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)

sample2.2s (21%)

Results

1.3s	6367×	1	valid
535.0ms	1719×	2	valid
16.0ms	170×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.4s

ival-sqrt: 345.0ms (25.1% of total)

ival-div: 333.0ms (24.2% of total)

backward-pass: 167.0ms (12.1% of total)

...c/correct-round.rkt:119:19: 140.0ms (10.2% of total)

ival-add: 105.0ms (7.6% of total)

ival-sub: 104.0ms (7.6% of total)

ival->: 96.0ms (7% of total)

ival-and: 39.0ms (2.8% of total)

ival-<: 30.0ms (2.2% of total)

const: 17.0ms (1.2% of total)

Bogosity

preprocess63.0ms (0.6%)

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)))

explain234.0ms (2.2%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
181	2	(1.3680736606843646e+215)	-	`(-.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

132.0ms	380×	1	valid
42.0ms	120×	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: 65.0ms

ival-sqrt: 20.0ms (30.7% of total)

ival-div: 18.0ms (27.6% of total)

backward-pass: 14.0ms (21.5% of total)

ival-sub: 6.0ms (9.2% of total)

ival-add: 6.0ms (9.2% of total)

const: 1.0ms (1.5% 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
▶	37.8%	(-.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)

simplify21.0ms (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)

localize127.0ms (1.2%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	37.9%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

90.0ms	190×	1	valid
22.0ms	60×	2	valid
1.0ms	6×	0	valid

Compiler

Compiled 34 to 9 computations (73.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 34.0ms

ival-sqrt: 11.0ms (31.9% of total)

ival-div: 9.0ms (26.1% of total)

backward-pass: 7.0ms (20.3% of total)

ival-add: 4.0ms (11.6% of total)

ival-sub: 3.0ms (8.7% of total)

const: 1.0ms (2.9% of total)

series6.0ms (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	@	0	(/ 1 (sqrt (+ x 1)))
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)))
1.0ms	x	@	-inf	(/ 1 (sqrt x))

rewrite271.0ms (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	601	15
3	7279	15
0	8160	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 -1 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 -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (+.f64 (/.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))) (+.f64 (/.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 #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 -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))) (*.f64 (+.f64 (/.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))) #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 -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 #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 #s(literal -1 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 -1 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 -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 (/.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 (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 (/.f64 #s(literal 1 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)) (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 -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 #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 -1 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 -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 -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 -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)))))
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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 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)))
(pow.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))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(*.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 -1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(*.f64 (/.f64 #s(literal -1 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) (pow.f64 (+.f64 #s(literal -1 binary64) (.f64 x x)) #s(literal 1/2 binary64))) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))

simplify202.0ms (1.9%)

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	394
2	1141	371
3	4906	370
0	8253	370

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 (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)))) (+.f64 (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 (.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))) (.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 (/ 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 (+.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))) (.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 (.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))))))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 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 (.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))) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))
(+ (* -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))))

eval48.0ms (0.5%)

Compiler: Compiled 6533 to 714 computations (89.1% saved)

prune60.0ms (0.6%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	254	14	268
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	255	14	269

Accuracy

82.3%

Counts

269 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	40.6%	(/.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)))
	40.6%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))))
	38.0%	(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 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))))
▶	81.0%	(/.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))
	6.3%	(/.f64 (.f64 (-.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal 1 binary64) (+.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 1 binary64) (.f64 x x)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))))
	40.6%	(/.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 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))
▶	37.9%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	27.2%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	21.0%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
▶	37.9%	(-.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)))))
	40.6%	(.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)))
	79.6%	(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
	66.1%	(.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 554 to 308 computations (44.4% saved)

simplify195.0ms (1.8%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
✓	cost-diff	0	(/.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)))
✓	cost-diff	256	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
✓	cost-diff	0	(sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal 1 binary64) x))))
✓	cost-diff	0	(-.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)))))
✓	cost-diff	128	(/.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) x)))
✓	cost-diff	384	(/.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal 1 binary64) 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	0	(.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	0	(+.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	0	(/.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))
✓	cost-diff	128	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64))))

Rules

2700×	`-lowering-.f32`
2700×	`-lowering-.f64`
2094×	`+-lowering-+.f64`
2094×	`+-lowering-+.f32`
1544×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	255
1	89	225
2	194	209
3	475	209
4	927	209
5	2334	209
0	8370	209

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

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

localize485.0ms (4.5%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
✓	accuracy	99.7%	(/.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)))
✓	accuracy	53.6%	(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))
✓	accuracy	9.6%	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
✓	accuracy	99.7%	(sqrt.f64 (/.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) x))))
✓	accuracy	53.5%	(/.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal 1 binary64) x)))
✓	accuracy	53.5%	(/.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) x)))
✓	accuracy	37.9%	(-.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)))))
✓	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	37.9%	(-.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	99.7%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
✓	accuracy	82.2%	(/.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))
✓	accuracy	71.4%	(.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	69.0%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))

Results

280.0ms	190×	1	valid
125.0ms	60×	2	valid
3.0ms	6×	0	valid

Compiler

Compiled 306 to 37 computations (87.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 232.0ms

ival-pow: 56.0ms (24.1% of total)

ival-sqrt: 54.0ms (23.3% of total)

backward-pass: 40.0ms (17.2% of total)

ival-div: 30.0ms (12.9% of total)

ival-mult: 27.0ms (11.6% of total)

ival-add: 13.0ms (5.6% of total)

ival-sub: 11.0ms (4.7% of total)

const: 2.0ms (0.9% of total)

series20.0ms (0.2%)

Counts

21 → 252

Calls

Call 1

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

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

63 calls:

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

rewrite363.0ms (3.4%)

Algorithm

1×	batch-egg-rewrite

Rules

4218×	`-lowering-.f32`
4218×	`-lowering-.f64`
2418×	`/-lowering-/.f32`
2418×	`/-lowering-/.f64`
1818×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	193
1	253	140
2	2372	131
0	9716	131

Stop Event

1×	iter limit
1×	node limit

Counts

21 → 807

Calls

Call 1

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

Outputs
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64)))
(+.f64 (*.f64 x #s(literal 1/8 binary64)) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64))
(fma.f64 x #s(literal 1/8 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/4 binary64) (*.f64 x #s(literal 1/2 binary64)) #s(literal 1/2 binary64))
(fma.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 1/2 binary64) #s(literal 1/2 binary64))
(fma.f64 #s(literal 1/8 binary64) x #s(literal 1/2 binary64))
(fma.f64 (*.f64 #s(literal 1/2 binary64) x) #s(literal 1/4 binary64) #s(literal 1/2 binary64))
(/.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/512 binary64))) (+.f64 #s(literal 1/4 binary64) (-.f64 (.f64 (.f64 x #s(literal 1/8 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 1/4 binary64) (.f64 (.f64 x #s(literal 1/8 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 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/4 binary64)) (-.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))))
(/.f64 (.f64 #s(literal 1/2 binary64) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/16 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/4 binary64) x)))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64))) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x #s(literal 1/4 binary64)) (-.f64 (*.f64 x #s(literal 1/4 binary64)) #s(literal 1 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal 1/16 binary64))) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1/4 binary64) x)))
(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64))))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64))) #s(literal 1/2 binary64))
(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))))))))
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(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 (.f64 x x)) (.f64 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 #s(literal -1/2 binary64) (log1p.f64 x)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) #s(literal -1 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal -1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log1p.f64 x)) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log1p.f64 x) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log1p.f64 x) #s(literal -1/4 binary64)) (.f64 (log1p.f64 x) #s(literal -1/4 binary64))))
(fabs.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))))
(/.f64 (sqrt.f64 x) (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))
(/.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) (sqrt.f64 x)) (neg.f64 (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(/.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 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (/.f64 x (+.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (sqrt.f64 (sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) x))) (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (sqrt.f64 (sqrt.f64 (.f64 x (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)))))
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
(pow.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) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal -2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64))
(pow.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log1p.f64 x))
(*.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(.f64 (sqrt.f64 x) (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
(.f64 (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)) #s(literal -1/2 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 0 binary64) x) #s(literal 1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x)))) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x))))))
(.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 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -3/4 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -3/4 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 x #s(literal 1 binary64))))))
(.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x))) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (sqrt.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(*.f64 (sqrt.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64))) (sqrt.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -3/4 binary64))))
(*.f64 (sqrt.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -3/4 binary64))) (sqrt.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.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 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x x)))) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(exp.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)))))
(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)
(fabs.f64 (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) (.f64 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 (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1 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))
(*.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)))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal 1 binary64) x)))) #s(literal 1/2 binary64)))
(.f64 (.f64 (sqrt.f64 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 (pow.f64 (sqrt.f64 (.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) x)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal 1 binary64) x))))))
(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(.f64 (sqrt.f64 (sqrt.f64 (.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) x))) (sqrt.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))

simplify272.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

2816×	`+-lowering-+.f64`
2816×	`+-lowering-+.f32`
2658×	`-lowering-.f32`
2658×	`-lowering-.f64`
1806×	`fnmadd-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	437	2999
1	1433	2182
2	5768	2148
0	8202	2148

Stop Event

1×	iter limit
1×	node limit

Counts

252 → 252

Calls

Call 1

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

eval249.0ms (2.3%)

Compiler: Compiled 37017 to 4149 computations (88.8% saved)

prune197.0ms (1.8%)

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	1468	17	1485
Fresh	7	2	9
Picked	3	2	5
Done	0	0	0
Total	1478	21	1499

Accuracy

100.0%

Counts

1499 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
	35.5%	(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
▶	5.7%	(pow.f64 x #s(literal -1/2 binary64))
▶	82.2%	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
▶	39.6%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 1/2 binary64) x))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
	39.9%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.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)))
	40.0%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (.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) (/.f64 #s(literal -1/8 binary64) x)) x)))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
▶	99.1%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) (/.f64 #s(literal 5/128 binary64) (.f64 x (.f64 x x)))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
	98.4%	(/.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)
	99.0%	(/.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)))
	98.6%	(/.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)))
▶	97.3%	(/.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
	7.4%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))))
	97.2%	(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/8 binary64))) x)
	79.6%	(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
	82.1%	(/.f64 #s(literal 1 binary64) (.f64 (+.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))))
	5.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	37.9%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	82.1%	(.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 x (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))))))
	79.6%	(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
	66.1%	(.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 637 to 405 computations (36.4% saved)

simplify193.0ms (1.8%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) 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	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
✓	cost-diff	0	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 1/2 binary64) x)))
✓	cost-diff	0	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 1/2 binary64) x))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
✓	cost-diff	64	(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
✓	cost-diff	256	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	0	(/.f64 (/.f64 #s(literal 1/2 binary64) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
✓	cost-diff	64	(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 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) (/.f64 #s(literal 5/128 binary64) (.f64 x (.f64 x x))))
✓	cost-diff	0	(/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) (/.f64 #s(literal 5/128 binary64) (.f64 x (.f64 x x)))) x)
✓	cost-diff	0	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) (/.f64 #s(literal 5/128 binary64) (.f64 x (.f64 x x)))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
✓	cost-diff	64	(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))

Rules

2028×	`sum4-define`
1930×	`-lowering-.f32`
1930×	`-lowering-.f64`
1512×	`fma-lowering-fma.f32`
1512×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	217
1	76	199
2	176	196
3	440	196
4	1153	196
5	3563	196
0	8028	196

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (/ (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x)))) x) (pow (+ 1 x) 1/2))
(/ (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x)))) x)
(- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x))))
(+ 1/2 (/ (- -1/8 (/ -1/16 x)) x))
1/2
(/ (- -1/8 (/ -1/16 x)) x)
(- -1/8 (/ -1/16 x))
-1/8
(/ -1/16 x)
-1/16
x
(/ 5/128 (* x (* x x)))
5/128
(* x (* x x))
(* x x)
(pow (+ 1 x) 1/2)
(+ 1 x)
1
(pow x -1/2)
x
-1/2
(/ (/ 1/2 x) (pow (+ 1 x) 1/2))
(/ 1/2 x)
1/2
x
(pow (+ 1 x) 1/2)
(+ 1 x)
1
(/ (/ (- (+ 1 x) x) (+ x (+ 1/2 x))) (pow (+ 1 x) 1/2))
(/ (- (+ 1 x) x) (+ x (+ 1/2 x)))
(- (+ 1 x) x)
(+ 1 x)
1
x
(+ x (+ 1/2 x))
(+ 1/2 x)
1/2
(pow (+ 1 x) 1/2)
(/ (pow (+ 1 x) -1/2) (+ x (sqrt (* x (+ 1 x)))))
(pow (+ 1 x) -1/2)
(+ 1 x)
1
x
-1/2
(+ x (sqrt (* x (+ 1 x))))
(sqrt (* x (+ 1 x)))
(* x (+ 1 x))

Outputs
(/ (/ (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x)))) x) (pow (+ 1 x) 1/2))
(/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (/.f64 #s(literal -5/128 binary64) (.f64 x (.f64 x x))))) (*.f64 x (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(/ (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x)))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (/.f64 #s(literal -5/128 binary64) (.f64 x (.f64 x x))))) x)
(- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x))))
(+.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x) (/.f64 #s(literal -5/128 binary64) (.f64 x (.f64 x x)))))
(+ 1/2 (/ (- -1/8 (/ -1/16 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
#s(literal 1/2 binary64)
(/ (- -1/8 (/ -1/16 x)) x)
(/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)
(- -1/8 (/ -1/16 x))
(+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x))
-1/8
#s(literal -1/8 binary64)
(/ -1/16 x)
(/.f64 #s(literal -1/16 binary64) x)
-1/16
#s(literal -1/16 binary64)
x
(/ 5/128 (* x (* x x)))
(/.f64 #s(literal 5/128 binary64) (.f64 x (.f64 x x)))
5/128
#s(literal 5/128 binary64)
(* x (* x x))
(.f64 x (.f64 x x))
(* x x)
(*.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)
(pow x -1/2)
(pow.f64 x #s(literal -1/2 binary64))
x
-1/2
#s(literal -1/2 binary64)
(/ (/ 1/2 x) (pow (+ 1 x) 1/2))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
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 x) x) (+ x (+ 1/2 x))) (pow (+ 1 x) 1/2))
(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64)))))
(/ (- (+ 1 x) x) (+ x (+ 1/2 x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64))))
(- (+ 1 x) x)
#s(literal 1 binary64)
(+ 1 x)
(+.f64 x #s(literal 1 binary64))
1
#s(literal 1 binary64)
x
(+ x (+ 1/2 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))
(+ 1/2 x)
(+.f64 #s(literal 1/2 binary64) x)
1/2
#s(literal 1/2 binary64)
(pow (+ 1 x) 1/2)
(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
(/ (pow (+ 1 x) -1/2) (+ x (sqrt (* x (+ 1 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))))))
(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)
x
-1/2
#s(literal -1/2 binary64)
(+ x (sqrt (* x (+ 1 x))))
(+.f64 x (sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64)))))
(sqrt (* x (+ 1 x)))
(sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))
(* x (+ 1 x))
(*.f64 x (+.f64 x #s(literal 1 binary64)))

localize347.0ms (3.3%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))
✓	accuracy	100.0%	(*.f64 x (+.f64 #s(literal 1 binary64) x))
✓	accuracy	99.7%	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
✓	accuracy	53.6%	(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))
✓	accuracy	100.0%	(+.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
✓	accuracy	99.7%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 1/2 binary64) x))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
✓	accuracy	9.6%	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
✓	accuracy	99.7%	(/.f64 (/.f64 #s(literal 1/2 binary64) x) (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 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)
✓	accuracy	99.8%	(.f64 x (.f64 x x))
✓	accuracy	99.7%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal -1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) (/.f64 #s(literal 5/128 binary64) (.f64 x (.f64 x x)))) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
✓	accuracy	99.6%	(/.f64 #s(literal 5/128 binary64) (.f64 x (.f64 x x)))

Results

268.0ms	234×	1	valid
10.0ms	22×	0	valid

Compiler

Compiled 240 to 33 computations (86.3% saved)

Precisions

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

ival-div: 34.0ms (26.6% of total)

ival-pow: 30.0ms (23.4% of total)

backward-pass: 25.0ms (19.5% of total)

ival-add: 13.0ms (10.2% of total)

ival-mult: 11.0ms (8.6% of total)

ival-sub: 8.0ms (6.2% of total)

ival-sqrt: 4.0ms (3.1% of total)

const: 2.0ms (1.6% of total)

series18.0ms (0.2%)

Counts

20 → 240

Calls

Call 1

Inputs
#<alt (pow (+ 1 x) 1/2)>
#<alt (/ (/ (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x)))) x) (pow (+ 1 x) 1/2))>
#<alt (/ (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x)))) x)>
#<alt (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x))))>
#<alt (pow x -1/2)>
#<alt (/ (/ 1/2 x) (pow (+ 1 x) 1/2))>
#<alt (/ 1/2 x)>
#<alt (+ 1 x)>
#<alt (- (+ 1 x) x)>
#<alt (/ (/ (- (+ 1 x) x) (+ x (+ 1/2 x))) (pow (+ 1 x) 1/2))>
#<alt (/ (- (+ 1 x) x) (+ x (+ 1/2 x)))>
#<alt (/ (pow (+ 1 x) -1/2) (+ x (sqrt (* x (+ 1 x)))))>
#<alt (pow (+ 1 x) -1/2)>
#<alt (+ x (sqrt (* x (+ 1 x))))>
#<alt (/ 5/128 (* x (* x x)))>
#<alt (* x (* x x))>
#<alt (/ (- -1/8 (/ -1/16 x)) x)>
#<alt (+ 1/2 x)>
#<alt (sqrt (* x (+ 1 x)))>
#<alt (* x (+ 1 x))>

Outputs
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (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)))) (* (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)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (/ -5/128 (pow x 4))>
#<alt (/ (- (* 21/256 x) 5/128) (pow x 4))>
#<alt (/ (- (* x (+ 21/256 (* -175/1024 x))) 5/128) (pow x 4))>
#<alt (/ (- (* x (+ 21/256 (* x (- (* 1225/2048 x) 175/1024)))) 5/128) (pow x 4))>
#<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)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 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))) (* 5/128 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (/ -5/128 (pow x 4))>
#<alt (/ (- (* 1/16 x) 5/128) (pow x 4))>
#<alt (/ (- (* x (+ 1/16 (* -1/8 x))) 5/128) (pow x 4))>
#<alt (/ (- (* x (+ 1/16 (* x (- (* 1/2 x) 1/8)))) 5/128) (pow x 4))>
#<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)) (* 5/128 (/ 1 (pow x 3))))) 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 (/ (- (* 5/128 (/ 1 x)) 1/16) x)) 1/8) x)) 1/2) x))>
#<alt (/ -5/128 (pow x 3))>
#<alt (/ (- (* 1/16 x) 5/128) (pow x 3))>
#<alt (/ (- (* x (+ 1/16 (* -1/8 x))) 5/128) (pow x 3))>
#<alt (/ (- (* x (+ 1/16 (* x (- (* 1/2 x) 1/8)))) 5/128) (pow x 3))>
#<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)) (* 5/128 (/ 1 (pow x 3)))))>
#<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 (/ (- 1/16 (* 5/128 (/ 1 x))) x))) 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 (/ 1/2 x)>
#<alt (/ (+ 1/2 (* -1/4 x)) x)>
#<alt (/ (+ 1/2 (* x (- (* 3/16 x) 1/4))) x)>
#<alt (/ (+ 1/2 (* x (- (* x (+ 3/16 (* -5/32 x))) 1/4))) x)>
#<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)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (+ (* 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))) (* 1/4 (sqrt (/ 1 (pow x 3))))) x))>
#<alt (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/4 (sqrt (/ 1 (pow x 5)))) (* 1/4 (sqrt (/ 1 (pow x 3)))))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* 1/4 (sqrt x))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/4 (sqrt (/ 1 (pow x 3)))))) x))>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<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>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 2>
#<alt (+ 2 (* -9 x))>
#<alt (+ 2 (* x (- (* 147/4 x) 9)))>
#<alt (+ 2 (* x (- (* x (+ 147/4 (* -1181/8 x))) 9)))>
#<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)))) (+ (* 1/32 (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)))) (+ (* -1/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 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 (/ (+ (* -1/32 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 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 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/16 (sqrt x)) (* 1/4 (sqrt x)))) x)) (+ (* -1/32 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 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 2>
#<alt (+ 2 (* -8 x))>
#<alt (+ 2 (* x (- (* 32 x) 8)))>
#<alt (+ 2 (* x (- (* x (+ 32 (* -128 x))) 8)))>
#<alt (/ 1/2 x)>
#<alt (/ (- 1/2 (* 1/8 (/ 1 x))) x)>
#<alt (/ (- (+ 1/2 (/ 1/32 (pow x 2))) (* 1/8 (/ 1 x))) x)>
#<alt (/ (- (+ 1/2 (/ 1/32 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 1/128 (/ 1 (pow x 3))))) x)>
#<alt (/ 1/2 x)>
#<alt (* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* 1/32 (/ 1 x)) 1/8) x)) 1/2) x))>
#<alt (* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/128 (/ 1 x)) 1/32) x)) 1/8) x)) 1/2) x))>
#<alt (sqrt (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x))))>
#<alt (+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x))))>
#<alt (+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x))))>
#<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)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)>
#<alt (* -1 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1))))>
#<alt (* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2))))) x)) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/16 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 3)))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))) (- (pow (sqrt -1) 2) 1))) (* 1/16 (/ 1 (* (pow (sqrt -1) 4) (pow (- (pow (sqrt -1) 2) 1) 2))))))))) (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* 1/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))))) x)) (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2))))) x)) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))>
#<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 (sqrt x)>
#<alt (+ x (sqrt x))>
#<alt (+ (sqrt x) (* x (+ 1 (* 1/2 (sqrt x)))))>
#<alt (+ (sqrt x) (* x (+ 1 (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* 1/2 (/ 1 x))))>
#<alt (* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))>
#<alt (* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))>
#<alt (* -1 (* x (- (pow (sqrt -1) 2) 1)))>
#<alt (* -1 (* x (- (pow (sqrt -1) 2) (+ 1 (* 1/2 (/ 1 x))))))>
#<alt (* -1 (* x (- (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2)) 1)))>
#<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)) 1)))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (pow x 3))>
#<alt (/ 5/128 (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 (/ 1/16 (pow x 2))>
#<alt (/ (+ 1/16 (* -1/8 x)) (pow x 2))>
#<alt (/ (+ 1/16 (* -1/8 x)) (pow x 2))>
#<alt (/ (+ 1/16 (* -1/8 x)) (pow x 2))>
#<alt (/ -1/8 x)>
#<alt (/ (- (* 1/16 (/ 1 x)) 1/8) x)>
#<alt (/ (- (* 1/16 (/ 1 x)) 1/8) x)>
#<alt (/ (- (* 1/16 (/ 1 x)) 1/8) x)>
#<alt (/ -1/8 x)>
#<alt (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))>
#<alt (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))>
#<alt (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))>
#<alt 1/2>
#<alt (+ 1/2 x)>
#<alt (+ 1/2 x)>
#<alt (+ 1/2 x)>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<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))))>
#<alt x>
#<alt (* x (+ 1 x))>
#<alt (* x (+ 1 x))>
#<alt (* x (+ 1 x))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>

Calls

60 calls:

Time	Variable		Point	Expression
3.0ms	x	@	-inf	(/ (/ (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x)))) x) (pow (+ 1 x) 1/2))
3.0ms	x	@	-inf	(pow (+ 1 x) 1/2)
0.0ms	x	@	-inf	(/ (/ 1/2 x) (pow (+ 1 x) 1/2))
0.0ms	x	@	-inf	(/ (/ (- (+ 1 x) x) (+ x (+ 1/2 x))) (pow (+ 1 x) 1/2))
0.0ms	x	@	inf	(/ (/ 1/2 x) (pow (+ 1 x) 1/2))

rewrite406.0ms (3.8%)

Algorithm

1×	batch-egg-rewrite

Rules

4014×	`/-lowering-/.f32`
4014×	`/-lowering-/.f64`
2280×	`-lowering-.f32`
2280×	`-lowering-.f64`
1752×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	32	163
1	246	137
2	2508	137
0	8720	137

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 692

Calls

Call 1

Inputs
(pow (+ 1 x) 1/2)
(/ (/ (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x)))) x) (pow (+ 1 x) 1/2))
(/ (- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x)))) x)
(- (+ 1/2 (/ (- -1/8 (/ -1/16 x)) x)) (/ 5/128 (* x (* x x))))
(pow x -1/2)
(/ (/ 1/2 x) (pow (+ 1 x) 1/2))
(/ 1/2 x)
(+ 1 x)
(- (+ 1 x) x)
(/ (/ (- (+ 1 x) x) (+ x (+ 1/2 x))) (pow (+ 1 x) 1/2))
(/ (- (+ 1 x) x) (+ x (+ 1/2 x)))
(/ (pow (+ 1 x) -1/2) (+ x (sqrt (* x (+ 1 x)))))
(pow (+ 1 x) -1/2)
(+ x (sqrt (* x (+ 1 x))))
(/ 5/128 (* x (* x x)))
(* x (* x x))
(/ (- -1/8 (/ -1/16 x)) x)
(+ 1/2 x)
(sqrt (* x (+ 1 x)))
(* x (+ 1 x))

Outputs
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)))
(exp.f64 (.f64 (log.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log1p.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log1p.f64 x) #s(literal 1/4 binary64)) (.f64 (log1p.f64 x) #s(literal 1/4 binary64))))
(exp.f64 (neg.f64 (*.f64 #s(literal -1/2 binary64) (log1p.f64 x))))
(exp.f64 (neg.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)))))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 x #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x)))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64))))))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (+.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x))))
(/.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (sqrt.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64)))))))
(/.f64 (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)))) (sqrt.f64 (neg.f64 (-.f64 #s(literal 1 binary64) x))))
(/.f64 (sqrt.f64 (-.f64 (*.f64 x x) #s(literal 1 binary64))) (sqrt.f64 (-.f64 x #s(literal 1 binary64))))
(/.f64 (neg.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64))) (neg.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 x #s(literal 1 binary64)))))))
(/.f64 (neg.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/2 binary64))) (neg.f64 (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))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) #s(literal -1 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)) #s(literal -2 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log1p.f64 x))
(*.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) (.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 (.f64 x x))) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 x #s(literal 1 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 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) #s(literal 1/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) x))))
(exp.f64 (.f64 (log.f64 (/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (/.f64 #s(literal 5/128 binary64) (.f64 x x))) x)) x))) #s(literal -1 binary64)))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) x)) (.f64 x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) (/.f64 (/.f64 #s(literal 5/128 binary64) (.f64 x (.f64 x x))) (.f64 x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
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(+.f64 x (*.f64 x x))
(+.f64 (*.f64 x x) x)
(exp.f64 (log.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))
(exp.f64 (.f64 (log.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) (.f64 x (+.f64 #s(literal 1 binary64) x)))) #s(literal 1/2 binary64)))
(fabs.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))
(-.f64 (/.f64 (.f64 x x) (-.f64 x (.f64 x x))) (/.f64 (.f64 (.f64 x x) (.f64 x x)) (-.f64 x (.f64 x x))))
(sqrt.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) (*.f64 x (+.f64 #s(literal 1 binary64) x))))
(fma.f64 #s(literal 1 binary64) x (*.f64 x x))
(fma.f64 x #s(literal 1 binary64) (*.f64 x x))
(fma.f64 x x x)
(/.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x)))))
(/.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))) (-.f64 x (*.f64 x x)))
(/.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 x #s(literal 1 binary64)))))
(/.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x))) (-.f64 #s(literal 1 binary64) x))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) x) (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 x #s(literal 1 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x) (-.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (+.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x))))) (neg.f64 (+.f64 (.f64 x x) (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 x (*.f64 x x))))))
(/.f64 (neg.f64 (-.f64 (.f64 x x) (.f64 (.f64 x x) (.f64 x x)))) (neg.f64 (-.f64 x (*.f64 x x))))
(/.f64 (neg.f64 (.f64 x (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 x #s(literal 1 binary64))))))
(/.f64 (neg.f64 (.f64 x (-.f64 #s(literal 1 binary64) (.f64 x x)))) (neg.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) x)) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 x (-.f64 x #s(literal 1 binary64))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x)) (neg.f64 (-.f64 #s(literal 1 binary64) x)))
(pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) (*.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(*.f64 (+.f64 #s(literal 1 binary64) x) x)
(.f64 (pow.f64 (.f64 x (+.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)))
(.f64 (sqrt.f64 x) (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(.f64 (sqrt.f64 (.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (sqrt.f64 x) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64)))
(.f64 (pow.f64 (sqrt.f64 (.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) 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) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) #s(literal 2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))

simplify295.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

2974×	`+-lowering-+.f64`
2974×	`+-lowering-+.f32`
2780×	`-lowering-.f32`
2780×	`-lowering-.f64`
1688×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	572	2702
1	1812	2060
2	6785	2045
0	8070	2045

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (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)))) (* (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)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(/ -5/128 (pow x 4))
(/ (- (* 21/256 x) 5/128) (pow x 4))
(/ (- (* x (+ 21/256 (* -175/1024 x))) 5/128) (pow x 4))
(/ (- (* x (+ 21/256 (* x (- (* 1225/2048 x) 175/1024)))) 5/128) (pow x 4))
(* 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)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 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))) (* 5/128 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/ -5/128 (pow x 4))
(/ (- (* 1/16 x) 5/128) (pow x 4))
(/ (- (* x (+ 1/16 (* -1/8 x))) 5/128) (pow x 4))
(/ (- (* x (+ 1/16 (* x (- (* 1/2 x) 1/8)))) 5/128) (pow x 4))
(/ 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)) (* 5/128 (/ 1 (pow x 3))))) 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 (/ (- (* 5/128 (/ 1 x)) 1/16) x)) 1/8) x)) 1/2) x))
(/ -5/128 (pow x 3))
(/ (- (* 1/16 x) 5/128) (pow x 3))
(/ (- (* x (+ 1/16 (* -1/8 x))) 5/128) (pow x 3))
(/ (- (* x (+ 1/16 (* x (- (* 1/2 x) 1/8)))) 5/128) (pow x 3))
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)) (* 5/128 (/ 1 (pow x 3)))))
1/2
(- 1/2 (* 1/8 (/ 1 x)))
(+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x)))
(+ 1/2 (* -1 (/ (+ 1/8 (* -1 (/ (- 1/16 (* 5/128 (/ 1 x))) x))) 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))
(/ 1/2 x)
(/ (+ 1/2 (* -1/4 x)) x)
(/ (+ 1/2 (* x (- (* 3/16 x) 1/4))) x)
(/ (+ 1/2 (* x (- (* x (+ 3/16 (* -5/32 x))) 1/4))) x)
(* 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)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (+ (* 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))) (* 1/4 (sqrt (/ 1 (pow x 3))))) x))
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/4 (sqrt (/ 1 (pow x 5)))) (* 1/4 (sqrt (/ 1 (pow x 3)))))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* 1/4 (sqrt x))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/4 (sqrt (/ 1 (pow x 3)))))) x))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
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
1
1
1
1
1
1
1
1
1
1
1
2
(+ 2 (* -9 x))
(+ 2 (* x (- (* 147/4 x) 9)))
(+ 2 (* x (- (* x (+ 147/4 (* -1181/8 x))) 9)))
(* 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)))) (+ (* 1/32 (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)))) (+ (* -1/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 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 (/ (+ (* -1/32 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 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 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/128 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* 1/16 (sqrt x)) (* 1/4 (sqrt x)))) x)) (+ (* -1/32 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 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))
2
(+ 2 (* -8 x))
(+ 2 (* x (- (* 32 x) 8)))
(+ 2 (* x (- (* x (+ 32 (* -128 x))) 8)))
(/ 1/2 x)
(/ (- 1/2 (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/32 (pow x 2))) (* 1/8 (/ 1 x))) x)
(/ (- (+ 1/2 (/ 1/32 (pow x 2))) (+ (* 1/8 (/ 1 x)) (* 1/128 (/ 1 (pow x 3))))) x)
(/ 1/2 x)
(* -1 (/ (- (* 1/8 (/ 1 x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (- (* 1/32 (/ 1 x)) 1/8) x)) 1/2) x))
(* -1 (/ (- (* -1 (/ (- (* -1 (/ (- (* 1/128 (/ 1 x)) 1/32) x)) 1/8) x)) 1/2) x))
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* x (- (* -1/2 (sqrt (/ 1 x))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (* 1/2 (/ 1 x)))))) (/ 1 x))))
(+ (sqrt (/ 1 x)) (* x (- (+ (* -1/2 (sqrt (/ 1 x))) (* x (+ (* -1 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (+ (* 3/8 (sqrt (/ 1 x))) (+ (* 1/2 (/ 1 x)) (* x (- (+ (* -5/16 (sqrt (/ 1 x))) (+ (* 1/2 (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))) (* 1/2 (/ 1 (pow x 2))))) (+ (* -1 (* (sqrt (/ 1 x)) (+ (* -1 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))) (* 3/8 (/ 1 x)))))))))) (/ 1 x))))
(* 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)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x)))))))) x)
(* -1 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1))))
(* -1 (/ (+ (* 1/2 (* (sqrt (/ 1 (pow x 3))) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3))))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2))))) x)) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/16 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 3)))) (+ (* 1/2 (/ (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))) (- (pow (sqrt -1) 2) 1))) (* 1/16 (/ 1 (* (pow (sqrt -1) 4) (pow (- (pow (sqrt -1) 2) 1) 2))))))))) (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* 1/4 (* (sqrt x) (/ 1 (pow (- (pow (sqrt -1) 2) 1) 2)))))) x)) (+ (* -1/2 (* (sqrt x) (/ 1 (- (pow (sqrt -1) 2) 1)))) (* (sqrt (/ 1 x)) (* (pow (sqrt -1) 2) (+ (* 1/8 (/ 1 (* (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2)))) (* 1/4 (/ 1 (pow (- (pow (sqrt -1) 2) 1) 3)))))))) x)) (* -1/2 (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (pow (- (pow (sqrt -1) 2) 1) 2))))) x)) (* (sqrt (/ 1 x)) (/ (pow (sqrt -1) 2) (- (pow (sqrt -1) 2) 1)))) x))
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))))
(sqrt x)
(+ x (sqrt x))
(+ (sqrt x) (* x (+ 1 (* 1/2 (sqrt x)))))
(+ (sqrt x) (* x (+ 1 (* x (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))))
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 x))))
(* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(* -1 (* x (- (pow (sqrt -1) 2) 1)))
(* -1 (* x (- (pow (sqrt -1) 2) (+ 1 (* 1/2 (/ 1 x))))))
(* -1 (* x (- (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2)) 1)))
(* -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)) 1)))
(/ 5/128 (pow x 3))
(/ 5/128 (pow x 3))
(/ 5/128 (pow x 3))
(/ 5/128 (pow x 3))
(/ 5/128 (pow x 3))
(/ 5/128 (pow x 3))
(/ 5/128 (pow x 3))
(/ 5/128 (pow x 3))
(/ 5/128 (pow x 3))
(/ 5/128 (pow x 3))
(/ 5/128 (pow x 3))
(/ 5/128 (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)
(/ 1/16 (pow x 2))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/ (+ 1/16 (* -1/8 x)) (pow x 2))
(/ -1/8 x)
(/ (- (* 1/16 (/ 1 x)) 1/8) x)
(/ (- (* 1/16 (/ 1 x)) 1/8) x)
(/ (- (* 1/16 (/ 1 x)) 1/8) x)
(/ -1/8 x)
(* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))
(* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))
(* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))
1/2
(+ 1/2 x)
(+ 1/2 x)
(+ 1/2 x)
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* 1/2 (/ 1 x))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (* 1/2 (/ 1 x))))
(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))))
x
(* x (+ 1 x))
(* x (+ 1 x))
(* x (+ 1 x))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))

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

eval202.0ms (1.9%)

Compiler: Compiled 35144 to 3528 computations (90% saved)

prune371.0ms (3.5%)

Pruning

25 alts after pruning (23 fresh and 2 done)

	Pruned	Kept	Total
New	1235	20	1255
Fresh	11	3	14
Picked	4	1	5
Done	1	1	2
Total	1251	25	1276

Accuracy

100.0%

Counts

1276 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	97.3%	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (/.f64 x #s(literal 1/2 binary64)))
	98.7%	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (-.f64 #s(literal 0 binary64) (*.f64 x (+.f64 #s(literal -2 binary64) (/.f64 #s(literal -1/2 binary64) x)))))
	98.7%	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (+.f64 x #s(literal 1/2 binary64))))
	99.0%	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (*.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))))
	99.1%	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (.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) (/.f64 #s(literal -1/8 binary64) x)) x))))))
✓	82.2%	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
	99.0%	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))))
▶	99.1%	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x (*.f64 x x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))))
	34.3%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))))
	99.1%	(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 5/128 binary64) x)) x)) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
▶	99.0%	(/.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)))
	97.3%	(/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) x)
	36.4%	(/.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
	97.3%	(/.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
▶	97.1%	(/.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
	7.4%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))))
	2.6%	(/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) x)
	99.1%	(/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/16 binary64) x)) (/.f64 #s(literal 5/128 binary64) (.f64 x x))) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) x)
	79.6%	(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
	97.5%	(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (+.f64 x (+.f64 x #s(literal 1/2 binary64)))))
	96.1%	(/.f64 #s(literal 1/2 binary64) (*.f64 x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
	7.7%	(/.f64 #s(literal 1/2 binary64) x)
✓	37.9%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	66.1%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
▶	4.6%	#s(literal 2 binary64)

Compiler

Compiled 693 to 482 computations (30.4% saved)

simplify194.0ms (1.8%)

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x))
✓	cost-diff	0	(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x)
✓	cost-diff	0	(/.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)))
✓	cost-diff	64	(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
✓	cost-diff	0	(/.f64 x #s(literal 1/2 binary64))
✓	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	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (/.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	0	(/.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
✓	cost-diff	0	(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
✓	cost-diff	0	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x (*.f64 x x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))))
✓	cost-diff	128	(.f64 x (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x (*.f64 x x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))))
✓	cost-diff	256	(+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))

Rules

1782×	`sum3-define`
1782×	`-lowering-.f32`
1782×	`-lowering-.f64`
1530×	`sum4-define`
1124×	`/-lowering-/.f32`

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	33	211
1	67	208
2	126	208
3	238	208
4	368	204
5	631	200
6	1411	195
7	5664	195
0	8104	195

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize223.0ms (2.1%)

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x)
✓	accuracy	100.0%	(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)
✓	accuracy	99.7%	(/.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)))
✓	accuracy	100.0%	(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(/.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) x)
✓	accuracy	99.7%	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (/.f64 x #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.7%	(/.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x (*.f64 x x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))))
✓	accuracy	99.8%	(.f64 x (.f64 x x))
✓	accuracy	99.7%	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (.f64 x (+.f64 #s(literal 2 binary64) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x (*.f64 x x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))))
✓	accuracy	99.6%	(/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))

Results

134.0ms

256×

valid

Compiler

Compiled 226 to 34 computations (85% saved)

Precisions

Click to see histograms. Total time spent on operations: 53.0ms

ival-div: 26.0ms (48.7% of total)

ival-pow: 11.0ms (20.6% of total)

ival-add: 7.0ms (13.1% of total)

ival-mult: 5.0ms (9.4% of total)

ival-sqrt: 2.0ms (3.7% of total)

ival-sub: 1.0ms (1.9% of total)

const: 1.0ms (1.9% of total)

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

series9.0ms (0.1%)

Counts

17 → 204

Calls

Call 1

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

Outputs
#<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 (- (* x (+ 1/2 (* 2 x))) 1/8))) (pow x 2))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* 1/2 (/ 1 x))))>
#<alt (* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))>
#<alt (* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (* 1/2 (/ 1 x))))>
#<alt (* -1 (* x (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2)))>
#<alt (* -1 (* x (- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2)))>
#<alt (* 16 (pow x 2))>
#<alt (* (pow x 2) (+ 16 (* 24 x)))>
#<alt (* (pow x 2) (+ 16 (* x (+ 24 (* -74 x)))))>
#<alt (* (pow x 2) (+ 16 (* x (+ 24 (* x (- (* -857 x) 74))))))>
#<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)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 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))) (* 5/128 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<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 (* 1/2 (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 (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 x)>
#<alt (/ 1/2 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 x)>
#<alt (/ (+ 1/2 (* -1/4 x)) x)>
#<alt (/ (+ 1/2 (* x (- (* 3/16 x) 1/4))) x)>
#<alt (/ (+ 1/2 (* x (- (* x (+ 3/16 (* -5/32 x))) 1/4))) x)>
#<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)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) x)>
#<alt (/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (+ (* 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))) (* 1/4 (sqrt (/ 1 (pow x 3))))) x))>
#<alt (* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/4 (sqrt (/ 1 (pow x 5)))) (* 1/4 (sqrt (/ 1 (pow x 3)))))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* 1/4 (sqrt x))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/4 (sqrt (/ 1 (pow x 3)))))) x))>
#<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 (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (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)))) (* (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)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<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 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (pow x 3))>
#<alt (/ 1/16 (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 (/ -1/16 (pow x 2))>
#<alt (/ (- (* 1/8 x) 1/16) (pow x 2))>
#<alt (/ (- (* 1/8 x) 1/16) (pow x 2))>
#<alt (/ (- (* 1/8 x) 1/16) (pow x 2))>
#<alt (/ 1/8 x)>
#<alt (/ (- 1/8 (* 1/16 (/ 1 x))) x)>
#<alt (/ (- 1/8 (* 1/16 (/ 1 x))) x)>
#<alt (/ (- 1/8 (* 1/16 (/ 1 x))) x)>
#<alt (/ 1/8 x)>
#<alt (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x))>
#<alt (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x))>
#<alt (* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x))>

Calls

51 calls:

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

rewrite434.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

4746×	`/-lowering-/.f32`
4746×	`/-lowering-/.f64`
3172×	`-lowering-.f32`
3172×	`-lowering-.f64`
1614×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	33	139
1	226	132
2	2226	132
0	8629	132

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 693

Calls

Call 1

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

Outputs
(+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) x) (*.f64 x x)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))
(+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (/.f64 (/.f64 #s(literal 1/16 binary64) x) (*.f64 x x)))
(-.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) x) (*.f64 x x)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (-.f64 #s(literal 0 binary64) x)))
(-.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) x) (*.f64 x x)) (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) x))
(-.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x x))))
(-.f64 (/.f64 (/.f64 (/.f64 #s(literal 1/256 binary64) (.f64 x x)) (.f64 (.f64 x x) (.f64 x 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))) x)) (/.f64 (/.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 x 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))) x)))
(-.f64 (/.f64 (/.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 x x)) (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) x)) (/.f64 (/.f64 (/.f64 #s(literal 1/256 binary64) (.f64 x x)) (.f64 (.f64 x x) (.f64 x x))) (/.f64 (-.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (/.f64 #s(literal 1/16 binary64) (.f64 x x))) x)))
(fma.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))
(fma.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (/.f64 #s(literal 1 binary64) x) (/.f64 (/.f64 #s(literal 1/16 binary64) x) (*.f64 x x)))
(fma.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1/16 binary64) x) (*.f64 x x)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))
(fma.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (/.f64 (/.f64 #s(literal 1/16 binary64) x) (*.f64 x x)))
(fma.f64 #s(literal -1/16 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))
(fma.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 (/.f64 #s(literal 1/16 binary64) x) (*.f64 x x)))
(fma.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (/.f64 (/.f64 #s(literal 1/16 binary64) x) (*.f64 x x)))
(fma.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))
(fma.f64 (/.f64 #s(literal 1/16 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))
(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (.f64 x x) (.f64 x x)) (+.f64 (.f64 #s(literal 1/16 binary64) x) (.f64 (.f64 x x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)))))))
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(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) (-.f64 #s(literal 0 binary64) x)))
(-.f64 (/.f64 (/.f64 #s(literal 1/64 binary64) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) x) (/.f64 (/.f64 (/.f64 #s(literal 1/256 binary64) (*.f64 x x)) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) x))
(-.f64 (/.f64 #s(literal 1/64 binary64) (.f64 x (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))) (/.f64 (/.f64 #s(literal 1/256 binary64) (.f64 x x)) (*.f64 x (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))))
(neg.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) (-.f64 #s(literal 0 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)
(/.f64 (+.f64 #s(literal -1/8 binary64) (neg.f64 (/.f64 #s(literal -1/16 binary64) x))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (+.f64 #s(literal 1/512 binary64) (/.f64 #s(literal -1/4096 binary64) (.f64 x (.f64 x x)))) (*.f64 x (+.f64 #s(literal 1/64 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) x) #s(literal 1/8 binary64)) (/.f64 x #s(literal -1/16 binary64))))))
(/.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (.f64 x x))) (.f64 x (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) #s(literal 1 binary64))))
(/.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) #s(literal 1 binary64)) x)
(/.f64 (.f64 (+.f64 #s(literal 1/512 binary64) (/.f64 #s(literal -1/4096 binary64) (.f64 x (.f64 x x)))) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1/64 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) x) #s(literal 1/8 binary64)) (/.f64 x #s(literal -1/16 binary64)))) x))
(/.f64 (.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (.f64 x x))) #s(literal 1 binary64)) (*.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x))
(/.f64 (neg.f64 (+.f64 #s(literal 1/512 binary64) (/.f64 #s(literal -1/4096 binary64) (.f64 x (.f64 x x))))) (neg.f64 (*.f64 x (+.f64 #s(literal 1/64 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) x) #s(literal 1/8 binary64)) (/.f64 x #s(literal -1/16 binary64)))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (.f64 x x)))) (neg.f64 (.f64 x (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))))
(/.f64 (neg.f64 (+.f64 #s(literal -1/8 binary64) (neg.f64 (/.f64 #s(literal -1/16 binary64) x)))) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 (.f64 (+.f64 #s(literal 1/512 binary64) (/.f64 #s(literal -1/4096 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1/64 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) x) #s(literal 1/8 binary64)) (/.f64 x #s(literal -1/16 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))
(/.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) #s(literal 1 binary64))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (neg.f64 (+.f64 #s(literal -1/8 binary64) (neg.f64 (/.f64 #s(literal -1/16 binary64) x))))) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/512 binary64) (/.f64 #s(literal -1/4096 binary64) (.f64 x (.f64 x x)))) #s(literal 1 binary64))) (neg.f64 (.f64 (+.f64 #s(literal 1/64 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) x) #s(literal 1/8 binary64)) (/.f64 x #s(literal -1/16 binary64)))) x)))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (.f64 x x))) #s(literal 1 binary64))) (neg.f64 (*.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/512 binary64) (/.f64 #s(literal -1/4096 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (+.f64 #s(literal 1/64 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) x) #s(literal 1/8 binary64)) (/.f64 x #s(literal -1/16 binary64))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) x))) (neg.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))
(pow.f64 (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 x (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x))
(*.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) (/.f64 #s(literal 1 binary64) x))
(*.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x) #s(literal 1 binary64))
(*.f64 (+.f64 #s(literal -1/8 binary64) (neg.f64 (/.f64 #s(literal -1/16 binary64) x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 x (+.f64 #s(literal 1/512 binary64) (/.f64 #s(literal -1/4096 binary64) (.f64 x (*.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) x) #s(literal 1/8 binary64)) (/.f64 x #s(literal -1/16 binary64))))))
(.f64 (pow.f64 (/.f64 x (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))))
(*.f64 (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (+.f64 #s(literal 1/512 binary64) (/.f64 #s(literal -1/4096 binary64) (.f64 x (*.f64 x x)))) x) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) x) #s(literal 1/8 binary64)) (/.f64 x #s(literal -1/16 binary64))))) #s(literal 1 binary64)))
(.f64 (/.f64 (+.f64 #s(literal 1/512 binary64) (/.f64 #s(literal -1/4096 binary64) (.f64 x (*.f64 x x)))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/64 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/16 binary64) x) #s(literal 1/8 binary64)) (/.f64 x #s(literal -1/16 binary64))))) x))
(.f64 (/.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (.f64 x x))) x) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) #s(literal 1 binary64)))
(.f64 (/.f64 (-.f64 #s(literal 1/64 binary64) (/.f64 #s(literal 1/256 binary64) (.f64 x x))) #s(literal 1 binary64)) (/.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x))) x))

simplify327.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

4690×	`-lowering-.f32`
4690×	`-lowering-.f64`
4002×	`+-lowering-+.f64`
4002×	`+-lowering-+.f32`
1286×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	328	1941
1	960	1639
2	3187	1599
0	8948	1599

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
(/ 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 (- (* x (+ 1/2 (* 2 x))) 1/8))) (pow x 2))
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 x))))
(* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(* 2 x)
(* x (+ 2 (* 1/2 (/ 1 x))))
(* -1 (* x (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2)))
(* -1 (* x (- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2)))
(* 16 (pow x 2))
(* (pow x 2) (+ 16 (* 24 x)))
(* (pow x 2) (+ 16 (* x (+ 24 (* -74 x)))))
(* (pow x 2) (+ 16 (* x (+ 24 (* x (- (* -857 x) 74))))))
(* 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)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 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))) (* 5/128 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))) x)) (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
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))))
(* 1/2 (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))))
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 x)
(/ 1/2 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 x)
(/ (+ 1/2 (* -1/4 x)) x)
(/ (+ 1/2 (* x (- (* 3/16 x) 1/4))) x)
(/ (+ 1/2 (* x (- (* x (+ 3/16 (* -5/32 x))) 1/4))) x)
(* 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)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (+ (* 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))) (* 1/4 (sqrt (/ 1 (pow x 3))))) x))
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/4 (sqrt (/ 1 (pow x 5)))) (* 1/4 (sqrt (/ 1 (pow x 3)))))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* 1/4 (sqrt x))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/4 (sqrt (/ 1 (pow x 3)))))) x))
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)))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (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)))) (* (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)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(/ 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 3))
(/ 1/16 (pow x 3))
(/ 1/16 (pow x 3))
(/ 1/16 (pow x 3))
(/ 1/16 (pow x 3))
(/ 1/16 (pow x 3))
(/ 1/16 (pow x 3))
(/ 1/16 (pow x 3))
(/ 1/16 (pow x 3))
(/ 1/16 (pow x 3))
(/ 1/16 (pow x 3))
(/ 1/16 (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)
(/ -1/16 (pow x 2))
(/ (- (* 1/8 x) 1/16) (pow x 2))
(/ (- (* 1/8 x) 1/16) (pow x 2))
(/ (- (* 1/8 x) 1/16) (pow x 2))
(/ 1/8 x)
(/ (- 1/8 (* 1/16 (/ 1 x))) x)
(/ (- 1/8 (* 1/16 (/ 1 x))) x)
(/ (- 1/8 (* 1/16 (/ 1 x))) x)
(/ 1/8 x)
(* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x))
(* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x))
(* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x))

Outputs
(/ 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 (- (* x (+ 1/2 (* 2 x))) 1/8))) (pow x 2))
(/.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))))) (.f64 x x))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))
(* x (- (+ 2 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (*.f64 x #s(literal 2 binary64)))
(* x (- (+ 2 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(+.f64 (/.f64 #s(literal -1/8 binary64) x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x (*.f64 x x))) #s(literal 2 binary64)))))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 x))) x)) 2)))
(+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (*.f64 x #s(literal 2 binary64)))
(* -1 (* x (- (* -1 (/ (+ 1/2 (* -1 (/ (- 1/8 (* 1/16 (/ 1 x))) x))) x)) 2)))
(*.f64 x (+.f64 #s(literal 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)))
(* 16 (pow x 2))
(.f64 (.f64 x x) #s(literal 16 binary64))
(* (pow x 2) (+ 16 (* 24 x)))
(.f64 x (.f64 x (+.f64 #s(literal 16 binary64) (*.f64 x #s(literal 24 binary64)))))
(* (pow x 2) (+ 16 (* x (+ 24 (* -74 x)))))
(.f64 (.f64 x x) (+.f64 #s(literal 16 binary64) (.f64 x (+.f64 #s(literal 24 binary64) (.f64 x #s(literal -74 binary64))))))
(* (pow x 2) (+ 16 (* x (+ 24 (* x (- (* -857 x) 74))))))
(.f64 x (.f64 x (+.f64 #s(literal 16 binary64) (.f64 x (+.f64 #s(literal 24 binary64) (.f64 x (+.f64 #s(literal -74 binary64) (*.f64 x #s(literal -857 binary64)))))))))
(* 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)))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.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 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -3/8 binary64)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (+ (* -5/128 (sqrt (/ 1 (pow x 7)))) (+ (* 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 -5/128 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (+.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 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -3/8 binary64))))) x)
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 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 #s(literal 1/8 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 (/ (+ (* -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 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))) x)) (-.f64 #s(literal 0 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))) (* 5/128 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))))) x)) (* -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 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -5/128 binary64)) (+.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -5/16 binary64)))) x)) x)) (-.f64 #s(literal 0 binary64) 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 (+.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))) (.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 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (.f64 #s(literal -1/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64)))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+.f64 (neg.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)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+.f64 (neg.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)))))))
(+ (* -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 (neg.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1/2 binary64) (.f64 (.f64 x #s(literal 1/4 binary64)) #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))))
(.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))))
(.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))))
(.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))))
(.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))))
(.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))))
(.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))))
(.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))))
(.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))))
(.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))))
(.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))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ 1/2 x)
(/.f64 #s(literal 1/2 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 x)
(/.f64 #s(literal 1/2 binary64) x)
(/ (+ 1/2 (* -1/4 x)) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) x)
(/ (+ 1/2 (* x (- (* 3/16 x) 1/4))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x #s(literal 3/16 binary64))))) x)
(/ (+ 1/2 (* x (- (* x (+ 3/16 (* -5/32 x))) 1/4))) x)
(/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/4 binary64) (.f64 x (+.f64 #s(literal 3/16 binary64) (*.f64 x #s(literal -5/32 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 (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 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/4 binary64))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 x))))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/4 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/4 binary64)))) x)
(/ (+ (* -1/4 (sqrt (/ 1 (pow x 3)))) (+ (* -1/4 (* (sqrt (/ 1 (pow x 7))) (+ 1 (* 1/4 x)))) (+ (* 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 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/4 binary64))) (.f64 #s(literal -1/4 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64))))))) x)
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -1/2 binary64))
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/4 (sqrt (/ 1 (pow x 3))))) x))
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/4 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) x)
(* -1 (/ (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (+ (* -1/4 (sqrt (/ 1 (pow x 5)))) (* 1/4 (sqrt (/ 1 (pow x 3)))))) x))
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/4 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal -1/4 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1/4 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* 1/4 (sqrt x))) (pow x 3))) (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 1/4 (sqrt (/ 1 (pow x 3)))))) 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) (.f64 x (.f64 x x)))) #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1/4 binary64) (.f64 #s(literal -1/4 binary64) (.f64 x #s(literal 1/4 binary64))))) (.f64 #s(literal 1/4 binary64) (sqrt.f64 x))) (.f64 x (.f64 x x))))) (-.f64 #s(literal 0 binary64) 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))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x #s(literal -1/8 binary64)) #s(literal 1/2 binary64))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 #s(literal 1/16 binary64) x))))))
(sqrt x)
(sqrt.f64 x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(.f64 x (+.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(.f64 x (+.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 x (+.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))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))))
(* -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)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 x (+.f64 (neg.f64 (+.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(/ 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 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(/ (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.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 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 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 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -3/8 binary64)))) x)
(* 1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 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 #s(literal 1/8 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 (/ (+ (* -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 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))) x)) (-.f64 #s(literal 0 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 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (+.f64 (+.f64 (.f64 #s(literal 1/4 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -5/16 binary64))) x)) x)) (-.f64 #s(literal 0 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 3))
(/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))
(/ 1/16 (pow x 3))
(/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))
(/ 1/16 (pow x 3))
(/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))
(/ 1/16 (pow x 3))
(/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))
(/ 1/16 (pow x 3))
(/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))
(/ 1/16 (pow x 3))
(/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))
(/ 1/16 (pow x 3))
(/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))
(/ 1/16 (pow x 3))
(/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))
(/ 1/16 (pow x 3))
(/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))
(/ 1/16 (pow x 3))
(/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))
(/ 1/16 (pow x 3))
(/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))
(/ 1/16 (pow x 3))
(/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(/ -1/16 (pow x 2))
(/.f64 #s(literal -1/16 binary64) (*.f64 x x))
(/ (- (* 1/8 x) 1/16) (pow x 2))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)
(/ (- (* 1/8 x) 1/16) (pow x 2))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)
(/ (- (* 1/8 x) 1/16) (pow x 2))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(/ (- 1/8 (* 1/16 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)
(/ (- 1/8 (* 1/16 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)
(/ (- 1/8 (* 1/16 (/ 1 x))) x)
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)
(/ 1/8 x)
(/.f64 #s(literal 1/8 binary64) x)
(* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)
(* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)
(* -1 (/ (- (* 1/16 (/ 1 x)) 1/8) x))
(/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)

eval117.0ms (1.1%)

Compiler: Compiled 25702 to 2816 computations (89% saved)

prune136.0ms (1.3%)

Pruning

27 alts after pruning (22 fresh and 5 done)

	Pruned	Kept	Total
New	1002	11	1013
Fresh	7	11	18
Picked	2	3	5
Done	0	2	2
Total	1011	27	1038

Accuracy

100.0%

Counts

1038 → 27

Alt Table

Click to see full alt table

Status	Accuracy	Program
	36.0%	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (/.f64 (+.f64 #s(literal 1/16 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 2 binary64))))))) (.f64 x x)))
✓	97.3%	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (/.f64 x #s(literal 1/2 binary64)))
	99.0%	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (*.f64 x #s(literal 2 binary64))))
	98.7%	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (+.f64 x #s(literal 1/2 binary64))))
✓	82.2%	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
	99.1%	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 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))))
	99.0%	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))))
	98.7%	(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 2 binary64) (/.f64 #s(literal 1/2 binary64) x))))
	99.1%	(/.f64 (/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) x) (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) x) (*.f64 x x)) #s(literal 2 binary64))))
	34.3%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (+.f64 #s(literal 1/2 binary64) x))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))))
	36.4%	(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
	35.0%	(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal -1/16 binary64) x)) x)) x) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 #s(literal 1/16 binary64) x)))))))
	97.3%	(/.f64 (/.f64 #s(literal 1/2 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) x)
	97.1%	(/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x)
	36.4%	(/.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
	97.3%	(/.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
✓	97.1%	(/.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
	7.4%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64))) (sqrt.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1 binary64) x))))
	2.6%	(/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/4 binary64))) x)
	97.5%	(/.f64 #s(literal 1 binary64) (*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (+.f64 x (+.f64 x #s(literal 1/2 binary64)))))
	96.0%	(/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3/2 binary64)))
	96.1%	(/.f64 #s(literal 1/2 binary64) (*.f64 x (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
	7.7%	(/.f64 #s(literal 1/2 binary64) x)
	35.3%	(/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))
✓	37.9%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	97.4%	(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -3/2 binary64)))
✓	4.6%	#s(literal 2 binary64)

Compiler

Compiled 1334 to 491 computations (63.2% saved)

regimes36.0ms (0.3%)

Counts

63 → 1

Calls

Call 1

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

Calls

2 calls:

17.0ms	x
15.0ms	(-.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
99.1%	1	`x`
99.1%	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)

regimes13.0ms (0.1%)

Counts

35 → 1

Calls

Call 1

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

Calls

1 calls:

10.0ms

Results

Accuracy	Segments	Branch
99.1%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes12.0ms (0.1%)

Counts

34 → 1

Calls

Call 1

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

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

Calls

1 calls:

10.0ms

Results

Accuracy	Segments	Branch
99.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes10.0ms (0.1%)

Counts

27 → 1

Calls

Call 1

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

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

Calls

1 calls:

9.0ms

Results

Accuracy	Segments	Branch
98.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes9.0ms (0.1%)

Counts

23 → 1

Calls

Call 1

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

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

Calls

1 calls:

8.0ms

Results

Accuracy	Segments	Branch
97.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0%)

Counts

11 → 1

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
36.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

4 → 1

Calls

Call 1

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

Outputs
(/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
35.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

2 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)
(/.f64 #s(literal 1/2 binary64) x)

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
7.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(literal 2 binary64)

Outputs
#s(literal 2 binary64)

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
4.6%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify58.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

330×	`unsub-neg_binary64`
328×	`distribute-lft-neg-in_binary64`
240×	`cancel-sign-sub_binary64`
222×	`neg-mul-1_binary64`
186×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	46	93
1	69	93
2	89	93
3	111	93
4	159	93
5	222	93
6	303	93
7	441	93
8	629	93
9	810	93
10	953	93
11	1095	93
12	1128	93
13	1159	93
14	1201	93
15	1241	93
16	1269	93
17	1281	93
18	1283	93

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 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 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 5/128 binary64) x)) x)) x)) 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)) (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (*.f64 x #s(literal 2 binary64))))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (+.f64 x #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -3/2 binary64)))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 2 binary64)

Outputs
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (*.f64 x (+.f64 #s(literal 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 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 (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 #s(literal 1/8 binary64) (/.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 5/128 binary64) x)) x)) x)) x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (/.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal 5/128 binary64) x)) x) #s(literal 1/8 binary64)) x)) x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (*.f64 x #s(literal 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)) (*.f64 x #s(literal 2 binary64))))
(/.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)) (+.f64 x (+.f64 x #s(literal 1/2 binary64))))
(/.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal -1/2 binary64)) (+.f64 x (+.f64 x #s(literal 1/2 binary64))))
(*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -3/2 binary64)))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)))
(/.f64 (/.f64 #s(literal 1/2 binary64) x) (+.f64 (*.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)))
(/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)))
(/.f64 #s(literal 1/2 binary64) x)
#s(literal 2 binary64)

soundness2.1s (20%)

Rules

4746×	`/-lowering-/.f32`
4746×	`/-lowering-/.f64`
4690×	`-lowering-.f32`
4690×	`-lowering-.f64`
4218×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	328	1941
1	960	1639
2	3187	1599
0	8948	1599
0	32	163
1	246	137
2	2508	137
0	8720	137
0	8	15
1	64	15
2	601	15
3	7279	15
0	8160	15
0	437	2999
1	1433	2182
2	5768	2148
0	8202	2148
0	572	2702
1	1812	2060
2	6785	2045
0	8070	2045
0	36	193
1	253	140
2	2372	131
0	9716	131
0	33	139
1	226	132
2	2226	132
0	8629	132

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 241 to 143 computations (40.7% saved)

preprocess55.0ms (0.5%)

Compiler: Compiled 244 to 126 computations (48.4% 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%)

sample2.2s (21%)

preprocess63.0ms (0.6%)

explain234.0ms (2.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify21.0ms (0.2%)

localize127.0ms (1.2%)

series6.0ms (0.1%)

rewrite271.0ms (2.5%)

simplify202.0ms (1.9%)

eval48.0ms (0.5%)

prune60.0ms (0.6%)

simplify195.0ms (1.8%)

localize485.0ms (4.5%)

series20.0ms (0.2%)

rewrite363.0ms (3.4%)

simplify272.0ms (2.6%)

eval249.0ms (2.3%)

prune197.0ms (1.8%)

simplify193.0ms (1.8%)

localize347.0ms (3.3%)

series18.0ms (0.2%)

rewrite406.0ms (3.8%)

simplify295.0ms (2.8%)

eval202.0ms (1.9%)

prune371.0ms (3.5%)

simplify194.0ms (1.8%)

localize223.0ms (2.1%)

series9.0ms (0.1%)

rewrite434.0ms (4.1%)

simplify327.0ms (3.1%)

eval117.0ms (1.1%)

prune136.0ms (1.3%)

regimes36.0ms (0.3%)

regimes13.0ms (0.1%)

regimes12.0ms (0.1%)

regimes10.0ms (0.1%)

regimes9.0ms (0.1%)

regimes5.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify58.0ms (0.5%)

soundness2.1s (20%)

preprocess55.0ms (0.5%)

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