Metrics for 2isqrt (example 3.6)

analyze5.0ms (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)

sample2.5s (25.1%)

Results

1.5s	6470×	1	valid
546.0ms	1589×	2	valid
65.0ms	197×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.6s

ival-sqrt: 490.0ms (30.4% of total)

ival-div: 324.0ms (20.1% of total)

backward-pass: 223.0ms (13.9% of total)

...c/correct-round.rkt:119:19: 178.0ms (11.1% of total)

ival-add: 116.0ms (7.2% of total)

ival-sub: 92.0ms (5.7% of total)

ival->: 68.0ms (4.2% of total)

ival-<: 68.0ms (4.2% of total)

ival-and: 33.0ms (2% of total)

const: 17.0ms (1.1% of total)

Bogosity

preprocess60.0ms (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	49	24
2	83	23
3	144	23
4	248	23
5	462	23
6	689	23
7	915	23
8	1054	23
9	1200	23
10	1311	23
11	1347	23
12	1355	23
0	8	7
1	23	7
2	31	7
3	43	7
4	57	7
5	94	7
6	165	7
7	261	7
8	360	7
9	492	7
10	604	7
11	640	7
12	648	7
0	648	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))))
(- (fast-isqrt x) (fast-isqrt (+ 1 x)))
(- (/ 1 (sqrt (neg x))) (/ 1 (sqrt (+ (neg x) 1))))
(- (fast-isqrt (neg x)) (fast-isqrt (- 1 x)))
(neg (- (/ 1 (sqrt (neg x))) (/ 1 (sqrt (+ (neg x) 1)))))
(- (fast-isqrt (- 1 x)) (fast-isqrt (neg x)))

explain213.0ms (2.2%)

FPErrors

Click to see full error table

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

Results

140.0ms	412×	1	valid
33.0ms	92×	2	valid
1.0ms	8×	0	valid

Compiler

Compiled 80 to 26 computations (67.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 63.0ms

ival-sqrt: 19.0ms (30.2% of total)

ival-div: 17.0ms (27% of total)

backward-pass: 14.0ms (22.3% of total)

ival-add: 6.0ms (9.5% of total)

ival-sub: 6.0ms (9.5% of total)

const: 1.0ms (1.6% 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
▶	39.2%	(-.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)

simplify25.0ms (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	23	24
2	31	24
3	43	24
4	57	24
5	94	24
6	165	24
7	261	24
8	360	24
9	492	24
10	604	24
11	640	24
12	648	24
0	648	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)

localize86.0ms (0.9%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	39.3%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

49.0ms	206×	1	valid
23.0ms	46×	2	valid
0.0ms	4×	0	valid

Compiler

Compiled 34 to 9 computations (73.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-sqrt: 15.0ms (40.1% of total)

ival-div: 9.0ms (24.1% of total)

backward-pass: 7.0ms (18.7% of total)

ival-add: 3.0ms (8% of total)

ival-sub: 3.0ms (8% of total)

const: 1.0ms (2.7% of total)

series5.0ms (0.1%)

Counts

4 → 48

Calls

Call 1

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

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

Calls

12 calls:

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

rewrite319.0ms (3.2%)

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	70	15
2	609	15
3	7338	15
0	8482	15

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 220

Calls

Call 1

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

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

simplify244.0ms (2.5%)

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	338	394
2	1145	371
3	4913	370
0	8260	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 (/.f64 #s(literal 1 binary64) (.f64 x 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 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)) (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (.f64 x x))
(/ (- (* -1/2 (* (sqrt (/ 1 (pow x 5))) (+ 1 (* 1/2 x)))) (+ (* -1/2 (sqrt x)) (+ (* -1/2 (* (sqrt (/ 1 (pow x 3))) (+ 1 (* 1/4 x)))) (* 1/2 (sqrt (/ 1 x)))))) (pow x 2))
(/.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)))) (sqrt.f64 x)) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x 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 (/.f64 #s(literal 1 binary64) (.f64 x 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 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))) (+.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))))
(- (+ (sqrt (/ 1 x)) (* -1 (/ (- (* -1/2 (* (sqrt (/ 1 x)) (+ 1 (* -1/4 (/ x (pow (sqrt -1) 2)))))) (* -1/2 (sqrt x))) (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))) (+.f64 (.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 x x)) (/.f64 #s(literal 1/2 binary64) x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
1
#s(literal 1 binary64)
(+ 1 (* -1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -1/2 binary64)))
(+ 1 (* x (- (* 3/8 x) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x #s(literal 3/8 binary64)))))
(+ 1 (* x (- (* x (+ 3/8 (* -5/16 x))) 1/2)))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal -1/2 binary64) (.f64 x (+.f64 #s(literal 3/8 binary64) (*.f64 x #s(literal -5/16 binary64)))))))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(+ (sqrt (/ 1 x)) (* -1/2 (sqrt (/ 1 (pow x 3)))))
(+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x 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 (/.f64 #s(literal 1 binary64) (.f64 x 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 (/.f64 #s(literal 1 binary64) (.f64 x 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 (/.f64 #s(literal 1 binary64) (.f64 x 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 (/.f64 #s(literal 1 binary64) (.f64 x 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 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)) #s(literal -1/2 binary64)) (-.f64 (/.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 x))) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))

eval34.0ms (0.3%)

Compiler: Compiled 6483 to 720 computations (88.9% saved)

prune38.0ms (0.4%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	256	12	268
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	257	12	269

Accuracy

82.1%

Counts

269 → 12

Alt Table

Click to see full alt table

Status	Accuracy	Program
	40.8%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	40.8%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
▶	81.2%	(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x 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))
	39.3%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	31.8%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	31.8%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
▶	28.7%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
▶	30.7%	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	40.8%	(.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	80.5%	(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
	64.5%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)))
▶	5.4%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 354 to 224 computations (36.7% saved)

simplify183.0ms (1.8%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

1830×	`-lowering-.f32`
1830×	`-lowering-.f64`
1740×	`sum5-define`
1644×	`sum3-define`
1476×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	191
1	75	177
2	145	173
3	332	173
4	594	173
5	1093	173
6	2177	173
7	4548	173
0	8180	173

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

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

localize556.0ms (5.6%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	99.9%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	accuracy	39.3%	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	39.3%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.9%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	99.9%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	98.8%	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	accuracy	82.0%	(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x 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	68.8%	(.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)) (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64)))))
✓	accuracy	66.0%	(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))

Results

399.0ms	196×	2	valid
87.0ms	60×	1	valid

Compiler

Compiled 235 to 30 computations (87.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 259.0ms

ival-div: 83.0ms (32% of total)

backward-pass: 57.0ms (22% of total)

ival-pow: 40.0ms (15.4% of total)

ival-sqrt: 27.0ms (10.4% of total)

ival-mult: 22.0ms (8.5% of total)

ival-sub: 14.0ms (5.4% of total)

ival-add: 14.0ms (5.4% of total)

const: 2.0ms (0.8% of total)

series14.0ms (0.1%)

Counts

16 → 192

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

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 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (- (sqrt (/ 1 x)) (* (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 (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 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 (/ 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 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 (/ 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 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<alt (/ 1 (pow x 2))>
#<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)))))))>

Calls

48 calls:

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

rewrite406.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

4200×	`-lowering-.f32`
4200×	`-lowering-.f64`
2794×	`+-lowering-+.f64`
2794×	`+-lowering-+.f32`
2580×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	118
1	211	94
2	1961	86
0	9549	86

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 551

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

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

simplify270.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

4238×	`-lowering-.f32`
4238×	`-lowering-.f64`
3068×	`+-lowering-+.f64`
3068×	`+-lowering-+.f32`
1420×	`associate-r`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	236	2012
1	769	1635
2	2800	1585
0	8472	1585

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

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)
0
0
0
0
0
0
0
0
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (sqrt (/ 1 x)) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- (sqrt (/ 1 x)) (* (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)))
(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))))
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 (/ 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))
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 (/ 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 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
(/ 1 (pow x 2))
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)))))))

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

eval146.0ms (1.5%)

Compiler: Compiled 25402 to 2366 computations (90.7% saved)

prune119.0ms (1.2%)

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	1121	14	1135
Fresh	2	5	7
Picked	3	2	5
Done	0	0	0
Total	1126	21	1147

Accuracy

100.0%

Counts

1147 → 21

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	38.0%	(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
	38.0%	(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
	5.4%	(pow.f64 x #s(literal -1/2 binary64))
	40.8%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
▶	98.9%	(/.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 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))) x) x)
	22.3%	(/.f64 (/.f64 (+.f64 (.f64 (.f64 (.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))) #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) x) (/.f64 #s(literal 1 binary64) x)) (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -3/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)))))) (.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) (+.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 x x))
▶	28.4%	(/.f64 (/.f64 (+.f64 (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -3/8 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (.f64 x (.f64 x x))))) (.f64 x x)) (.f64 x x))
	46.1%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal -3/2 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 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))))) (pow.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x))) #s(literal 2 binary64))))) (*.f64 x x))
	40.8%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
	98.1%	(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -5/8 binary64) x))) (-.f64 #s(literal 0 binary64) x))
	80.4%	(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
	96.7%	(/.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 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))) x)))
	5.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
▶	39.3%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	31.8%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	40.8%	(.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)))
	98.9%	(.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 (.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))) x) (/.f64 #s(literal 1 binary64) x))
	80.5%	(.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
	64.5%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)))
✓	5.4%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
▶	37.0%	#s(literal 0 binary64)

Compiler

Compiled 852 to 482 computations (43.4% saved)

simplify182.0ms (1.8%)

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Program
✓	cost-diff	(.f64 (sqrt.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -3/8 binary64))))
✓	cost-diff	(+.f64 (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -3/8 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (.f64 x (.f64 x x)))))
✓	cost-diff	(/.f64 (+.f64 (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -3/8 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (.f64 x (.f64 x x))))) (*.f64 x x))
✓	cost-diff	(/.f64 (/.f64 (+.f64 (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -3/8 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (.f64 x (.f64 x x))))) (.f64 x x)) (.f64 x x))
✓	cost-diff	(+.f64 #s(literal 1 binary64) x)
✓	cost-diff	(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
✓	cost-diff	(pow.f64 x #s(literal -1/2 binary64))
✓	cost-diff	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	cost-diff	(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
✓	cost-diff	(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal -3/2 binary64)))
✓	cost-diff	(+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal -3/2 binary64))) (/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x))))
✓	cost-diff	(/.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 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))) x)
✓	cost-diff	(/.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 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))) x) x)

Rules

2034×	`sum5-define`
1938×	`-lowering-.f32`
1938×	`-lowering-.f64`
1570×	`sum4-define`
1354×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	39	268
1	86	256
2	169	256
3	319	256
4	565	256
5	1234	256
6	3943	256
7	7707	256
0	8125	256

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (/ (+ (* (+ 1/2 (* x 1/8)) (pow x -3/2)) (/ (* -1/2 (- (/ 1 x) x)) (/ (+ 1 x) (sqrt x)))) x) x)
(/ (+ (* (+ 1/2 (* x 1/8)) (pow x -3/2)) (/ (* -1/2 (- (/ 1 x) x)) (/ (+ 1 x) (sqrt x)))) x)
(+ (* (+ 1/2 (* x 1/8)) (pow x -3/2)) (/ (* -1/2 (- (/ 1 x) x)) (/ (+ 1 x) (sqrt x))))
(* (+ 1/2 (* x 1/8)) (pow x -3/2))
(+ 1/2 (* x 1/8))
1/2
(* x 1/8)
x
1/8
(pow x -3/2)
-3/2
(/ (* -1/2 (- (/ 1 x) x)) (/ (+ 1 x) (sqrt x)))
(* -1/2 (- (/ 1 x) x))
-1/2
(- (/ 1 x) x)
(/ 1 x)
1
(/ (+ 1 x) (sqrt x))
(+ 1 x)
(sqrt x)
0
(pow (/ 1 (* x x)) 1/4)
(/ 1 (* x x))
1
(* x x)
x
1/4
(- (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 x) (+ 1/2 (* x -3/8))) (* (* 1/2 x) (sqrt (* x (* x x))))) (* x x)) (* x x))
(/ (+ (* (sqrt x) (+ 1/2 (* x -3/8))) (* (* 1/2 x) (sqrt (* x (* x x))))) (* x x))
(+ (* (sqrt x) (+ 1/2 (* x -3/8))) (* (* 1/2 x) (sqrt (* x (* x x)))))
(* (sqrt x) (+ 1/2 (* x -3/8)))
(sqrt x)
x
(+ 1/2 (* x -3/8))
1/2
(* x -3/8)
-3/8
(* (* 1/2 x) (sqrt (* x (* x x))))
(* 1/2 x)
(sqrt (* x (* x x)))
(* x (* x x))
(* x x)

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

localize423.0ms (4.3%)

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	82.0%	(/.f64 (/.f64 (+.f64 (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -3/8 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (.f64 x (.f64 x x))))) (.f64 x x)) (.f64 x x))
✓	accuracy	72.0%	(+.f64 (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -3/8 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (.f64 x (.f64 x x)))))
✓	accuracy	66.5%	(sqrt.f64 (.f64 x (.f64 x x)))
✓	accuracy	39.1%	(/.f64 (+.f64 (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -3/8 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (.f64 x (.f64 x x))))) (*.f64 x 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	100.0%	(pow.f64 x #s(literal -1/2 binary64))
✓	accuracy	39.3%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	98.8%	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	accuracy	51.0%	(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
✓	accuracy	99.6%	(/.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 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))) x)
✓	accuracy	99.3%	(/.f64 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))
✓	accuracy	99.3%	(/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x))
✓	accuracy	68.8%	(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal -3/2 binary64)))

Results

238.0ms	195×	1	valid
110.0ms	57×	2	valid
2.0ms	4×	0	valid

Compiler

Compiled 305 to 40 computations (86.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 196.0ms

ival-pow: 69.0ms (35.1% of total)

backward-pass: 32.0ms (16.3% of total)

ival-mult: 32.0ms (16.3% of total)

ival-div: 30.0ms (15.3% of total)

ival-add: 14.0ms (7.1% of total)

ival-sub: 9.0ms (4.6% of total)

ival-sqrt: 8.0ms (4.1% of total)

const: 2.0ms (1% of total)

series117.0ms (1.2%)

Counts

18 → 216

Calls

Call 1

Inputs
#<alt (/ (/ (+ (* (+ 1/2 (* x 1/8)) (pow x -3/2)) (/ (* -1/2 (- (/ 1 x) x)) (/ (+ 1 x) (sqrt x)))) x) x)>
#<alt (/ (+ (* (+ 1/2 (* x 1/8)) (pow x -3/2)) (/ (* -1/2 (- (/ 1 x) x)) (/ (+ 1 x) (sqrt x)))) x)>
#<alt (+ (* (+ 1/2 (* x 1/8)) (pow x -3/2)) (/ (* -1/2 (- (/ 1 x) x)) (/ (+ 1 x) (sqrt x))))>
#<alt (* (+ 1/2 (* x 1/8)) (pow x -3/2))>
#<alt (pow (/ 1 (* x x)) 1/4)>
#<alt (/ 1 (* x x))>
#<alt (* x x)>
#<alt (- (pow x -1/2) (pow (+ 1 x) -1/2))>
#<alt (pow x -1/2)>
#<alt (pow (+ 1 x) -1/2)>
#<alt (+ 1 x)>
#<alt (/ (/ (+ (* (sqrt x) (+ 1/2 (* x -3/8))) (* (* 1/2 x) (sqrt (* x (* x x))))) (* x x)) (* x x))>
#<alt (/ (+ (* (sqrt x) (+ 1/2 (* x -3/8))) (* (* 1/2 x) (sqrt (* x (* x x))))) (* x x))>
#<alt (+ (* (sqrt x) (+ 1/2 (* x -3/8))) (* (* 1/2 x) (sqrt (* x (* x x)))))>
#<alt (* (sqrt x) (+ 1/2 (* x -3/8)))>
#<alt (/ (+ 1 x) (sqrt x))>
#<alt (/ (* -1/2 (- (/ 1 x) x)) (/ (+ 1 x) (sqrt x)))>
#<alt (sqrt (* x (* x x)))>

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

Calls

54 calls:

Time	Variable		Point	Expression
103.0ms	x	@	0	(pow (/ 1 (* x x)) 1/4)
1.0ms	x	@	-inf	(/ (/ (+ (* (+ 1/2 (* x 1/8)) (pow x -3/2)) (/ (* -1/2 (- (/ 1 x) x)) (/ (+ 1 x) (sqrt x)))) x) x)
1.0ms	x	@	-inf	(/ (/ (+ (* (sqrt x) (+ 1/2 (* x -3/8))) (* (* 1/2 x) (sqrt (* x (* x x))))) (* x x)) (* x x))
1.0ms	x	@	0	(/ (/ (+ (* (+ 1/2 (* x 1/8)) (pow x -3/2)) (/ (* -1/2 (- (/ 1 x) x)) (/ (+ 1 x) (sqrt x)))) x) x)
1.0ms	x	@	inf	(/ (/ (+ (* (+ 1/2 (* x 1/8)) (pow x -3/2)) (/ (* -1/2 (- (/ 1 x) x)) (/ (+ 1 x) (sqrt x)))) x) x)

rewrite348.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

3218×	`-lowering-.f32`
3218×	`-lowering-.f64`
2940×	`/-lowering-/.f32`
2940×	`/-lowering-/.f64`
1542×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	38	200
1	241	179
2	2205	173
0	8266	173

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 687

Calls

Call 1

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

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

simplify281.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

3974×	`-lowering-.f32`
3974×	`-lowering-.f64`
2996×	`+-lowering-+.f64`
2996×	`+-lowering-+.f32`
1510×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	260	2668
1	856	2169
2	3288	2122
0	8625	2122

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

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

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

eval149.0ms (1.5%)

Compiler: Compiled 32765 to 3032 computations (90.7% saved)

prune119.0ms (1.2%)

Pruning

23 alts after pruning (18 fresh and 5 done)

	Pruned	Kept	Total
New	1021	11	1032
Fresh	7	7	14
Picked	2	3	5
Done	0	2	2
Total	1030	23	1053

Accuracy

100.0%

Counts

1053 → 23

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	38.0%	(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
	38.0%	(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
▶	5.4%	(pow.f64 x #s(literal -1/2 binary64))
	40.8%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	98.0%	(/.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 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (sqrt.f64 x))) x) x)
▶	98.8%	(/.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 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (/.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 x))))) x) x)
	46.3%	(/.f64 (/.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))))) (.f64 x (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (+.f64 x #s(literal 1 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (+.f64 x #s(literal 1 binary64)))))) (/.f64 #s(literal 1 binary64) 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 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x #s(literal 1 binary64))) (pow.f64 x #s(literal -1/2 binary64)))))) x)
	98.9%	(/.f64 (/.f64 (.f64 x (-.f64 #s(literal 0 binary64) (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))))) x) x)
	98.1%	(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x) x)
	98.9%	(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 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 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 x))))))
	40.8%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
	19.1%	(/.f64 (+.f64 (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -3/8 binary64)))) (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64)))) (.f64 x (.f64 x (.f64 x x))))
▶	99.0%	(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))) (-.f64 #s(literal 0 binary64) x))
▶	98.2%	(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
	80.4%	(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
	96.7%	(/.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 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 x)))) x)))
	5.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	39.3%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	31.8%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
▶	80.5%	(.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
	63.2%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
✓	5.4%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	37.0%	#s(literal 0 binary64)

Compiler

Compiled 762 to 471 computations (38.2% saved)

simplify176.0ms (1.8%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

2612×	`fma-lowering-fma.f32`
2612×	`fma-lowering-fma.f64`
2070×	`sum3-define`
1804×	`fmsub-define`
1772×	`-lowering-.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	36	240
1	74	235
2	177	235
3	569	232
4	1860	232
5	5729	232
0	8574	232

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (* (- 0 (sqrt (/ 1 x))) (- 1/2 (/ 3/8 x))) (- 0 x))
(* (- 0 (sqrt (/ 1 x))) (- 1/2 (/ 3/8 x)))
(- 0 (sqrt (/ 1 x)))
0
(sqrt (/ 1 x))
(/ 1 x)
1
x
(- 1/2 (/ 3/8 x))
1/2
(/ 3/8 x)
3/8
(- 0 x)
(pow x -1/2)
x
-1/2
(/ (* 1/2 (sqrt (/ 1 x))) x)
(* 1/2 (sqrt (/ 1 x)))
1/2
(sqrt (/ 1 x))
(/ 1 x)
1
x
(* (/ -1/2 (* x x)) (- (sqrt (/ 1 x)) (sqrt x)))
(/ -1/2 (* x x))
-1/2
(* x x)
x
(- (sqrt (/ 1 x)) (sqrt x))
(sqrt (/ 1 x))
(/ 1 x)
1
(sqrt x)
(/ (/ (+ (* (+ 1/2 (* x 1/8)) (pow x -3/2)) (* (- (/ 1 x) x) (/ -1/2 (/ (+ x 1) (sqrt x))))) x) x)
(/ (+ (* (+ 1/2 (* x 1/8)) (pow x -3/2)) (* (- (/ 1 x) x) (/ -1/2 (/ (+ x 1) (sqrt x))))) x)
(+ (* (+ 1/2 (* x 1/8)) (pow x -3/2)) (* (- (/ 1 x) x) (/ -1/2 (/ (+ x 1) (sqrt x)))))
(* (+ 1/2 (* x 1/8)) (pow x -3/2))
(+ 1/2 (* x 1/8))
1/2
(* x 1/8)
x
1/8
(pow x -3/2)
-3/2
(* (- (/ 1 x) x) (/ -1/2 (/ (+ x 1) (sqrt x))))
(- (/ 1 x) x)
(/ 1 x)
1
(/ -1/2 (/ (+ x 1) (sqrt x)))
-1/2
(/ (+ x 1) (sqrt x))
(+ x 1)
(sqrt x)

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

localize189.0ms (1.9%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(*.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (/.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 x))))
✓	accuracy	99.6%	(/.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 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (/.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 x))))) x)
✓	accuracy	99.3%	(/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 x))
✓	accuracy	68.8%	(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal -3/2 binary64)))
✓	accuracy	100.0%	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
✓	accuracy	99.9%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	98.8%	(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
✓	accuracy	83.3%	(.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	accuracy	99.9%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.8%	(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
✓	accuracy	100.0%	(pow.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))
✓	accuracy	100.0%	(*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)))
✓	accuracy	99.9%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.7%	(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))) (-.f64 #s(literal 0 binary64) x))

Results

132.0ms

256×

valid

Compiler

Compiled 273 to 37 computations (86.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 57.0ms

ival-div: 16.0ms (28% of total)

ival-pow: 13.0ms (22.8% of total)

ival-mult: 12.0ms (21% of total)

ival-sub: 6.0ms (10.5% of total)

ival-add: 4.0ms (7% of total)

ival-sqrt: 4.0ms (7% of total)

const: 1.0ms (1.8% of total)

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

series9.0ms (0.1%)

Counts

19 → 228

Calls

Call 1

Inputs
#<alt (/ (* (- 0 (sqrt (/ 1 x))) (- 1/2 (/ 3/8 x))) (- 0 x))>
#<alt (* (- 0 (sqrt (/ 1 x))) (- 1/2 (/ 3/8 x)))>
#<alt (- 0 (sqrt (/ 1 x)))>
#<alt (sqrt (/ 1 x))>
#<alt (pow x -1/2)>
#<alt (/ (* 1/2 (sqrt (/ 1 x))) x)>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ 1 x)>
#<alt (* (/ -1/2 (* x x)) (- (sqrt (/ 1 x)) (sqrt x)))>
#<alt (/ -1/2 (* x x))>
#<alt (* x x)>
#<alt (- (sqrt (/ 1 x)) (sqrt x))>
#<alt (/ (/ (+ (* (+ 1/2 (* x 1/8)) (pow x -3/2)) (* (- (/ 1 x) x) (/ -1/2 (/ (+ x 1) (sqrt x))))) x) x)>
#<alt (/ (+ (* (+ 1/2 (* x 1/8)) (pow x -3/2)) (* (- (/ 1 x) x) (/ -1/2 (/ (+ x 1) (sqrt x))))) x)>
#<alt (+ (* (+ 1/2 (* x 1/8)) (pow x -3/2)) (* (- (/ 1 x) x) (/ -1/2 (/ (+ x 1) (sqrt x)))))>
#<alt (* (+ 1/2 (* x 1/8)) (pow x -3/2))>
#<alt (- 1/2 (/ 3/8 x))>
#<alt (/ (+ x 1) (sqrt x))>
#<alt (* (- (/ 1 x) x) (/ -1/2 (/ (+ x 1) (sqrt x))))>

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

Calls

57 calls:

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

rewrite414.0ms (4.2%)

Algorithm

1×	batch-egg-rewrite

Rules

4800×	`-lowering-.f32`
4800×	`-lowering-.f64`
3070×	`/-lowering-/.f32`
3070×	`/-lowering-/.f64`
2632×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	174
1	236	159
2	2223	157
0	9612	157

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 755

Calls

Call 1

Inputs
(/ (* (- 0 (sqrt (/ 1 x))) (- 1/2 (/ 3/8 x))) (- 0 x))
(* (- 0 (sqrt (/ 1 x))) (- 1/2 (/ 3/8 x)))
(- 0 (sqrt (/ 1 x)))
(sqrt (/ 1 x))
(pow x -1/2)
(/ (* 1/2 (sqrt (/ 1 x))) x)
(* 1/2 (sqrt (/ 1 x)))
(/ 1 x)
(* (/ -1/2 (* x x)) (- (sqrt (/ 1 x)) (sqrt x)))
(/ -1/2 (* x x))
(* x x)
(- (sqrt (/ 1 x)) (sqrt x))
(/ (/ (+ (* (+ 1/2 (* x 1/8)) (pow x -3/2)) (* (- (/ 1 x) x) (/ -1/2 (/ (+ x 1) (sqrt x))))) x) x)
(/ (+ (* (+ 1/2 (* x 1/8)) (pow x -3/2)) (* (- (/ 1 x) x) (/ -1/2 (/ (+ x 1) (sqrt x))))) x)
(+ (* (+ 1/2 (* x 1/8)) (pow x -3/2)) (* (- (/ 1 x) x) (/ -1/2 (/ (+ x 1) (sqrt x)))))
(* (+ 1/2 (* x 1/8)) (pow x -3/2))
(- 1/2 (/ 3/8 x))
(/ (+ x 1) (sqrt x))
(* (- (/ 1 x) x) (/ -1/2 (/ (+ x 1) (sqrt x))))

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

simplify254.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

3492×	`-lowering-.f32`
3492×	`-lowering-.f64`
1930×	`fma-lowering-fma.f32`
1930×	`fma-lowering-fma.f64`
1480×	`fma-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	160	2420
1	446	1916
2	1526	1812
3	4044	1804
0	8238	1804

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

Calls

Call 1

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

Outputs
(* -3/8 (sqrt (/ 1 (pow x 5))))
(*.f64 #s(literal -3/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))
(/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
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eval164.0ms (1.7%)

Compiler: Compiled 37474 to 3780 computations (89.9% saved)

prune179.0ms (1.8%)

Pruning

19 alts after pruning (14 fresh and 5 done)

	Pruned	Kept	Total
New	1264	10	1274
Fresh	9	4	13
Picked	4	1	5
Done	1	4	5
Total	1278	19	1297

Accuracy

100.0%

Counts

1297 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	5.4%	(pow.f64 x #s(literal -1/2 binary64))
	40.8%	(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
	98.9%	(/.f64 (/.f64 (.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x)))) x) x)
	98.2%	(/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x)
	40.8%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
	99.0%	(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))) (-.f64 #s(literal 0 binary64) x))
	72.5%	(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -3/2 binary64))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x)) (-.f64 #s(literal 0 binary64) x))) (/.f64 #s(literal 1 binary64) x))
	99.0%	(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 9/64 binary64) (.f64 x x)))))) (-.f64 #s(literal 0 binary64) x))
	99.0%	(/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x))) x)
	80.4%	(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
	5.4%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	39.3%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	31.8%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
	98.1%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/2 binary64) x))
	98.4%	(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
	98.9%	(.f64 (/.f64 #s(literal -1 binary64) x) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x))))
	99.2%	(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x)) (pow.f64 x #s(literal -3/2 binary64)))
✓	5.4%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	37.0%	#s(literal 0 binary64)

Compiler

Compiled 1126 to 360 computations (68% saved)

regimes27.0ms (0.3%)

Counts

48 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(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 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x)
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/2 binary64) x))
(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) x)
(/.f64 (/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x) x)
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x)) (pow.f64 x #s(literal -3/2 binary64)))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)))
(/.f64 (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x))) x)
(/.f64 (*.f64 (/.f64 #s(literal -1 binary64) (sqrt.f64 x)) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))) (-.f64 #s(literal 0 binary64) x))
(.f64 (/.f64 #s(literal -1 binary64) x) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -1/2 binary64))) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x))))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -5/8 binary64) x))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (/.f64 (.f64 x (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x)))) x) x)
(/.f64 (*.f64 (-.f64 #s(literal 0 binary64) (pow.f64 x #s(literal -3/2 binary64))) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x)) (-.f64 #s(literal 0 binary64) x))) (/.f64 #s(literal 1 binary64) x))
(/.f64 (/.f64 (.f64 x (-.f64 #s(literal 0 binary64) (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))))) x) x)
(/.f64 (.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 9/64 binary64) (.f64 x x)))))) (-.f64 #s(literal 0 binary64) x))
(-.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 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
(/.f64 (+.f64 (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -3/8 binary64)))) (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 5/2 binary64)))) (.f64 x (.f64 x (.f64 x 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 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (sqrt.f64 x))) x) x)
(/.f64 (/.f64 (+.f64 (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -3/8 binary64)))) (.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (.f64 x (.f64 x x))))) (.f64 x x)) (.f64 x 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 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (/.f64 #s(literal -1/2 binary64) (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 x))))) x) 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 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))) x) 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 (.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))) x) (/.f64 #s(literal 1 binary64) x))
(/.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 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))) x)))
(/.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 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 x)))) x)))
(/.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 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 (*.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 (+.f64 x #s(literal 1 binary64)) (sqrt.f64 x))))))
(/.f64 (/.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))))) (.f64 x (.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (+.f64 x #s(literal 1 binary64))) (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (+.f64 x #s(literal 1 binary64)))))) (/.f64 #s(literal 1 binary64) 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 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (+.f64 x #s(literal 1 binary64))) (pow.f64 x #s(literal -1/2 binary64)))))) x)
(/.f64 (/.f64 (+.f64 (.f64 (.f64 (.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))) #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) x) (/.f64 #s(literal 1 binary64) x)) (.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -3/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/64 binary64)))))) (.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) x)) (+.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 x x))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)) (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (.f64 x x))
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal -3/2 binary64))) (.f64 #s(literal 1/2 binary64) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 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))))) (pow.f64 (/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x))) #s(literal 2 binary64))))) (*.f64 x x))

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

Calls

2 calls:

13.0ms	x
12.0ms	(-.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
99.2%	1	`x`
99.2%	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)

regimes5.0ms (0%)

Counts

12 → 1

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
98.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Accuracy

Total -20.9b remaining (-51.9%)

Threshold costs -20.9b (-51.9%)

Counts

4 → 1

Calls

Call 1

Inputs
#s(literal 0 binary64)
(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
#s(literal 0 binary64)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
37.0%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
2×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	15
1	13	15

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

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

#s(literal 0 binary64)

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

soundness1.6s (16.1%)

Rules

4800×	`-lowering-.f32`
4800×	`-lowering-.f64`
4200×	`-lowering-.f32`
4200×	`-lowering-.f64`
3974×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	114	458
1	338	394
2	1145	371
3	4913	370
0	8260	370
0	36	174
1	236	159
2	2223	157
0	9612	157
0	29	118
1	211	94
2	1961	86
0	9549	86
0	260	2668
1	856	2169
2	3288	2122
0	8625	2122

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

Compiler

Compiled 54 to 40 computations (25.9% saved)

preprocess38.0ms (0.4%)

Compiler: Compiled 88 to 54 computations (38.6% saved)

Iter	Nodes	Cost
0	8	24
1	23	24
2	31	24
3	43	24
4	57	24
5	94	24
6	165	24
7	261	24
8	360	24
9	492	24
10	604	24
11	640	24
12	648	24
0	648	24

Iter	Nodes	Cost
0	8	24
1	23	24
2	31	24
3	43	24
4	57	24
5	94	24
6	165	24
7	261	24
8	360	24
9	492	24
10	604	24
11	640	24
12	648	24
0	648	24

analyze5.0ms (0%)

sample2.5s (25.1%)

preprocess60.0ms (0.6%)

explain213.0ms (2.2%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify25.0ms (0.2%)

localize86.0ms (0.9%)

series5.0ms (0.1%)

rewrite319.0ms (3.2%)

simplify244.0ms (2.5%)

eval34.0ms (0.3%)

prune38.0ms (0.4%)

simplify183.0ms (1.8%)

localize556.0ms (5.6%)

series14.0ms (0.1%)

rewrite406.0ms (4.1%)

simplify270.0ms (2.7%)

eval146.0ms (1.5%)

prune119.0ms (1.2%)

simplify182.0ms (1.8%)

localize423.0ms (4.3%)

series117.0ms (1.2%)

rewrite348.0ms (3.5%)

simplify281.0ms (2.8%)

eval149.0ms (1.5%)

prune119.0ms (1.2%)

simplify176.0ms (1.8%)

localize189.0ms (1.9%)

series9.0ms (0.1%)

rewrite414.0ms (4.2%)

simplify254.0ms (2.6%)

eval164.0ms (1.7%)

prune179.0ms (1.8%)

regimes27.0ms (0.3%)

regimes5.0ms (0%)

regimes2.0ms (0%)

simplify7.0ms (0.1%)

soundness1.6s (16.1%)

preprocess38.0ms (0.4%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	8	24
1	23	24
2	31	24
3	43	24
4	57	24
5	94	24
6	165	24
7	261	24
8	360	24
9	492	24
10	604	24
11	640	24
12	648	24
0	648	24