Metrics for 2isqrt (example 3.6)

analyze4.0ms (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: 3.0ms

ival->: 2.0ms (67.7% of total)

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)

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

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

sample2.1s (19.4%)

Results

1.2s	6437×	1	valid
504.0ms	1660×	2	valid
14.0ms	159×	0	valid

Precisions

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

ival-sqrt: 367.0ms (27.5% of total)

ival-div: 275.0ms (20.6% of total)

...c/correct-round.rkt:119:19: 147.0ms (11% of total)

backward-pass: 128.0ms (9.6% of total)

ival-sub: 119.0ms (8.9% of total)

ival->: 115.0ms (8.6% of total)

ival-add: 100.0ms (7.5% of total)

ival-<: 48.0ms (3.6% of total)

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

const: 14.0ms (1% of total)

Bogosity

preprocess55.0ms (0.5%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

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

explain145.0ms (1.3%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
184	2	(2.511014590447071e+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

66.0ms	390×	1	valid
39.0ms	110×	2	valid
1.0ms	12×	0	valid

Compiler

Compiled 80 to 26 computations (67.5% saved)

Precisions

Click to see histograms. Total time spent on operations: 64.0ms

ival-div: 21.0ms (33% of total)

ival-sqrt: 18.0ms (28.3% of total)

backward-pass: 11.0ms (17.3% of total)

ival-add: 7.0ms (11% of total)

ival-sub: 6.0ms (9.4% of total)

const: 1.0ms (1.6% of total)

eval0.0ms (0%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	35.6%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Compiler

Compiled 12 to 8 computations (33.3% saved)

simplify25.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	24
1	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)

localize69.0ms (0.6%)

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	35.6%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

38.0ms	195×	1	valid
14.0ms	55×	2	valid
0.0ms	6×	0	valid

Compiler

Compiled 34 to 9 computations (73.5% saved)

Precisions

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

ival-div: 9.0ms (27.2% of total)

ival-sqrt: 9.0ms (27.2% of total)

ival-sub: 6.0ms (18.2% of total)

backward-pass: 5.0ms (15.1% of total)

ival-add: 3.0ms (9.1% of total)

const: 1.0ms (3% of total)

series5.0ms (0%)

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))

rewrite217.0ms (2%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	15
1	64	15
2	601	15
3	7279	15
0	8160	15

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 220

Calls

Call 1

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

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

simplify190.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	114	458
1	334	394
2	1141	371
3	4906	370
0	8253	370

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval30.0ms (0.3%)

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

prune40.0ms (0.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

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

Accuracy

80.6%

Counts

269 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	38.1%	(/.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)))
▶	35.7%	(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x))) (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
▶	79.8%	(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (*.f64 x x))
▶	38.1%	(/.f64 (.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))
	38.1%	(/.f64 (.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 x #s(literal -1/2 binary64))) (.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
	35.6%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
▶	27.7%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	26.7%	(-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	38.1%	(.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) (*.f64 x x)) #s(literal 1/2 binary64))) (sqrt.f64 (+.f64 x #s(literal -1 binary64))))
	38.1%	(.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)))
	78.9%	(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
	63.4%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
▶	5.6%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 464 to 284 computations (38.8% saved)

simplify166.0ms (1.5%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) x)
✓	cost-diff	256	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
✓	cost-diff	384	(.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)))
✓	cost-diff	384	(/.f64 (.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))
✓	cost-diff	0	(/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x))) (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
✓	cost-diff	-64	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	cost-diff	-64	(-.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	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	0	(pow.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	128	(.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64))))
✓	cost-diff	128	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64)))))
✓	cost-diff	128	(+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
✓	cost-diff	128	(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/4 binary64))))) (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) (*.f64 x x))

Rules

2814×	`-lowering-.f32`
2814×	`-lowering-.f64`
1778×	`--lowering--.f32`
1778×	`--lowering--.f64`
1666×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	275
1	90	250
2	187	240
3	449	240
4	912	240
5	2832	240
6	6218	240
0	8224	240

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize403.0ms (3.6%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))
✓	accuracy	99.6%	(/.f64 (.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))
✓	accuracy	53.0%	(pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
✓	accuracy	8.0%	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
✓	accuracy	100.0%	(pow.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	accuracy	81.7%	(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x))) (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
✓	accuracy	54.7%	(+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x)))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	100.0%	(pow.f64 x #s(literal -1/2 binary64))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64))))
✓	accuracy	35.6%	(-.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 #s(literal 1 binary64) x)
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.4%	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
✓	accuracy	80.4%	(/.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	72.2%	(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (.f64 #s(literal 1/2 binary64) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/4 binary64)))))
✓	accuracy	65.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))

Results

225.0ms	197×	1	valid
90.0ms	53×	2	valid
5.0ms	6×	0	valid

Compiler

Compiled 314 to 40 computations (87.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 226.0ms

ival-pow: 73.0ms (32.3% of total)

ival-mult: 37.0ms (16.4% of total)

backward-pass: 35.0ms (15.5% of total)

ival-div: 33.0ms (14.6% of total)

ival-add: 24.0ms (10.6% of total)

ival-sqrt: 16.0ms (7.1% of total)

ival-sub: 8.0ms (3.5% of total)

const: 2.0ms (0.9% of total)

series24.0ms (0.2%)

Counts

23 → 276

Calls

Call 1

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

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

Calls

69 calls:

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

rewrite621.0ms (5.6%)

Algorithm

1×	batch-egg-rewrite

Rules

2612×	`/-lowering-/.f32`
2612×	`/-lowering-/.f64`
2466×	`-lowering-.f32`
2466×	`-lowering-.f64`
1930×	`pow-lowering-pow.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	39	193
1	279	141
2	2838	135
0	9173	135

Stop Event

1×	iter limit
1×	node limit

Counts

23 → 1112

Calls

Call 1

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

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

simplify293.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

3166×	`-lowering-.f32`
3166×	`-lowering-.f64`
2970×	`+-lowering-+.f64`
2970×	`+-lowering-+.f32`
1966×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	544	3359
1	1780	2771
2	6524	2763
0	8050	2763

Stop Event

1×	iter limit
1×	node limit

Counts

276 → 276

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

eval315.0ms (2.9%)

Compiler: Compiled 55558 to 5560 computations (90% saved)

prune242.0ms (2.2%)

Pruning

24 alts after pruning (22 fresh and 2 done)

	Pruned	Kept	Total
New	2004	20	2024
Fresh	6	2	8
Picked	3	2	5
Done	0	0	0
Total	2013	24	2037

Accuracy

100.0%

Counts

2037 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	34.5%	(pow.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) #s(literal 1/4 binary64))
	34.5%	(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
▶	5.6%	(pow.f64 x #s(literal -1/2 binary64))
	99.0%	(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)) x) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))
	80.4%	(/.f64 (/.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 x (+.f64 #s(literal 1 binary64) x)))
▶	80.4%	(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.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))))
	78.8%	(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
	98.1%	(/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))
	35.0%	(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
▶	99.0%	(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64))) x)
	78.9%	(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64))) (*.f64 x x))
	80.4%	(/.f64 (.f64 (.f64 (+.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64)) (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) (.f64 (+.f64 x (+.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
	78.8%	(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
	78.9%	(/.f64 (.f64 #s(literal -1/2 binary64) (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (.f64 x x))
	98.1%	(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))) x)))
	5.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
	35.6%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
▶	6.7%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64)))
✓	27.7%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	98.9%	(.f64 (/.f64 (+.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal 1/8 binary64))) (pow.f64 x #s(literal 3/2 binary64))) (*.f64 #s(literal -1/2 binary64) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))) x) (/.f64 #s(literal 1 binary64) x))
	78.9%	(.f64 (-.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (/.f64 #s(literal -1/2 binary64) (.f64 x x)))
	80.4%	(.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))
▶	64.3%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)))
✓	5.6%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 684 to 454 computations (33.6% saved)

simplify165.0ms (1.5%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(*.f64 x (+.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))
✓	cost-diff	64	(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.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))))
✓	cost-diff	0	(*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64))
✓	cost-diff	0	(pow.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	cost-diff	0	(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
✓	cost-diff	0	(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))
✓	cost-diff	0	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)))
✓	cost-diff	0	(pow.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64)))
✓	cost-diff	0	(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64))) x)

Rules

2856×	`sum4-define`
2262×	`sum3-define`
1840×	`fma-define`
1628×	`fma-lowering-fma.f32`
1628×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	27	178
1	59	167
2	100	167
3	240	167
4	638	166
5	1205	164
6	3340	164
7	4849	164
8	5974	164
0	8200	164

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize289.0ms (2.6%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	accuracy	98.9%	(/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))
✓	accuracy	81.7%	(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.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))))
✓	accuracy	100.0%	(*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(pow.f64 x #s(literal -1/2 binary64))
✓	accuracy	51.7%	(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64))
✓	accuracy	35.6%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64)))
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)))
✓	accuracy	99.9%	(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
✓	accuracy	98.9%	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	accuracy	65.8%	(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))
✓	accuracy	100.0%	(pow.f64 x #s(literal -1/2 binary64))
✓	accuracy	99.7%	(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)) #s(literal -3/8 binary64))) x)
✓	accuracy	99.6%	(.f64 (sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x)) #s(literal -3/8 binary64))
✓	accuracy	98.9%	(/.f64 #s(literal 1 binary64) (*.f64 x x))
✓	accuracy	65.8%	(sqrt.f64 (/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x))

Results

155.0ms	197×	1	valid
75.0ms	53×	2	valid
2.0ms	6×	0	valid

Compiler

Compiled 220 to 28 computations (87.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 155.0ms

ival-pow: 62.0ms (40% of total)

ival-div: 26.0ms (16.8% of total)

ival-mult: 23.0ms (14.8% of total)

backward-pass: 19.0ms (12.3% of total)

ival-add: 11.0ms (7.1% of total)

ival-sqrt: 10.0ms (6.5% of total)

ival-sub: 3.0ms (1.9% of total)

const: 2.0ms (1.3% of total)

series67.0ms (0.6%)

Counts

18 → 216

Calls

Call 1

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

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

Calls

54 calls:

Time	Variable		Point	Expression
54.0ms	x	@	0	(- (pow x -1/2) (pow (* (+ 1 x) (+ 1 x)) -1/4))
2.0ms	x	@	0	(/ (+ (* 1/2 (sqrt (/ 1 x))) (* (sqrt (/ (/ 1 (* x x)) x)) -3/8)) x)
1.0ms	x	@	-inf	(/ (/ 1 (* x (+ 1 x))) (+ (pow x -1/2) (pow (+ 1 x) -1/2)))
1.0ms	x	@	0	(/ (/ 1 (* x (+ 1 x))) (+ (pow x -1/2) (pow (+ 1 x) -1/2)))
1.0ms	x	@	-inf	(/ (+ (* 1/2 (sqrt (/ 1 x))) (* (sqrt (/ (/ 1 (* x x)) x)) -3/8)) x)

rewrite355.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

3420×	`/-lowering-/.f32`
3420×	`/-lowering-/.f64`
3386×	`-lowering-.f32`
3386×	`-lowering-.f64`
1872×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	126
1	174	99
2	1285	98
0	8280	98

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 958

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 x (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))))) #s(literal -1 binary64)))
(-.f64 (/.f64 (/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))) x) (/.f64 (/.f64 (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))) x))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))) (-.f64 #s(literal 0 binary64) x)))
(-.f64 (/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 x (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)))) (/.f64 (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64)) (.f64 x (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)))))
(neg.f64 (/.f64 (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))) (-.f64 #s(literal 0 binary64) x)))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)))) x))
(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 x (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)))))))
(/.f64 (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 x (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)))) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (+.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal -9/2 binary64)) #s(literal -27/512 binary64))) (.f64 x (+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -3/8 binary64)) (/.f64 (-.f64 (*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (sqrt.f64 x))))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (.f64 x (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))))
(/.f64 (.f64 (+.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal -9/2 binary64)) #s(literal -27/512 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -3/8 binary64)) (/.f64 (-.f64 (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) x))
(/.f64 (.f64 (+.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal -9/2 binary64)) #s(literal -27/512 binary64))) #s(literal -1 binary64)) (.f64 (+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -3/8 binary64)) (/.f64 (-.f64 (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) #s(literal 1 binary64)) (.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) x))
(/.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) #s(literal -1 binary64)) (.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))))) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 (neg.f64 (+.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal -9/2 binary64)) #s(literal -27/512 binary64)))) (neg.f64 (.f64 x (+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -3/8 binary64)) (/.f64 (-.f64 (*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))))))
(/.f64 (neg.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64)))) (neg.f64 (.f64 x (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)))))
(/.f64 (.f64 (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))) #s(literal 1 binary64)) x)
(/.f64 (.f64 (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 (+.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal -9/2 binary64)) #s(literal -27/512 binary64))) (/.f64 #s(literal 1 binary64) x)) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -3/8 binary64)) (/.f64 (-.f64 (*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))))
(/.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)))
(/.f64 (neg.f64 (.f64 (+.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal -9/2 binary64)) #s(literal -27/512 binary64))) #s(literal 1 binary64))) (neg.f64 (.f64 (+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -3/8 binary64)) (/.f64 (-.f64 (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) x)))
(/.f64 (neg.f64 (.f64 (+.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/8 binary64)) (.f64 (pow.f64 x #s(literal -9/2 binary64)) #s(literal -27/512 binary64))) #s(literal -1 binary64))) (neg.f64 (.f64 (+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -3/8 binary64)) (/.f64 (-.f64 (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (sqrt.f64 x)))) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) #s(literal 1 binary64))) (neg.f64 (.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) x)))
(/.f64 (neg.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) #s(literal -1 binary64))) (neg.f64 (.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) (-.f64 #s(literal 0 binary64) x))))
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(.f64 (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (-.f64 (pow.f64 x #s(literal -3/2 binary64)) (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 (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 -3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -3/2 binary64)))) (/.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal 1 binary64) 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 (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 -1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 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 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/4 binary64)))))
(.f64 (/.f64 (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (+.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -3/2 binary64))))) (/.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (+.f64 (/.f64 #s(literal 1 binary64) 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 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (/.f64 (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))) (-.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x))))) (/.f64 (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))) (-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))

simplify282.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

4118×	`-lowering-.f32`
4118×	`-lowering-.f64`
2258×	`+-lowering-+.f64`
2258×	`+-lowering-+.f32`
1386×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	287	2091
1	913	1753
2	3358	1720
0	8884	1720

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

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

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

eval241.0ms (2.2%)

Compiler: Compiled 40483 to 4826 computations (88.1% saved)

prune235.0ms (2.1%)

Pruning

25 alts after pruning (20 fresh and 5 done)

	Pruned	Kept	Total
New	1615	14	1629
Fresh	11	6	17
Picked	2	3	5
Done	0	2	2
Total	1628	25	1653

Accuracy

100.0%

Counts

1653 → 25

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	5.6%	(pow.f64 x #s(literal -1/2 binary64))
	98.8%	(/.f64 (/.f64 (-.f64 (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64)) (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (/.f64 (-.f64 (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (sqrt.f64 x))) x)
	99.0%	(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/2 binary64) x)) x) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x)))
▶	98.8%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))))) x)
	64.9%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x) (-.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))))
	80.4%	(/.f64 (/.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 x (+.f64 #s(literal 1 binary64) x)))
✓	80.4%	(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.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))))
	78.9%	(/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
▶	99.5%	(/.f64 (/.f64 #s(literal 1 binary64) x) (*.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)))
▶	98.7%	(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (.f64 x (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))))
	35.0%	(/.f64 (+.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal -1 binary64) (+.f64 #s(literal 1 binary64) x))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
	99.1%	(/.f64 (+.f64 (.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal -3/8 binary64)) (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64)))) x)
	80.7%	(/.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (/.f64 #s(literal 1 binary64) x)) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)))
▶	78.8%	(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
	98.0%	(/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)))))
▶	5.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
	35.6%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	6.7%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64)))
✓	27.7%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	98.4%	(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
	80.8%	(.f64 (/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) x) (/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))) #s(literal 1 binary64)))
	98.0%	(*.f64 #s(literal 1/2 binary64) (pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)))
	63.5%	(.f64 #s(literal 1/2 binary64) (pow.f64 (.f64 x (*.f64 x x)) #s(literal -1/2 binary64)))
	78.9%	(.f64 #s(literal 1/2 binary64) (pow.f64 (.f64 x x) #s(literal -3/4 binary64)))
✓	5.6%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 778 to 498 computations (36% saved)

simplify196.0ms (1.8%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	384	(-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 x x)) #s(literal 9/64 binary64)))
✓	cost-diff	512	(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))))
✓	cost-diff	768	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64)))))
✓	cost-diff	768	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))))) x)
✓	cost-diff	128	(*.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))
✓	cost-diff	256	(.f64 x (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)))
✓	cost-diff	384	(-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 x x)) #s(literal 9/64 binary64)))
✓	cost-diff	640	(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (.f64 x (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 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	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	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 (+.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))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(/.f64 (/.f64 #s(literal 1 binary64) x) (*.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)))

Rules

3834×	`-lowering-.f32`
3834×	`-lowering-.f64`
1888×	`/-lowering-/.f32`
1888×	`/-lowering-/.f64`
1652×	`fma-define`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	280
1	102	272
2	308	259
3	1103	240
4	4420	236
0	8195	236

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ (/ 1 x) (* (+ (pow x -1/2) (pow (+ 1 x) -1/2)) (+ 1 x)))
(/ 1 x)
1
x
(* (+ (pow x -1/2) (pow (+ 1 x) -1/2)) (+ 1 x))
(+ (pow x -1/2) (pow (+ 1 x) -1/2))
(pow x -1/2)
-1/2
(pow (+ 1 x) -1/2)
(+ 1 x)
(/ 1 (sqrt x))
1
(sqrt x)
x
(/ (* 1/2 (sqrt x)) (* x x))
(* 1/2 (sqrt x))
1/2
(sqrt x)
x
(* x x)
(/ (- (* (/ 1 x) 1/4) (* (/ (/ 1 x) (* x x)) 9/64)) (* x (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x))))
(- (* (/ 1 x) 1/4) (* (/ (/ 1 x) (* x x)) 9/64))
(* (/ 1 x) 1/4)
(/ 1 x)
1
x
1/4
(* (/ (/ 1 x) (* x x)) 9/64)
(/ (/ 1 x) (* x x))
(* x x)
9/64
(* x (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x)))
(/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x))
(- 1/2 (* -3/8 (/ 1 x)))
1/2
(* -3/8 (/ 1 x))
-3/8
(sqrt x)
(/ (/ 1 (/ (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x)) (- (* (/ 1 x) 1/4) (* (/ (/ 1 x) (* x x)) 9/64)))) x)
(/ 1 (/ (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x)) (- (* (/ 1 x) 1/4) (* (/ (/ 1 x) (* x x)) 9/64))))
1
(/ (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x)) (- (* (/ 1 x) 1/4) (* (/ (/ 1 x) (* x x)) 9/64)))
(/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x))
(- 1/2 (* -3/8 (/ 1 x)))
1/2
(* -3/8 (/ 1 x))
-3/8
(/ 1 x)
x
(sqrt x)
(- (* (/ 1 x) 1/4) (* (/ (/ 1 x) (* x x)) 9/64))
(* (/ 1 x) 1/4)
1/4
(* (/ (/ 1 x) (* x x)) 9/64)
(/ (/ 1 x) (* x x))
(* x x)
9/64

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

localize172.0ms (1.6%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64)))))
✓	accuracy	99.6%	(/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
✓	accuracy	99.4%	(*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.4%	(/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))))
✓	accuracy	99.6%	(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) (.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x x)) #s(literal 9/64 binary64))) (.f64 x (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))))
✓	accuracy	99.6%	(/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))
✓	accuracy	99.6%	(.f64 x (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)))
✓	accuracy	99.4%	(*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) 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	80.4%	(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(pow.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	accuracy	99.6%	(/.f64 (/.f64 #s(literal 1 binary64) x) (*.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)))
✓	accuracy	99.6%	(*.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))

Results

106.0ms

256×

valid

Compiler

Compiled 353 to 32 computations (90.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 50.0ms

ival-div: 15.0ms (30.2% of total)

ival-pow: 14.0ms (28.2% of total)

ival-mult: 12.0ms (24.2% of total)

ival-add: 3.0ms (6% of total)

ival-sub: 2.0ms (4% of total)

ival-sqrt: 2.0ms (4% of total)

const: 1.0ms (2% of total)

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

series14.0ms (0.1%)

Counts

19 → 228

Calls

Call 1

Inputs
#<alt (/ (/ 1 x) (* (+ (pow x -1/2) (pow (+ 1 x) -1/2)) (+ 1 x)))>
#<alt (/ 1 x)>
#<alt (* (+ (pow x -1/2) (pow (+ 1 x) -1/2)) (+ 1 x))>
#<alt (+ (pow x -1/2) (pow (+ 1 x) -1/2))>
#<alt (/ 1 (sqrt x))>
#<alt (sqrt x)>
#<alt (/ (* 1/2 (sqrt x)) (* x x))>
#<alt (* 1/2 (sqrt x))>
#<alt (* x x)>
#<alt (/ (- (* (/ 1 x) 1/4) (* (/ (/ 1 x) (* x x)) 9/64)) (* x (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x))))>
#<alt (- (* (/ 1 x) 1/4) (* (/ (/ 1 x) (* x x)) 9/64))>
#<alt (* x (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x)))>
#<alt (* (/ 1 x) 1/4)>
#<alt (/ (/ 1 (/ (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x)) (- (* (/ 1 x) 1/4) (* (/ (/ 1 x) (* x x)) 9/64)))) x)>
#<alt (/ 1 (/ (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x)) (- (* (/ 1 x) 1/4) (* (/ (/ 1 x) (* x x)) 9/64))))>
#<alt (/ (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x)) (- (* (/ 1 x) 1/4) (* (/ (/ 1 x) (* x x)) 9/64)))>
#<alt (pow x -1/2)>
#<alt (* -3/8 (/ 1 x))>
#<alt (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x))>

Outputs
#<alt (sqrt (/ 1 x))>
#<alt (+ (sqrt (/ 1 x)) (* -1 (* x (+ (sqrt (/ 1 x)) (/ 1 x)))))>
#<alt (+ (sqrt (/ 1 x)) (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (* (+ 1 (sqrt x)) (+ (sqrt (/ 1 x)) (/ 1 x))))) (* 1/2 (/ 1 x))))) (+ (sqrt (/ 1 x)) (/ 1 x)))))>
#<alt (+ (sqrt (/ 1 x)) (* x (- (* x (- (* x (- (* 1/8 (/ 1 x)) (+ (* -1 (* (sqrt (/ 1 x)) (* (+ 1 (sqrt x)) (+ (* -1 (* (sqrt (/ 1 x)) (* (+ 1 (sqrt x)) (+ (sqrt (/ 1 x)) (/ 1 x))))) (* 1/2 (/ 1 x)))))) (* -1/2 (* (sqrt (/ 1 x)) (+ (sqrt (/ 1 x)) (/ 1 x))))))) (+ (* -1 (* (sqrt (/ 1 x)) (* (+ 1 (sqrt x)) (+ (sqrt (/ 1 x)) (/ 1 x))))) (* 1/2 (/ 1 x))))) (+ (sqrt (/ 1 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 (/ (+ (* -1/2 (sqrt x)) (* -1/8 (sqrt (pow x 3)))) (pow x 2))) (* 1/2 (sqrt x))) (* 1/2 (sqrt (/ 1 x)))) (pow x 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* -1 (+ (* -1/2 (sqrt x)) (* -1/8 (sqrt (pow x 3))))) (+ (* 1/8 (sqrt (pow x 3))) (* 1/4 (* x (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x))))))) (pow x 3))) (* 1/2 (sqrt x))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 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 (/ (+ (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) (* 1/2 (sqrt x))) x)) (* 1/2 (sqrt x))) (pow x 2))>
#<alt (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (* x (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x)))) (pow (sqrt -1) 2))) (+ (* 1/4 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x)))) x)) (+ (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x)))) x)) (* 1/2 (sqrt x))) x)) (* 1/2 (sqrt x))) (pow x 2))>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (/ 1 x)>
#<alt (sqrt (/ 1 x))>
#<alt (/ (+ (sqrt x) (* x (+ 1 (sqrt x)))) x)>
#<alt (/ (+ (sqrt x) (* x (+ 1 (+ (sqrt x) (* 1/2 x))))) x)>
#<alt (/ (+ (sqrt x) (* x (+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x))))))) x)>
#<alt (* 2 (sqrt x))>
#<alt (* x (+ (* 2 (sqrt (/ 1 x))) (* 2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 2 (sqrt (/ 1 x))) (* 2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (+ (* 2 (sqrt (/ 1 x))) (* 2 (sqrt (/ 1 (pow x 3)))))))))>
#<alt (* 2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1/2 (sqrt (/ 1 x))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))))>
#<alt (* -1 (* x (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x))) x)) (* 1/2 (sqrt x))) x)) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))))>
#<alt (sqrt (/ 1 x))>
#<alt (/ (+ x (sqrt x)) x)>
#<alt (/ (+ (sqrt x) (* x (+ 1 (* -1/2 x)))) x)>
#<alt (/ (+ (sqrt x) (* x (+ 1 (* x (- (* 3/8 x) 1/2))))) x)>
#<alt (* 2 (sqrt (/ 1 x)))>
#<alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))>
#<alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt (/ 1 x)))))>
#<alt (+ (* -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)))) (* 2 (sqrt (/ 1 x))))))>
#<alt (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 2 (* (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)))) (* 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))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (* -1/2 (* (sqrt (/ 1 (pow x 3))) (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 (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 (* -3/8 (sqrt (/ 1 (pow x 5))))>
#<alt (/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (/ -9/64 (pow x 3))>
#<alt (/ (- (* 1/4 (pow x 2)) 9/64) (pow x 3))>
#<alt (/ (- (* 1/4 (pow x 2)) 9/64) (pow x 3))>
#<alt (/ (- (* 1/4 (pow x 2)) 9/64) (pow x 3))>
#<alt (/ 1/4 x)>
#<alt (/ (- 1/4 (* 9/64 (/ 1 (pow x 2)))) x)>
#<alt (/ (- 1/4 (* 9/64 (/ 1 (pow x 2)))) x)>
#<alt (/ (- 1/4 (* 9/64 (/ 1 (pow x 2)))) x)>
#<alt (/ 1/4 x)>
#<alt (* -1 (/ (- (* 9/64 (/ 1 (pow x 2))) 1/4) x))>
#<alt (* -1 (/ (- (* 9/64 (/ 1 (pow x 2))) 1/4) x))>
#<alt (* -1 (/ (- (* 9/64 (/ 1 (pow x 2))) 1/4) x))>
#<alt (* 3/8 (sqrt (/ 1 x)))>
#<alt (/ (+ (* 3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (* 3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (* 3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (* 1/2 (sqrt x))>
#<alt (* x (+ (* 3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* 3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* 3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* 1/2 (sqrt x))>
#<alt (* -1 (* x (+ (* -1/2 (sqrt (/ 1 x))) (* -3/8 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* -1 (* x (+ (* -1/2 (sqrt (/ 1 x))) (* -3/8 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* -1 (* x (+ (* -1/2 (sqrt (/ 1 x))) (* -3/8 (sqrt (/ 1 (pow x 3)))))))>
#<alt (/ 1/4 x)>
#<alt (/ 1/4 x)>
#<alt (/ 1/4 x)>
#<alt (/ 1/4 x)>
#<alt (/ 1/4 x)>
#<alt (/ 1/4 x)>
#<alt (/ 1/4 x)>
#<alt (/ 1/4 x)>
#<alt (/ 1/4 x)>
#<alt (/ 1/4 x)>
#<alt (/ 1/4 x)>
#<alt (/ 1/4 x)>
#<alt (* -3/8 (sqrt (/ 1 (pow x 5))))>
#<alt (/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)>
#<alt (* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))>
#<alt (* -1 (/ (+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -1 (/ (+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))>
#<alt (* -3/8 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 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))) (* 3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))>
#<alt (* -8/3 (sqrt (pow x 3)))>
#<alt (* x (+ (* -32/9 (sqrt (pow x 3))) (* -8/3 (sqrt x))))>
#<alt (* x (+ (* -8/3 (sqrt x)) (* x (+ (* -128/27 (sqrt (pow x 3))) (* -32/9 (sqrt x))))))>
#<alt (* x (+ (* -8/3 (sqrt x)) (* x (+ (* -32/9 (sqrt x)) (* x (+ (* -512/81 (sqrt (pow x 3))) (* -128/27 (sqrt x))))))))>
#<alt (* 2 (sqrt x))>
#<alt (* x (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* 9/8 (sqrt (/ 1 (pow x 5)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))>
#<alt (* x (+ (* 27/32 (sqrt (/ 1 (pow x 7)))) (+ (* 9/8 (sqrt (/ 1 (pow x 5)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))>
#<alt (* 2 (sqrt x))>
#<alt (* -1 (* x (+ (* -2 (sqrt (/ 1 x))) (* -3/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* -1 (* x (+ (* -2 (sqrt (/ 1 x))) (* -1 (/ (+ (* 9/8 (sqrt (/ 1 (pow x 3)))) (* 3/2 (sqrt (/ 1 x)))) x)))))>
#<alt (* -1 (* x (+ (* -2 (sqrt (/ 1 x))) (* -1 (/ (+ (* -1 (/ (+ (* -9/8 (sqrt (/ 1 x))) (* -27/32 (sqrt (/ 1 (pow x 3))))) x)) (* 3/2 (sqrt (/ 1 x)))) x)))))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (sqrt (/ 1 x))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))>
#<alt (/ -3/8 x)>
#<alt (/ -3/8 x)>
#<alt (/ -3/8 x)>
#<alt (/ -3/8 x)>
#<alt (/ -3/8 x)>
#<alt (/ -3/8 x)>
#<alt (/ -3/8 x)>
#<alt (/ -3/8 x)>
#<alt (/ -3/8 x)>
#<alt (/ -3/8 x)>
#<alt (/ -3/8 x)>
#<alt (/ -3/8 x)>
#<alt (* 3/8 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* 3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* 3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* 3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (+ (* 3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* 3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* 3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (+ (* 3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* 3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* 3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>

Calls

57 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/ (- (* (/ 1 x) 1/4) (* (/ (/ 1 x) (* x x)) 9/64)) (* x (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x))))
1.0ms	x	@	-inf	(* x (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x)))
1.0ms	x	@	0	(/ (- (* (/ 1 x) 1/4) (* (/ (/ 1 x) (* x x)) 9/64)) (* x (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x))))
1.0ms	x	@	inf	(/ (- (* (/ 1 x) 1/4) (* (/ (/ 1 x) (* x x)) 9/64)) (* x (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x))))
0.0ms	x	@	-inf	(/ (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x)) (- (* (/ 1 x) 1/4) (* (/ (/ 1 x) (* x x)) 9/64)))

rewrite623.0ms (5.6%)

Algorithm

1×	batch-egg-rewrite

Rules

3682×	`/-lowering-/.f32`
3682×	`/-lowering-/.f64`
2950×	`-lowering-.f32`
2950×	`-lowering-.f64`
1430×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	179
1	235	163
2	1955	150
0	8287	150

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 1131

Calls

Call 1

Inputs
(/ (/ 1 x) (* (+ (pow x -1/2) (pow (+ 1 x) -1/2)) (+ 1 x)))
(/ 1 x)
(* (+ (pow x -1/2) (pow (+ 1 x) -1/2)) (+ 1 x))
(+ (pow x -1/2) (pow (+ 1 x) -1/2))
(/ 1 (sqrt x))
(sqrt x)
(/ (* 1/2 (sqrt x)) (* x x))
(* 1/2 (sqrt x))
(* x x)
(/ (- (* (/ 1 x) 1/4) (* (/ (/ 1 x) (* x x)) 9/64)) (* x (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x))))
(- (* (/ 1 x) 1/4) (* (/ (/ 1 x) (* x x)) 9/64))
(* x (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x)))
(* (/ 1 x) 1/4)
(/ (/ 1 (/ (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x)) (- (* (/ 1 x) 1/4) (* (/ (/ 1 x) (* x x)) 9/64)))) x)
(/ 1 (/ (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x)) (- (* (/ 1 x) 1/4) (* (/ (/ 1 x) (* x x)) 9/64))))
(/ (/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x)) (- (* (/ 1 x) 1/4) (* (/ (/ 1 x) (* x x)) 9/64)))
(pow x -1/2)
(* -3/8 (/ 1 x))
(/ (- 1/2 (* -3/8 (/ 1 x))) (sqrt x))

Outputs
(exp.f64 (.f64 (log.f64 (.f64 x (+.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) (/.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(neg.f64 (/.f64 (/.f64 #s(literal -1 binary64) x) (+.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.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 x (+.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.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 x (+.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x (+.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) (neg.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (.f64 x (+.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))))
(/.f64 #s(literal 1 binary64) (neg.f64 (.f64 (+.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) x))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.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 #s(literal 0 binary64) x) (+.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 #s(literal -1 binary64) (neg.f64 (.f64 x (+.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.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 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (-.f64 #s(literal 0 binary64) x)))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (.f64 x (+.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))))))
(/.f64 (/.f64 #s(literal -1 binary64) x) (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(/.f64 (/.f64 #s(literal -1 binary64) x) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))))
(/.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) x)
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.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 (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 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) x)))
(/.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64))))
(/.f64 (.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (+.f64 (*.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 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 (neg.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (neg.f64 (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) (neg.f64 (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))
(/.f64 (neg.f64 (.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(pow.f64 (.f64 x (+.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (.f64 x (+.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (/.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1 binary64) x)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))))
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(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 27/512 binary64) (.f64 x (.f64 x x)))) #s(literal -1 binary64))) (neg.f64 (.f64 (+.f64 #s(literal 1/4 binary64) (*.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x)))) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 9/64 binary64) (.f64 x x))) #s(literal 1 binary64))) (neg.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x)) (sqrt.f64 x))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 9/64 binary64) (.f64 x x))) #s(literal -1 binary64))) (neg.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x)) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))))
(/.f64 (neg.f64 (-.f64 (.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal -3/2 binary64))) (.f64 #s(literal -27/512 binary64) (pow.f64 x #s(literal -9/2 binary64))))) (neg.f64 (+.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 2 binary64)) (*.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -3/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))))))
(/.f64 (neg.f64 (-.f64 (pow.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) #s(literal 2 binary64)) (pow.f64 (/.f64 #s(literal -3/8 binary64) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 2 binary64)))) (neg.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal -3/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))))
(/.f64 (neg.f64 (*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) #s(literal -1 binary64))) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(/.f64 (neg.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 27/512 binary64) (.f64 x (.f64 x x)))) (pow.f64 x #s(literal -1/2 binary64)))) (neg.f64 (+.f64 #s(literal 1/4 binary64) (.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x))))))
(/.f64 (neg.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 9/64 binary64) (.f64 x x))) (pow.f64 x #s(literal -1/2 binary64)))) (neg.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x))))
(pow.f64 (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) (sqrt.f64 x)) #s(literal 1 binary64))
(pow.f64 (/.f64 (sqrt.f64 x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (sqrt.f64 x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) (sqrt.f64 x)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))) #s(literal -1 binary64)))
(*.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))
(.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) #s(literal 1 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x))) #s(literal -1 binary64)) (pow.f64 x #s(literal -1/2 binary64)))
(.f64 (pow.f64 (/.f64 (sqrt.f64 x) (+.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 27/512 binary64) (.f64 x (.f64 x x))))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/4 binary64) (.f64 (/.f64 #s(literal -3/8 binary64) x) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x))))))
(.f64 (pow.f64 (/.f64 (sqrt.f64 x) (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 9/64 binary64) (.f64 x x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -3/8 binary64) x))))
(*.f64 (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)))) #s(literal -1 binary64)) (/.f64 #s(literal -1 binary64) (sqrt.f64 x)))

simplify427.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

4152×	`-lowering-.f32`
4152×	`-lowering-.f64`
3008×	`+-lowering-+.f64`
3008×	`+-lowering-+.f32`
1270×	`distribute-lft-in`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	317	2150
1	1002	1953
2	3841	1920
0	8878	1920

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

Calls

Call 1

Inputs
(sqrt (/ 1 x))
(+ (sqrt (/ 1 x)) (* -1 (* x (+ (sqrt (/ 1 x)) (/ 1 x)))))
(+ (sqrt (/ 1 x)) (* x (- (* -1 (* x (+ (* -1 (* (sqrt (/ 1 x)) (* (+ 1 (sqrt x)) (+ (sqrt (/ 1 x)) (/ 1 x))))) (* 1/2 (/ 1 x))))) (+ (sqrt (/ 1 x)) (/ 1 x)))))
(+ (sqrt (/ 1 x)) (* x (- (* x (- (* x (- (* 1/8 (/ 1 x)) (+ (* -1 (* (sqrt (/ 1 x)) (* (+ 1 (sqrt x)) (+ (* -1 (* (sqrt (/ 1 x)) (* (+ 1 (sqrt x)) (+ (sqrt (/ 1 x)) (/ 1 x))))) (* 1/2 (/ 1 x)))))) (* -1/2 (* (sqrt (/ 1 x)) (+ (sqrt (/ 1 x)) (/ 1 x))))))) (+ (* -1 (* (sqrt (/ 1 x)) (* (+ 1 (sqrt x)) (+ (sqrt (/ 1 x)) (/ 1 x))))) (* 1/2 (/ 1 x))))) (+ (sqrt (/ 1 x)) (/ 1 x)))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/2 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/ (- (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* -1/8 (sqrt (pow x 3)))) (pow x 2))) (* 1/2 (sqrt x))) (* 1/2 (sqrt (/ 1 x)))) (pow x 2))
(/ (- (+ (* -1 (/ (+ (* -1 (+ (* -1/2 (sqrt x)) (* -1/8 (sqrt (pow x 3))))) (+ (* 1/8 (sqrt (pow x 3))) (* 1/4 (* x (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x))))))) (pow x 3))) (* 1/2 (sqrt x))) (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/8 (sqrt (/ 1 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 (/ (+ (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x)) (* 1/2 (sqrt x))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/4 (/ (* x (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x)))) (pow (sqrt -1) 2))) (+ (* 1/4 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x)))) x)) (+ (* 1/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x)))) x)) (* 1/2 (sqrt x))) x)) (* 1/2 (sqrt x))) (pow x 2))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(sqrt (/ 1 x))
(/ (+ (sqrt x) (* x (+ 1 (sqrt x)))) x)
(/ (+ (sqrt x) (* x (+ 1 (+ (sqrt x) (* 1/2 x))))) x)
(/ (+ (sqrt x) (* x (+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x))))))) x)
(* 2 (sqrt x))
(* x (+ (* 2 (sqrt (/ 1 x))) (* 2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 2 (sqrt (/ 1 x))) (* 2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* -1/2 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (+ (* 2 (sqrt (/ 1 x))) (* 2 (sqrt (/ 1 (pow x 3)))))))))
(* 2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1/2 (sqrt (/ 1 x))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))))
(* -1 (* x (+ (* -2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (+ (* -1/2 (sqrt x)) (* 1/2 (sqrt x))) x)) (* 1/2 (sqrt x))) x)) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)))))
(sqrt (/ 1 x))
(/ (+ x (sqrt x)) x)
(/ (+ (sqrt x) (* x (+ 1 (* -1/2 x)))) x)
(/ (+ (sqrt x) (* x (+ 1 (* x (- (* 3/8 x) 1/2))))) x)
(* 2 (sqrt (/ 1 x)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 2 (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)))) (* 2 (sqrt (/ 1 x))))))
(* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(+ (* -1/2 (sqrt (/ 1 (pow x 3)))) (+ (* 1/2 (sqrt (/ 1 (pow x 5)))) (* 2 (* (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)))) (* 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))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (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)))
(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)
(* -3/8 (sqrt (/ 1 (pow x 5))))
(/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(/ -9/64 (pow x 3))
(/ (- (* 1/4 (pow x 2)) 9/64) (pow x 3))
(/ (- (* 1/4 (pow x 2)) 9/64) (pow x 3))
(/ (- (* 1/4 (pow x 2)) 9/64) (pow x 3))
(/ 1/4 x)
(/ (- 1/4 (* 9/64 (/ 1 (pow x 2)))) x)
(/ (- 1/4 (* 9/64 (/ 1 (pow x 2)))) x)
(/ (- 1/4 (* 9/64 (/ 1 (pow x 2)))) x)
(/ 1/4 x)
(* -1 (/ (- (* 9/64 (/ 1 (pow x 2))) 1/4) x))
(* -1 (/ (- (* 9/64 (/ 1 (pow x 2))) 1/4) x))
(* -1 (/ (- (* 9/64 (/ 1 (pow x 2))) 1/4) x))
(* 3/8 (sqrt (/ 1 x)))
(/ (+ (* 3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* 3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* 3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(* 1/2 (sqrt x))
(* x (+ (* 3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* 3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* 3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* 1/2 (sqrt x))
(* -1 (* x (+ (* -1/2 (sqrt (/ 1 x))) (* -3/8 (sqrt (/ 1 (pow x 3)))))))
(* -1 (* x (+ (* -1/2 (sqrt (/ 1 x))) (* -3/8 (sqrt (/ 1 (pow x 3)))))))
(* -1 (* x (+ (* -1/2 (sqrt (/ 1 x))) (* -3/8 (sqrt (/ 1 (pow x 3)))))))
(/ 1/4 x)
(/ 1/4 x)
(/ 1/4 x)
(/ 1/4 x)
(/ 1/4 x)
(/ 1/4 x)
(/ 1/4 x)
(/ 1/4 x)
(/ 1/4 x)
(/ 1/4 x)
(/ 1/4 x)
(/ 1/4 x)
(* -3/8 (sqrt (/ 1 (pow x 5))))
(/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 3))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(/ (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))) x)
(* -1/2 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)))
(* -1 (/ (+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -1 (/ (+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x))
(* -3/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* 1/2 (sqrt (/ 1 x)))
(+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* 3/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(* -8/3 (sqrt (pow x 3)))
(* x (+ (* -32/9 (sqrt (pow x 3))) (* -8/3 (sqrt x))))
(* x (+ (* -8/3 (sqrt x)) (* x (+ (* -128/27 (sqrt (pow x 3))) (* -32/9 (sqrt x))))))
(* x (+ (* -8/3 (sqrt x)) (* x (+ (* -32/9 (sqrt x)) (* x (+ (* -512/81 (sqrt (pow x 3))) (* -128/27 (sqrt x))))))))
(* 2 (sqrt x))
(* x (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(* x (+ (* 9/8 (sqrt (/ 1 (pow x 5)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))
(* x (+ (* 27/32 (sqrt (/ 1 (pow x 7)))) (+ (* 9/8 (sqrt (/ 1 (pow x 5)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
(* 2 (sqrt x))
(* -1 (* x (+ (* -2 (sqrt (/ 1 x))) (* -3/2 (sqrt (/ 1 (pow x 3)))))))
(* -1 (* x (+ (* -2 (sqrt (/ 1 x))) (* -1 (/ (+ (* 9/8 (sqrt (/ 1 (pow x 3)))) (* 3/2 (sqrt (/ 1 x)))) x)))))
(* -1 (* x (+ (* -2 (sqrt (/ 1 x))) (* -1 (/ (+ (* -1 (/ (+ (* -9/8 (sqrt (/ 1 x))) (* -27/32 (sqrt (/ 1 (pow x 3))))) x)) (* 3/2 (sqrt (/ 1 x)))) x)))))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(/ -3/8 x)
(/ -3/8 x)
(/ -3/8 x)
(/ -3/8 x)
(/ -3/8 x)
(/ -3/8 x)
(/ -3/8 x)
(/ -3/8 x)
(/ -3/8 x)
(/ -3/8 x)
(/ -3/8 x)
(/ -3/8 x)
(* 3/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* 3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* 3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* 3/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* 1/2 (sqrt (/ 1 x)))
(+ (* 3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* 3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* 3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* 1/2 (sqrt (/ 1 x)))
(+ (* 3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* 3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* 3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))

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

eval330.0ms (3%)

Compiler: Compiled 69424 to 4833 computations (93% saved)

prune306.0ms (2.8%)

Pruning

26 alts after pruning (18 fresh and 8 done)

	Pruned	Kept	Total
New	1948	12	1960
Fresh	9	6	15
Picked	2	3	5
Done	0	5	5
Total	1959	26	1985

Accuracy

100.0%

Counts

1985 → 26

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	5.6%	(pow.f64 x #s(literal -1/2 binary64))
	99.0%	(/.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 9/64 binary64) (.f64 x x))) x) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) (sqrt.f64 x)))
	98.9%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (/.f64 (-.f64 #s(literal 1/2 binary64) (*.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x)) (/.f64 #s(literal 1/4 binary64) x))) x)
	64.9%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) x) (-.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))))
	98.7%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) (/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 9/64 binary64) (.f64 x x))) x))) (sqrt.f64 x))) x)
	80.4%	(/.f64 (/.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 x (+.f64 #s(literal 1 binary64) x)))
✓	80.4%	(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x (+.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))))
	78.9%	(/.f64 (/.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))
✓	99.5%	(/.f64 (/.f64 #s(literal 1 binary64) x) (*.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)))
	98.1%	(/.f64 (/.f64 #s(literal 1 binary64) x) (.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)) (+.f64 #s(literal 1 binary64) x)))
	98.1%	(/.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x)
	98.9%	(/.f64 (/.f64 #s(literal 1/4 binary64) x) (.f64 x (/.f64 (-.f64 #s(literal 1/2 binary64) (.f64 #s(literal -3/8 binary64) (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 x))))
	97.9%	(/.f64 (*.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) x)
✓	78.8%	(/.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 x x))
	5.6%	(/.f64 (sqrt.f64 x) x)
	97.3%	(/.f64 #s(literal 1 binary64) (/.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 1/2 binary64)))
✓	5.6%	(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
	35.6%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal -1/2 binary64)))
✓	6.7%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64)))
✓	27.7%	(-.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))
	98.1%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1/2 binary64) x))
	98.4%	(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64))
	80.9%	(.f64 (/.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 9/64 binary64) (.f64 x x))) x) (*.f64 x (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)))) (sqrt.f64 x))
	98.1%	(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
	63.5%	(.f64 #s(literal 1/2 binary64) (pow.f64 (.f64 x (*.f64 x x)) #s(literal -1/2 binary64)))
✓	5.6%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))

Compiler

Compiled 1273 to 425 computations (66.6% saved)

regimes34.0ms (0.3%)

Counts

60 → 1

Calls

Call 1

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

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

Calls

2 calls:

17.0ms	x
12.0ms	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))

Results

Accuracy	Segments	Branch
99.5%	1	`x`
99.5%	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)

regimes25.0ms (0.2%)

Counts

44 → 1

Calls

Call 1

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

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

Calls

2 calls:

13.0ms	x
9.0ms	(-.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)

regimes23.0ms (0.2%)

Counts

40 → 1

Calls

Call 1

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

Outputs
(/.f64 (/.f64 (-.f64 #s(literal 1/4 binary64) (/.f64 #s(literal 9/64 binary64) (.f64 x x))) x) (.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 3/8 binary64) x)) (sqrt.f64 x)))

Calls

2 calls:

12.0ms	x
8.0ms	(-.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
99.0%	1	`x`
99.0%	1	`(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1 binary64) (sqrt.f64 (+.f64 x #s(literal 1 binary64)))))`

Compiler

Compiled 14 to 9 computations (35.7% saved)

regimes8.0ms (0.1%)

Counts

23 → 1

Calls

Call 1

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

Outputs

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

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
98.9%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes39.0ms (0.4%)

Counts

22 → 1

Calls

Call 1

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

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

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
98.9%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes7.0ms (0.1%)

Counts

21 → 1

Calls

Call 1

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

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

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
98.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

4 → 1

Calls

Call 1

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
5.6%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

46×	`neg-mul-1_binary64`
38×	`unsub-neg_binary64`
30×	`*-commutative_binary64`
28×	`+-commutative_binary64`
20×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	90
1	61	90
2	79	90
3	97	90
4	110	90
5	119	90
6	151	90
7	199	90

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness2.2s (19.5%)

Rules

4152×	`-lowering-.f32`
4152×	`-lowering-.f64`
3682×	`/-lowering-/.f32`
3682×	`/-lowering-/.f64`
3420×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	179
1	235	163
2	1955	150
0	8287	150
0	114	458
1	334	394
2	1141	371
3	4906	370
0	8253	370
0	8	15
1	64	15
2	601	15
3	7279	15
0	8160	15
0	317	2150
1	1002	1953
2	3841	1920
0	8878	1920
0	544	3359
1	1780	2771
2	6524	2763
0	8050	2763
0	39	193
1	279	141
2	2838	135
0	9173	135
0	27	126
1	174	99
2	1285	98
0	8280	98

Stop Event

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

Compiler

Compiled 202 to 124 computations (38.6% saved)

preprocess54.0ms (0.5%)

Compiler: Compiled 238 to 118 computations (50.4% saved)

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

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

analyze4.0ms (0%)

sample2.1s (19.4%)

preprocess55.0ms (0.5%)

explain145.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify25.0ms (0.2%)

localize69.0ms (0.6%)

series5.0ms (0%)

rewrite217.0ms (2%)

simplify190.0ms (1.7%)

eval30.0ms (0.3%)

prune40.0ms (0.4%)

simplify166.0ms (1.5%)

localize403.0ms (3.6%)

series24.0ms (0.2%)

rewrite621.0ms (5.6%)

simplify293.0ms (2.7%)

eval315.0ms (2.9%)

prune242.0ms (2.2%)

simplify165.0ms (1.5%)

localize289.0ms (2.6%)

series67.0ms (0.6%)

rewrite355.0ms (3.2%)

simplify282.0ms (2.6%)

eval241.0ms (2.2%)

prune235.0ms (2.1%)

simplify196.0ms (1.8%)

localize172.0ms (1.6%)

series14.0ms (0.1%)

rewrite623.0ms (5.6%)

simplify427.0ms (3.9%)

eval330.0ms (3%)

prune306.0ms (2.8%)

regimes34.0ms (0.3%)

regimes25.0ms (0.2%)

regimes23.0ms (0.2%)

regimes8.0ms (0.1%)

regimes39.0ms (0.4%)

regimes7.0ms (0.1%)

regimes2.0ms (0%)

simplify12.0ms (0.1%)

soundness2.2s (19.5%)

preprocess54.0ms (0.5%)

end0.0ms (0%)

Profiling

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