Metrics for 2isqrt (example 3.6)

analyze3.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 19 to 12 computations (36.8% saved)

Precisions

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

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

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

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

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

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

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

const: 0.0ms (0% of total)

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

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

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

sample2.1s (25%)

Results

1.3s	6407×	1	valid
455.0ms	1664×	2	valid
16.0ms	185×	0	valid

Precisions

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

ival-sqrt: 331.0ms (24.6% of total)

ival-div: 312.0ms (23.2% of total)

...c/correct-round.rkt:119:19: 148.0ms (11% of total)

backward-pass: 131.0ms (9.8% of total)

ival-sub: 125.0ms (9.3% of total)

ival->: 118.0ms (8.8% of total)

ival-add: 105.0ms (7.8% of total)

ival-<: 34.0ms (2.5% of total)

ival-and: 25.0ms (1.9% of total)

const: 14.0ms (1% of total)

Bogosity

preprocess66.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

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

explain182.0ms (2.1%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
171	2	(3.034311695357153e+215)	-	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`
0	0	-	-	`x`
0	0	-	-	`(sqrt.f64 (+.f64 x #s(literal 1 binary64)))`
0	0	-	-	`#s(literal 1 binary64)`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 x))`
0	0	-	-	`(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))`
0	0	-	-	`(sqrt.f64 x)`
0	0	-	-	`(+.f64 x #s(literal 1 binary64))`

Results

83.0ms	404×	1	valid
59.0ms	98×	2	valid
1.0ms	10×	0	valid

Compiler

Compiled 80 to 26 computations (67.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 67.0ms

ival-sqrt: 24.0ms (36% of total)

ival-div: 16.0ms (24% of total)

backward-pass: 15.0ms (22.5% of total)

ival-add: 6.0ms (9% of total)

ival-sub: 5.0ms (7.5% of total)

const: 1.0ms (1.5% of total)

eval0.0ms (0%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	41.5%	(-.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)

simplify22.0ms (0.3%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize93.0ms (1.1%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	accuracy	41.5%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

35.0ms	202×	1	valid
35.0ms	49×	2	valid
9.0ms	5×	0	valid

Compiler

Compiled 34 to 9 computations (73.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 59.0ms

ival-sqrt: 31.0ms (52.3% of total)

ival-add: 12.0ms (20.2% of total)

ival-div: 9.0ms (15.2% of total)

backward-pass: 5.0ms (8.4% of total)

ival-sub: 3.0ms (5.1% of total)

const: 1.0ms (1.7% 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))

rewrite230.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 220

Calls

Call 1

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

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

simplify224.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval30.0ms (0.4%)

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

prune51.0ms (0.6%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	257	11	268
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	258	11	269

Accuracy

85.3%

Counts

269 → 11

Alt Table

Click to see full alt table

Status	Accuracy	Program
	43.2%	(/.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
	43.3%	(/.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)))
▶	84.5%	(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (*.f64 x x))
▶	41.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
	41.6%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
▶	32.9%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
▶	28.8%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
	43.2%	(.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)))
	83.7%	(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
	68.6%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
▶	5.5%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 348 to 212 computations (39.1% saved)

simplify176.0ms (2.1%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

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

Rules

1912×	`-lowering-.f32`
1912×	`-lowering-.f64`
1736×	`sum5-define`
1624×	`sum3-define`
1512×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	206
1	74	197
2	151	193
3	347	193
4	637	193
5	1163	193
6	2307	193
7	4719	193
0	8123	193

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize435.0ms (5.1%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))
✓	accuracy	99.8%	(/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
✓	accuracy	98.0%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
✓	accuracy	41.5%	(-.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 #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	accuracy	41.5%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 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	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.2%	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
✓	accuracy	85.1%	(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (*.f64 x x))
✓	accuracy	71.1%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
✓	accuracy	66.3%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64)))))

Results

358.0ms

256×

valid

Compiler

Compiled 251 to 33 computations (86.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 252.0ms

ival-pow: 82.0ms (32.5% of total)

backward-pass: 36.0ms (14.3% of total)

ival-div: 35.0ms (13.9% of total)

ival-sqrt: 33.0ms (13.1% of total)

ival-mult: 28.0ms (11.1% of total)

ival-sub: 19.0ms (7.5% of total)

ival-add: 19.0ms (7.5% of total)

const: 2.0ms (0.8% of total)

series16.0ms (0.2%)

Counts

20 → 240

Calls

Call 1

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

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

60 calls:

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

rewrite318.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

3786×	`-lowering-.f32`
3786×	`-lowering-.f64`
2530×	`+-lowering-+.f64`
2530×	`+-lowering-+.f32`
2144×	`/-lowering-/.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	137
1	223	111
2	1969	107
0	9398	107

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 881

Calls

Call 1

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

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

simplify267.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

3572×	`-lowering-.f32`
3572×	`-lowering-.f64`
2236×	`+-lowering-+.f64`
2236×	`+-lowering-+.f32`
1408×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	318	2772
1	1089	2278
2	4421	2240
0	8757	2240

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

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

eval215.0ms (2.5%)

Compiler: Compiled 32737 to 3254 computations (90.1% saved)

prune212.0ms (2.5%)

Pruning

22 alts after pruning (19 fresh and 3 done)

	Pruned	Kept	Total
New	1402	13	1415
Fresh	0	6	6
Picked	2	3	5
Done	0	0	0
Total	1404	22	1426

Accuracy

100.0%

Counts

1426 → 22

Alt Table

Click to see full alt table

Status	Accuracy	Program
	40.6%	(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
	5.5%	(pow.f64 x #s(literal -1/2 binary64))
	43.2%	(/.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
	43.3%	(/.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)))
▶	99.1%	(/.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)
	84.3%	(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal -2 binary64))))) (*.f64 x x))
	98.2%	(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 5/8 binary64)) x)) x)
	83.5%	(/.f64 (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (/.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 5/8 binary64)) x))) (.f64 x x))
▶	83.7%	(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
	97.2%	(/.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)))
✓	41.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
▶	83.7%	(/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
	68.6%	(/.f64 #s(literal 1 binary64) (.f64 (sqrt.f64 (.f64 x (*.f64 x x))) #s(literal 2 binary64)))
	5.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
	41.6%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	32.9%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	43.2%	(.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)))
	99.0%	(.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)) (/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x)))) x) (/.f64 #s(literal 1 binary64) x))
▶	83.7%	(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
	68.6%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
✓	5.5%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
▶	39.4%	#s(literal 0 binary64)

Compiler

Compiled 688 to 437 computations (36.5% saved)

simplify150.0ms (1.8%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

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

Rules

2318×	`sum4-define`
1822×	`fma-define`
1572×	`-lowering-.f32`
1572×	`-lowering-.f64`
1556×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	261
1	86	252
2	205	252
3	470	252
4	856	252
5	1898	252
6	5938	252
0	8015	252

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

localize185.0ms (2.2%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.2%	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
✓	accuracy	98.1%	(/.f64 #s(literal 1 binary64) (.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
✓	accuracy	86.9%	(.f64 (.f64 (.f64 x x) #s(literal 2 binary64)) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
✓	accuracy	71.1%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
✓	accuracy	100.0%	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.2%	(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
✓	accuracy	86.1%	(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	85.1%	(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x 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 #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	99.2%	(/.f64 (+.f64 #s(literal 1 binary64) x) (sqrt.f64 x))
✓	accuracy	63.5%	(/.f64 (+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64)))

Results

99.0ms

256×

valid

Compiler

Compiled 297 to 37 computations (87.5% saved)

Precisions

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

ival-div: 22.0ms (36.6% of total)

ival-mult: 14.0ms (23.3% of total)

ival-pow: 8.0ms (13.3% of total)

ival-add: 7.0ms (11.7% of total)

ival-sqrt: 5.0ms (8.3% of total)

ival-sub: 2.0ms (3.3% of total)

const: 1.0ms (1.7% of total)

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

series19.0ms (0.2%)

Counts

20 → 240

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

Calls

60 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(/ (+ 1/2 (* x 1/8)) (pow x 3/2))
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	@	0	(/ (/ (+ (/ (+ 1/2 (* x 1/8)) (pow x 3/2)) (/ (* -1/2 (- (/ 1 x) x)) (/ (+ 1 x) (sqrt x)))) x) x)
0.0ms	x	@	-inf	(/ (+ (/ (+ 1/2 (* x 1/8)) (pow x 3/2)) (/ (* -1/2 (- (/ 1 x) x)) (/ (+ 1 x) (sqrt x)))) x)
0.0ms	x	@	inf	(/ (/ (+ (/ (+ 1/2 (* x 1/8)) (pow x 3/2)) (/ (* -1/2 (- (/ 1 x) x)) (/ (+ 1 x) (sqrt x)))) x) x)

rewrite355.0ms (4.2%)

Algorithm

1×	batch-egg-rewrite

Rules

3260×	`/-lowering-/.f32`
3260×	`/-lowering-/.f64`
2440×	`-lowering-.f32`
2440×	`-lowering-.f64`
1942×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	35	193
1	233	170
2	2286	164
0	8728	164

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 793

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

simplify238.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

4114×	`-lowering-.f32`
4114×	`-lowering-.f64`
1906×	`fma-define`
1772×	`fma-lowering-fma.f32`
1772×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	181	2299
1	526	2025
2	1810	1919
3	5428	1914
0	8193	1914

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

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

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

eval158.0ms (1.9%)

Compiler: Compiled 34033 to 3870 computations (88.6% saved)

prune164.0ms (1.9%)

Pruning

18 alts after pruning (14 fresh and 4 done)

	Pruned	Kept	Total
New	1333	8	1341
Fresh	8	6	14
Picked	4	1	5
Done	0	3	3
Total	1345	18	1363

Accuracy

100.0%

Counts

1363 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	5.5%	(pow.f64 x #s(literal -1/2 binary64))
	43.2%	(/.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
	43.3%	(/.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)))
▶	98.1%	(/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) x)
	83.6%	(/.f64 (.f64 #s(literal 1/2 binary64) (/.f64 x (sqrt.f64 x))) (.f64 x x))
✓	41.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
	83.7%	(/.f64 #s(literal 1 binary64) (.f64 (.f64 (*.f64 x x) #s(literal 2 binary64)) (+.f64 (pow.f64 x #s(literal -3/2 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
	5.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
	41.6%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	32.9%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	98.2%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/2 binary64) x))
▶	98.5%	(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
	43.2%	(.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)))
	83.7%	(.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))
▶	98.3%	(*.f64 (-.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal -1/2 binary64) x))
▶	46.5%	(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (pow.f64 x #s(literal -3/2 binary64)) (.f64 x x))) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
✓	5.5%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	39.4%	#s(literal 0 binary64)

Compiler

Compiled 396 to 245 computations (38.1% saved)

simplify104.0ms (1.2%)

Algorithm

1×	egg-herbie

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	320	(.f64 (pow.f64 x #s(literal -3/2 binary64)) (.f64 x x))
✓	cost-diff	320	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (pow.f64 x #s(literal -3/2 binary64)) (.f64 x x)))
✓	cost-diff	320	(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (pow.f64 x #s(literal -3/2 binary64)) (.f64 x x))) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
✓	cost-diff	0	(pow.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(pow.f64 x #s(literal -3/2 binary64))
✓	cost-diff	6336	(-.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
✓	cost-diff	6464	(*.f64 (-.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal -1/2 binary64) x))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	64	(*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
✓	cost-diff	192	(/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) x)
✓	cost-diff	0	(pow.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(pow.f64 x #s(literal -3/2 binary64))
✓	cost-diff	0	(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))

Rules

2416×	`sum3-define`
1900×	`fnmadd-define`
1466×	`fma-lowering-fma.f32`
1466×	`fma-lowering-fma.f64`
1340×	`sum4-define`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	22	114
1	48	110
2	107	106
3	262	104
4	727	103
5	2065	101
6	6020	101
0	8101	101

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize115.0ms (1.3%)

Localize:

Found 15 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.2%	(/.f64 #s(literal -1/2 binary64) (*.f64 x x))
✓	accuracy	86.1%	(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (pow.f64 x #s(literal -3/2 binary64)) (.f64 x x))) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
✓	accuracy	50.0%	(.f64 (pow.f64 x #s(literal -3/2 binary64)) (.f64 x x))
✓	accuracy	100.0%	(pow.f64 x #s(literal -3/2 binary64))
✓	accuracy	100.0%	(/.f64 #s(literal -1/2 binary64) x)
✓	accuracy	100.0%	(-.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
✓	accuracy	99.6%	(*.f64 (-.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal -1/2 binary64) x))
✓	accuracy	100.0%	(/.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.7%	(/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) x)
✓	accuracy	99.4%	(*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
✓	accuracy	100.0%	(pow.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(pow.f64 x #s(literal -3/2 binary64))
✓	accuracy	100.0%	(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))

Results

79.0ms

256×

valid

Compiler

Compiled 128 to 23 computations (82% saved)

Precisions

Click to see histograms. Total time spent on operations: 44.0ms

ival-pow: 16.0ms (36.3% of total)

ival-div: 11.0ms (24.9% of total)

ival-mult: 10.0ms (22.7% of total)

ival-sqrt: 4.0ms (9.1% of total)

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

const: 1.0ms (2.3% of total)

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

series7.0ms (0.1%)

Counts

15 → 180

Calls

Call 1

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

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

Calls

45 calls:

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

rewrite304.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

5150×	`-lowering-.f32`
5150×	`-lowering-.f64`
2188×	`/-lowering-/.f32`
2188×	`/-lowering-/.f64`
1404×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	80
1	121	69
2	983	67
0	9033	67

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 1391

Calls

Call 1

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

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

simplify245.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

2274×	`-lowering-.f32`
2274×	`-lowering-.f64`
1842×	`fnmadd-define`
1486×	`fma-lowering-fma.f32`
1486×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	61	1219
1	135	1064
2	400	1034
3	979	1034
4	2961	1028
5	7452	1028
0	8134	1028

Stop Event

1×	iter limit
1×	node limit

Counts

180 → 180

Calls

Call 1

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

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

eval201.0ms (2.4%)

Compiler: Compiled 32895 to 2973 computations (91% saved)

prune196.0ms (2.3%)

Pruning

30 alts after pruning (23 fresh and 7 done)

	Pruned	Kept	Total
New	1802	18	1820
Fresh	4	5	9
Picked	2	3	5
Done	0	4	4
Total	1808	30	1838

Accuracy

100.0%

Counts

1838 → 30

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	5.5%	(pow.f64 x #s(literal -1/2 binary64))
	43.2%	(/.f64 (/.f64 (/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
	43.3%	(/.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)))
	98.2%	(/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x)
	98.2%	(/.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
	83.6%	(/.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (.f64 (pow.f64 x #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) x))))
	66.1%	(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal -1 binary64) x)) (/.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal -3/2 binary64))) (/.f64 #s(literal -1/2 binary64) x)))
✓	98.1%	(/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) x)
	96.5%	(/.f64 (.f64 (/.f64 #s(literal -1/2 binary64) x) (-.f64 (/.f64 #s(literal 1 binary64) x) x)) (.f64 x (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal 1 binary64)))))
	32.5%	(/.f64 (.f64 (+.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))) (.f64 (pow.f64 x #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) x))) (.f64 (.f64 x x) (*.f64 #s(literal -2 binary64) (+.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))))))
	83.6%	(/.f64 (sqrt.f64 x) (/.f64 x (/.f64 #s(literal 1/2 binary64) x)))
	5.5%	(/.f64 (sqrt.f64 x) x)
	96.6%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x #s(literal -1/2 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (-.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1 binary64)))))
	32.5%	(/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))) (.f64 x x)) (.f64 (.f64 (+.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) x))) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) x))) #s(literal -1/2 binary64))))
✓	41.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
	5.5%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
	96.6%	(/.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal 3/2 binary64)))
	41.6%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	32.9%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	83.7%	(.f64 (pow.f64 (.f64 x x) #s(literal -3/4 binary64)) #s(literal 1/2 binary64))
✓	98.5%	(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
	43.2%	(.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)))
	52.2%	(.f64 (/.f64 (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal -1 binary64) x)) (/.f64 x #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (.f64 (+.f64 x #s(literal 1 binary64)) (pow.f64 x #s(literal -3/2 binary64)))))
	98.2%	(.f64 (/.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) x)) x) (/.f64 #s(literal -1/2 binary64) x))
	98.1%	(.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (.f64 (pow.f64 x #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) x)))) (/.f64 #s(literal -1/2 binary64) x))
	83.7%	(.f64 (/.f64 #s(literal -1/2 binary64) (.f64 x x)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (-.f64 #s(literal 1 binary64) x)))
	46.5%	(.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 (pow.f64 x #s(literal -3/2 binary64)) (.f64 x x))) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
	75.6%	(.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) x) (/.f64 #s(literal 1 binary64) (.f64 (/.f64 x (/.f64 #s(literal -1/2 binary64) x)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 x #s(literal 1 binary64))))))
✓	5.5%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	39.4%	#s(literal 0 binary64)

Compiler

Compiled 1171 to 424 computations (63.8% saved)

regimes35.0ms (0.4%)

Counts

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

Outputs

(/.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)

Calls

2 calls:

19.0ms	x
11.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
99.1%	1	`x`
99.1%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes25.0ms (0.3%)

Counts

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

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

Calls

2 calls:

13.0ms	x
10.0ms	(-.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
98.5%	1	`x`
98.5%	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)

regimes3.0ms (0%)

Accuracy

Total -22.5b remaining (-58%)

Threshold costs -22.5b (-58%)

Counts

5 → 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 (sqrt.f64 x) x)

Outputs
#s(literal 0 binary64)

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
39.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
8×	`*-commutative_binary64`
4×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	34
1	34	34
2	38	34
3	40	34
4	41	34

Stop Event

1×

saturated

Calls

Call 1

Inputs

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

#s(literal 0 binary64)

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

soundness1.3s (15.2%)

Rules

3786×	`-lowering-.f32`
3786×	`-lowering-.f64`
3572×	`-lowering-.f32`
3572×	`-lowering-.f64`
3318×	`-lowering-.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	114	458
1	334	397
2	1139	374
3	4889	373
0	8236	373
0	318	2772
1	1089	2278
2	4421	2240
0	8757	2240
0	35	193
1	233	170
2	2286	164
0	8728	164
0	32	137
1	223	111
2	1969	107
0	9398	107

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 62 to 44 computations (29% saved)

preprocess52.0ms (0.6%)

Compiler: Compiled 126 to 82 computations (34.9% saved)

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

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

analyze3.0ms (0%)

sample2.1s (25%)

preprocess66.0ms (0.8%)

explain182.0ms (2.1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify22.0ms (0.3%)

localize93.0ms (1.1%)

series5.0ms (0.1%)

rewrite230.0ms (2.7%)

simplify224.0ms (2.6%)

eval30.0ms (0.4%)

prune51.0ms (0.6%)

simplify176.0ms (2.1%)

localize435.0ms (5.1%)

series16.0ms (0.2%)

rewrite318.0ms (3.7%)

simplify267.0ms (3.1%)

eval215.0ms (2.5%)

prune212.0ms (2.5%)

simplify150.0ms (1.8%)

localize185.0ms (2.2%)

series19.0ms (0.2%)

rewrite355.0ms (4.2%)

simplify238.0ms (2.8%)

eval158.0ms (1.9%)

prune164.0ms (1.9%)

simplify104.0ms (1.2%)

localize115.0ms (1.3%)

series7.0ms (0.1%)

rewrite304.0ms (3.6%)

simplify245.0ms (2.9%)

eval201.0ms (2.4%)

prune196.0ms (2.3%)

regimes35.0ms (0.4%)

regimes25.0ms (0.3%)

regimes3.0ms (0%)

simplify8.0ms (0.1%)

soundness1.3s (15.2%)

preprocess52.0ms (0.6%)

end0.0ms (0%)

Profiling

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