- 1/2 (* 1/8 (/ 1 x)))>
#<alt (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x)))>
#<alt (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x)))>
#<alt 1/2>
#<alt (- 1/2 (* 1/8 (/ 1 x)))>
#<alt (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)))>
#<alt (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)))>
#<alt (/ 1/16 (pow x 2))>
#<alt (/ 1/16 (pow x 2))>
#<alt (/ 1/16 (pow x 2))>
#<alt (/ 1/16 (pow x 2))>
#<alt (/ 1/16 (pow x 2))>
#<alt (/ 1/16 (pow x 2))>
#<alt (/ 1/16 (pow x 2))>
#<alt (/ 1/16 (pow x 2))>
#<alt (/ 1/16 (pow x 2))>
#<alt (/ 1/16 (pow x 2))>
#<alt (/ 1/16 (pow x 2))>
#<alt (/ 1/16 (pow x 2))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* -1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* -1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* -1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* -1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (sqrt (pow x 3))>
#<alt (* (sqrt (pow x 3)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (pow x 3)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (pow x 3)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (pow x 3)) (pow (sqrt -1) 2))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (sqrt (/ 1 (pow x 3)))>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ (- (* 9/16 x) 1/8) (pow x 2))>
#<alt (/ (- (* x (+ 9/16 (* -19/64 x))) 1/8) (pow x 2))>
#<alt (/ (- (* x (+ 9/16 (* x (- (* 29/128 x) 19/64)))) 1/8) (pow x 2))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))) x)>
#<alt (* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/16 (sqrt (/ 1 x))) (* 1/4 (sqrt x)))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (/ -1/8 (pow x 2))>
#<alt (/ (- (* 1/2 x) 1/8) (pow x 2))>
#<alt (/ (- (* 1/2 x) 1/8) (pow x 2))>
#<alt (/ (- (* 1/2 x) 1/8) (pow x 2))>
#<alt (/ 1/2 x)>
#<alt (/ (- 1/2 (* 1/8 (/ 1 x))) x)>
#<alt (/ (- 1/2 (* 1/8 (/ 1 x))) x)>
#<alt (/ (- 1/2 (* 1/8 (/ 1 x))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))>
#<alt (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))>
#<alt (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))>
#<alt (/ -1/8 x)>
#<alt (/ (- (* 1/2 x) 1/8) x)>
#<alt (/ (- (* 1/2 x) 1/8) x)>
#<alt (/ (- (* 1/2 x) 1/8) x)>
#<alt 1/2>
#<alt (- 1/2 (* 1/8 (/ 1 x)))>
#<alt (- 1/2 (* 1/8 (/ 1 x)))>
#<alt (- 1/2 (* 1/8 (/ 1 x)))>
#<alt 1/2>
#<alt (- 1/2 (* 1/8 (/ 1 x)))>
#<alt (- 1/2 (* 1/8 (/ 1 x)))>
#<alt (- 1/2 (* 1/8 (/ 1 x)))>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<alt (/ -1/8 x)>
#<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)>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>

Calls

51 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(* (/ (+ (/ 1/16 (* x x)) (+ 1/2 (/ -1/8 x))) x) (pow (+ 1 x) -1/2))
1.0ms	x	@	-inf	(pow x 3/2)
1.0ms	x	@	inf	(* (/ (+ (/ 1/16 (* x x)) (+ 1/2 (/ -1/8 x))) x) (pow (+ 1 x) -1/2))
0.0ms	x	@	0	(pow x 3/2)
0.0ms	x	@	-inf	(/ 1/2 (pow x 3/2))

rewrite471.0ms (4.9%)

Algorithm

1×	batch-egg-rewrite

Rules

5046×	`-lowering-.f32`
5046×	`-lowering-.f64`
3912×	`/-lowering-/.f32`
3912×	`/-lowering-/.f64`
2578×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	106
1	152	101
2	1267	101
0	8305	101

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 749

Calls

Call 1

Inputs
(* (/ (+ (/ 1/16 (* x x)) (+ 1/2 (/ -1/8 x))) x) (pow (+ 1 x) -1/2))
(/ (+ (/ 1/16 (* x x)) (+ 1/2 (/ -1/8 x))) x)
(+ (/ 1/16 (* x x)) (+ 1/2 (/ -1/8 x)))
(/ 1/16 (* x x))
(/ 1 (sqrt x))
(sqrt x)
(/ 1/2 (pow x 3/2))
(pow x 3/2)
(* 1/2 (/ (/ 1 x) (sqrt x)))
(/ (/ 1 x) (sqrt x))
(/ 1 x)
(* (/ (+ 1/2 (/ -1/8 x)) x) (pow (+ 1 x) -1/2))
(/ (+ 1/2 (/ -1/8 x)) x)
(+ 1/2 (/ -1/8 x))
(/ -1/8 x)
(* x x)
(+ 1 x)

Outputs
(/.f64 #s(literal 1 binary64) (/.f64 x (.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)))))
(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 x (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64))))))
(/.f64 (.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64))) x)
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(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 x #s(literal 1 binary64))))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x)))

simplify243.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

2998×	`-lowering-.f32`
2998×	`-lowering-.f64`
1628×	`fma-lowering-fma.f32`
1628×	`fma-lowering-fma.f64`
1612×	`+-lowering-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	1376
1	498	1193
2	1470	1162
3	4132	1154
0	8363	1154

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
(/ 1/16 (pow x 3))
(/ (+ 1/16 (* -5/32 x)) (pow x 3))
(/ (+ 1/16 (* x (- (* 75/128 x) 5/32))) (pow x 3))
(/ (+ 1/16 (* x (- (* x (+ 75/128 (* -81/256 x))) 5/32))) (pow x 3))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))) x)
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/4 (sqrt (/ 1 x))) (* -1/16 (sqrt (/ 1 x))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/ 1/16 (pow x 3))
(/ (+ 1/16 (* -1/8 x)) (pow x 3))
(/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 3))
(/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 3))
(/ 1/2 x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)
(/ 1/2 x)
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))
(/ 1/16 (pow x 2))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 2))
(/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 2))
1/2
(- 1/2 (* 1/8 (/ 1 x)))
(- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x)))
(- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x)))
1/2
(- 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)))
(+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)))
(/ 1/16 (pow x 2))
(/ 1/16 (pow x 2))
(/ 1/16 (pow x 2))
(/ 1/16 (pow x 2))
(/ 1/16 (pow x 2))
(/ 1/16 (pow x 2))
(/ 1/16 (pow x 2))
(/ 1/16 (pow x 2))
(/ 1/16 (pow x 2))
(/ 1/16 (pow x 2))
(/ 1/16 (pow x 2))
(/ 1/16 (pow x 2))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* -1/2 (sqrt (/ 1 (pow x 3))))
(* -1/2 (sqrt (/ 1 (pow x 3))))
(* -1/2 (sqrt (/ 1 (pow x 3))))
(* -1/2 (sqrt (/ 1 (pow x 3))))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(sqrt (pow x 3))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(sqrt (/ 1 (pow x 3)))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ -1/8 (pow x 2))
(/ (- (* 9/16 x) 1/8) (pow x 2))
(/ (- (* x (+ 9/16 (* -19/64 x))) 1/8) (pow x 2))
(/ (- (* x (+ 9/16 (* x (- (* 29/128 x) 19/64)))) 1/8) (pow x 2))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))) x)
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/16 (sqrt (/ 1 x))) (* 1/4 (sqrt x)))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/ -1/8 (pow x 2))
(/ (- (* 1/2 x) 1/8) (pow x 2))
(/ (- (* 1/2 x) 1/8) (pow x 2))
(/ (- (* 1/2 x) 1/8) (pow x 2))
(/ 1/2 x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ 1/2 x)
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(/ -1/8 x)
(/ (- (* 1/2 x) 1/8) x)
(/ (- (* 1/2 x) 1/8) x)
(/ (- (* 1/2 x) 1/8) x)
1/2
(- 1/2 (* 1/8 (/ 1 x)))
(- 1/2 (* 1/8 (/ 1 x)))
(- 1/2 (* 1/8 (/ 1 x)))
1/2
(- 1/2 (* 1/8 (/ 1 x)))
(- 1/2 (* 1/8 (/ 1 x)))
(- 1/2 (* 1/8 (/ 1 x)))
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(/ -1/8 x)
(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)
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))

Outputs
(/ 1/16 (pow x 3))
(/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))
(/ (+ 1/16 (* -5/32 x)) (pow x 3))
(/.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -5/32 binary64))) (.f64 x (*.f64 x x)))
(/ (+ 1/16 (* x (- (* 75/128 x) 5/32))) (pow x 3))
(/.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x (+.f64 #s(literal -5/32 binary64) (.f64 x #s(literal 75/128 binary64))))) (.f64 x (.f64 x x)))
(/ (+ 1/16 (* x (- (* x (+ 75/128 (* -81/256 x))) 5/32))) (pow x 3))
(/.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x (+.f64 #s(literal -5/32 binary64) (.f64 x (+.f64 #s(literal 75/128 binary64) (.f64 x #s(literal -81/256 binary64))))))) (.f64 x (*.f64 x x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))) x)
(/.f64 (+.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)) #s(literal -3/8 binary64)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))) x)
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 3/8 binary64)) (*.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)) #s(literal -3/8 binary64)))) x)
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)) #s(literal -1/2 binary64))
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(/.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1/8 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/.f64 (+.f64 (/.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)) #s(literal -1/16 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64))) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) x)
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (+ (* -1/4 (sqrt x)) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))) (+ (* -1/4 (sqrt (/ 1 x))) (* -1/16 (sqrt (/ 1 x))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/.f64 (+.f64 (/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64)) (/.f64 (.f64 #s(literal 1/4 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) x)) x) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) x)
(/ 1/16 (pow x 3))
(/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))
(/ (+ 1/16 (* -1/8 x)) (pow x 3))
(/.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (.f64 x (*.f64 x x)))
(/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 3))
(/.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))) (.f64 x (.f64 x x)))
(/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 3))
(/.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))) (.f64 x (.f64 x x)))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x)
(/ (- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x)
(* -1 (/ (- (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x)) 1/2) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x)
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))) (.f64 x x))
(/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))) (*.f64 x x))
(/ (+ 1/16 (* x (- (* 1/2 x) 1/8))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/2 binary64))))) (*.f64 x x))
1/2
#s(literal 1/2 binary64)
(- 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
(- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x))
(- (+ 1/2 (/ 1/16 (pow x 2))) (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x))
1/2
#s(literal 1/2 binary64)
(- 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
(+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x))
(+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x))
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(/ 1/16 (pow x 2))
(/.f64 #s(literal 1/16 binary64) (*.f64 x x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(* -1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)) #s(literal -1/2 binary64))
(* -1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)) #s(literal -1/2 binary64))
(* -1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)) #s(literal -1/2 binary64))
(* -1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)) #s(literal -1/2 binary64))
(sqrt (pow x 3))
(sqrt.f64 (.f64 x (.f64 x x)))
(sqrt (pow x 3))
(sqrt.f64 (.f64 x (.f64 x x)))
(sqrt (pow x 3))
(sqrt.f64 (.f64 x (.f64 x x)))
(sqrt (pow x 3))
(sqrt.f64 (.f64 x (.f64 x x)))
(sqrt (pow x 3))
(sqrt.f64 (.f64 x (.f64 x x)))
(sqrt (pow x 3))
(sqrt.f64 (.f64 x (.f64 x x)))
(sqrt (pow x 3))
(sqrt.f64 (.f64 x (.f64 x x)))
(sqrt (pow x 3))
(sqrt.f64 (.f64 x (.f64 x x)))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 x (.f64 x x))))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 x (.f64 x x))))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 x (.f64 x x))))
(* (sqrt (pow x 3)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (.f64 x (.f64 x x))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))
(sqrt (/ 1 (pow x 3)))
(sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ (- (* 9/16 x) 1/8) (pow x 2))
(/.f64 (+.f64 #s(literal 9/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(/ (- (* x (+ 9/16 (* -19/64 x))) 1/8) (pow x 2))
(/.f64 (+.f64 (+.f64 #s(literal 9/16 binary64) (*.f64 x #s(literal -19/64 binary64))) (/.f64 #s(literal -1/8 binary64) x)) x)
(/ (- (* x (+ 9/16 (* x (- (* 29/128 x) 19/64)))) 1/8) (pow x 2))
(/.f64 (+.f64 (+.f64 #s(literal 9/16 binary64) (.f64 x (+.f64 #s(literal -19/64 binary64) (.f64 x #s(literal 29/128 binary64))))) (/.f64 #s(literal -1/8 binary64) x)) x)
(* 1/2 (sqrt (/ 1 (pow x 3))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))) x)
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)) #s(literal -3/8 binary64))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* 1/16 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))))) x)
(/.f64 (+.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)) #s(literal -3/8 binary64))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 5/16 binary64))) x)
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)) #s(literal -1/2 binary64))
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))) x))
(/.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) x) x)) #s(literal 1/8 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x)
(* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/.f64 (+.f64 (/.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) x)
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (sqrt (/ 1 x))) (+ (* -1/16 (sqrt (/ 1 x))) (* 1/4 (sqrt x)))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/.f64 (+.f64 (/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64)) (/.f64 (+.f64 (.f64 #s(literal -1/4 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 5/16 binary64))) x)) x) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) x)
(/ -1/8 (pow x 2))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/ (- (* 1/2 x) 1/8) (pow x 2))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(/ (- (* 1/2 x) 1/8) (pow x 2))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(/ (- (* 1/2 x) 1/8) (pow x 2))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ (- (* 1/2 x) 1/8) x)
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
(/ (- (* 1/2 x) 1/8) x)
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
(/ (- (* 1/2 x) 1/8) x)
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
1/2
#s(literal 1/2 binary64)
(- 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
(- 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
(- 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
1/2
#s(literal 1/2 binary64)
(- 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
(- 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
(- 1/2 (* 1/8 (/ 1 x)))
(+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) x)
(/ -1/8 x)
(/.f64 #s(literal -1/8 binary64) 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)
(pow x 2)
(*.f64 x x)
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
x
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))
(* x (+ 1 (/ 1 x)))
(+.f64 x #s(literal 1 binary64))

eval174.0ms (1.8%)

Compiler: Compiled 26733 to 3149 computations (88.2% saved)

prune121.0ms (1.3%)

Pruning

21 alts after pruning (18 fresh and 3 done)

	Pruned	Kept	Total
New	1082	12	1094
Fresh	2	6	8
Picked	3	2	5
Done	1	1	2
Total	1088	21	1109

Accuracy

100.0%

Counts

1109 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.0%	(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 x (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))))
	98.6%	(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
	83.0%	(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))))
	96.7%	(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 x #s(literal -1/2 binary64)))
	97.2%	(/.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
	8.0%	(/.f64 (+.f64 #s(literal 9/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
	97.8%	(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)))))
✓	96.7%	(/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3/2 binary64)))
	96.4%	(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) x)))
	34.4%	(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
✓	38.3%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	32.6%	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	97.6%	(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
	98.9%	(.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/256 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal 1/2 binary64))) (/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal 1/2 binary64)))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	98.8%	(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	98.8%	(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 x x)))))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	98.8%	(.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/2 binary64))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	98.8%	(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	98.5%	(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	97.4%	(*.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	97.4%	(*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) x))

Compiler

Compiled 1110 to 419 computations (62.3% saved)

regimes32.0ms (0.3%)

Counts

58 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/.f64 (+.f64 #s(literal 9/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(pow.f64 x #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 (sqrt.f64 x) x)
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3/2 binary64)))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
(*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) x))
(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)))
(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 x #s(literal -1/2 binary64)))
(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)))))
(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/2 binary64))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 x (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))))
(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 x x)))))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/256 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal 1/2 binary64))) (/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal 1/2 binary64)))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)) x) (/.f64 #s(literal -1/2 binary64) x))
(/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) x)
(/.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)) (/.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(/.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) x) x)
(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(*.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 (/.f64 #s(literal -1/2 binary64) x) x))
(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))))
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64))) (*.f64 x x))
(/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (*.f64 (+.f64 #s(literal 1/2 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (.f64 x (.f64 x x)))
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(/.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (*.f64 x x))
(.f64 (pow.f64 (.f64 (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (sqrt.f64 x)) #s(literal -1 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))

Outputs

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

Calls

2 calls:

14.0ms	x
13.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
99.3%	1	`x`
99.3%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes77.0ms (0.8%)

Counts

57 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/.f64 (+.f64 #s(literal 9/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(pow.f64 x #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 (sqrt.f64 x) x)
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3/2 binary64)))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
(*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) x))
(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)))
(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 x #s(literal -1/2 binary64)))
(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)))))
(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/2 binary64))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 x (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))))
(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 x x)) #s(literal 1/4 binary64)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/2 binary64)))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 x x)))))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(.f64 (/.f64 (-.f64 (/.f64 (/.f64 #s(literal 1/256 binary64) (.f64 (.f64 x x) (.f64 x x))) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal 1/2 binary64))) (/.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (-.f64 (/.f64 (-.f64 (/.f64 #s(literal 1/16 binary64) x) #s(literal -1/8 binary64)) x) #s(literal 1/2 binary64)))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))
(*.f64 (/.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)) x) (/.f64 #s(literal -1/2 binary64) x))
(/.f64 (*.f64 (/.f64 #s(literal -1/2 binary64) x) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) x)
(/.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)) (/.f64 (*.f64 x x) #s(literal -1/2 binary64)))
(/.f64 (/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x))) x) x)
(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(*.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 (/.f64 #s(literal -1/2 binary64) x) x))
(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))))
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64))) (*.f64 x x))
(/.f64 #s(literal 1 binary64) (+.f64 (.f64 x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (*.f64 (+.f64 #s(literal 1/2 binary64) x) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (.f64 x (.f64 x x)))
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(/.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (*.f64 x x))

Outputs

(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 x (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))))

Calls

2 calls:

60.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
14.0ms	x

Results

Accuracy	Segments	Branch
99.0%	1	`x`
99.0%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes42.0ms (0.4%)

Counts

27 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/.f64 (+.f64 #s(literal 9/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(pow.f64 x #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 (sqrt.f64 x) x)
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3/2 binary64)))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
(*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) x))
(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)))
(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 x #s(literal -1/2 binary64)))
(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)))))
(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(.f64 (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) #s(literal 1/2 binary64))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))

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

Calls

1 calls:

40.0ms

Results

Accuracy	Segments	Branch
98.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes8.0ms (0.1%)

Counts

24 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/.f64 (+.f64 #s(literal 9/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(pow.f64 x #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 (sqrt.f64 x) x)
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3/2 binary64)))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
(*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) x))
(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)))
(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 x #s(literal -1/2 binary64)))
(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 x (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)))))

Outputs
(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
98.6%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes20.0ms (0.2%)

Counts

22 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/.f64 (+.f64 #s(literal 9/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(pow.f64 x #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 (sqrt.f64 x) x)
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3/2 binary64)))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
(*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) x))
(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)))
(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 x #s(literal -1/2 binary64)))
(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))

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

Calls

1 calls:

12.0ms

Results

Accuracy	Segments	Branch
98.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes7.0ms (0.1%)

Counts

21 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/.f64 (+.f64 #s(literal 9/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(pow.f64 x #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 (sqrt.f64 x) x)
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
(/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3/2 binary64)))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
(*.f64 #s(literal 1/2 binary64) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) x))
(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
(*.f64 #s(literal 1/2 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))
(/.f64 #s(literal 1/2 binary64) (/.f64 (sqrt.f64 x) (/.f64 #s(literal 1 binary64) x)))
(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
(*.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)))
(.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(/.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 x #s(literal -1/2 binary64)))

Outputs
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
97.6%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes3.0ms (0%)

Counts

6 → 2

Calls

Call 1

Inputs
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))
(/.f64 (+.f64 #s(literal 9/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(pow.f64 x #s(literal -1/2 binary64))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 (sqrt.f64 x) x)

Outputs
(/.f64 (+.f64 #s(literal 9/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
37.2%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))

Outputs
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
34.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch26.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
23.0ms	1.9879446139419483e+150	1.9031934515726594e+154

Results

19.0ms

128×

valid

Compiler

Compiled 144 to 107 computations (25.7% saved)

Precisions

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

ival-sqrt: 5.0ms (37.6% of total)

ival-div: 4.0ms (30.1% of total)

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

ival-add: 1.0ms (7.5% of total)

ival-sub: 1.0ms (7.5% of total)

const: 0.0ms (0% of total)

simplify34.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

20×	`+-commutative_binary64`
16×	`*-commutative_binary64`
8×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	107
1	62	107
2	69	107
3	75	107
4	80	107
5	82	107

Stop Event

1×

saturated

Calls

Call 1

Inputs
(.f64 (pow.f64 (.f64 (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (sqrt.f64 x)) #s(literal -1 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 x (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))))
(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
(if (<=.f64 x #s(literal 6400000000000000296006920697868766336078481433284652063480878540881443440241897659096538872461019208447338396831340197818841452129052274984624128583008256 binary64)) (/.f64 (+.f64 #s(literal 9/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))

Outputs
(.f64 (pow.f64 (.f64 (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (sqrt.f64 x)) #s(literal -1 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (.f64 (sqrt.f64 x) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))) #s(literal -1 binary64)) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)))
(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 x (+.f64 (/.f64 #s(literal 1/16 binary64) (*.f64 x x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))))
(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x))
(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(*.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -3/2 binary64)))
(if (<=.f64 x #s(literal 6400000000000000296006920697868766336078481433284652063480878540881443440241897659096538872461019208447338396831340197818841452129052274984624128583008256 binary64)) (/.f64 (+.f64 #s(literal 9/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))
(if (<=.f64 x #s(literal 6400000000000000296006920697868766336078481433284652063480878540881443440241897659096538872461019208447338396831340197818841452129052274984624128583008256 binary64)) (/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 9/16 binary64)) x) (/.f64 #s(literal -1/8 binary64) (*.f64 x x)))
(/.f64 #s(literal -1/8 binary64) (*.f64 x x))

soundness2.3s (24.4%)

Rules

5046×	`-lowering-.f32`
5046×	`-lowering-.f64`
4190×	`-lowering-.f32`
4190×	`-lowering-.f64`
3912×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	126
1	172	105
2	1320	103
0	8371	103
0	114	458
1	334	397
2	1139	374
3	4889	373
0	8236	373
0	8	15
1	64	15
2	598	15
3	7261	15
0	8224	15
0	25	106
1	152	101
2	1267	101
0	8305	101
0	183	1376
1	498	1193
2	1470	1162
3	4132	1154
0	8363	1154
0	33	168
1	221	133
2	1990	124
0	8663	124
0	350	2397
1	1102	2051
2	4203	2017
0	8353	2017

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

Compiler

Compiled 305 to 197 computations (35.4% saved)

preprocess83.0ms (0.9%)

Compiler: Compiled 272 to 120 computations (55.9% saved)

Iter	Nodes	Cost
0	8	24
1	17	24
2	25	24
3	36	24
4	50	24
5	87	24
6	157	24
7	252	24
8	351	24
9	483	24
10	594	24
11	630	24
12	638	24
0	638	24

Iter	Nodes	Cost
0	8	24
1	17	24
2	25	24
3	36	24
4	50	24
5	87	24
6	157	24
7	252	24
8	351	24
9	483	24
10	594	24
11	630	24
12	638	24
0	638	24

analyze3.0ms (0%)

sample2.1s (22.2%)

preprocess51.0ms (0.5%)

explain158.0ms (1.7%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify20.0ms (0.2%)

localize65.0ms (0.7%)

series5.0ms (0.1%)

rewrite241.0ms (2.5%)

simplify209.0ms (2.2%)

eval30.0ms (0.3%)

prune56.0ms (0.6%)

simplify158.0ms (1.7%)

localize359.0ms (3.8%)

series25.0ms (0.3%)

rewrite327.0ms (3.4%)

simplify257.0ms (2.7%)

eval179.0ms (1.9%)

prune164.0ms (1.7%)

simplify178.0ms (1.9%)

localize167.0ms (1.8%)

series15.0ms (0.2%)

rewrite315.0ms (3.3%)

simplify238.0ms (2.5%)

eval171.0ms (1.8%)

prune180.0ms (1.9%)

simplify48.0ms (0.5%)

localize120.0ms (1.3%)

series10.0ms (0.1%)

rewrite471.0ms (4.9%)

simplify243.0ms (2.6%)

eval174.0ms (1.8%)

prune121.0ms (1.3%)

regimes32.0ms (0.3%)

regimes77.0ms (0.8%)

regimes42.0ms (0.4%)

regimes8.0ms (0.1%)

regimes20.0ms (0.2%)

regimes7.0ms (0.1%)

regimes3.0ms (0%)

regimes2.0ms (0%)

bsearch26.0ms (0.3%)

simplify34.0ms (0.4%)

soundness2.3s (24.4%)

preprocess83.0ms (0.9%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	24
1	17	24
2	25	24
3	36	24
4	50	24
5	87	24
6	157	24
7	252	24
8	351	24
9	483	24
10	594	24
11	630	24
12	638	24
0	638	24