Metrics for Main:bigenough3 from C

analyze2.0ms (0%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	100%	0%	0%	0%	0%	0
0%	0%	100%	0%	0%	0%	0%	1
50%	50%	50%	0%	0%	0%	0%	2
66.7%	50%	25%	0%	0%	25%	0%	3
80%	50%	12.5%	0%	0%	37.5%	0%	4
88.9%	50%	6.2%	0%	0%	43.7%	0%	5
94.1%	50%	3.1%	0%	0%	46.9%	0%	6
97%	50%	1.6%	0%	0%	48.4%	0%	7
98.5%	50%	0.8%	0%	0%	49.2%	0%	8
99.2%	50%	0.4%	0%	0%	49.6%	0%	9
99.6%	50%	0.2%	0%	0%	49.8%	0%	10
99.8%	50%	0.1%	0%	0%	49.9%	0%	11
99.9%	50%	0%	0%	0%	49.9%	0%	12

Compiler

Compiled 9 to 7 computations (22.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 1.0ms

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

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

const: 0.0ms (0% of total)

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

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

sample1.2s (10%)

Results

380.0ms	1675×	2	valid
307.0ms	2356×	1	valid
269.0ms	4225×	0	valid
0.0ms	4×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 542.0ms

ival-sqrt: 223.0ms (41.1% of total)

ival-add: 117.0ms (21.6% of total)

backward-pass: 95.0ms (17.5% of total)

ival-sub: 91.0ms (16.8% of total)

const: 16.0ms (3% of total)

Bogosity

preprocess42.0ms (0.3%)

Algorithm

2×	egg-herbie

Rules

270×	`sum3-define`
244×	`fnmadd-define`
184×	`fmsub-define`
168×	`fnmsub-define`
168×	`fma-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	25	24
2	52	23
3	99	23
4	190	23
5	387	23
6	579	23
7	755	23
8	849	23
9	955	23
10	1033	23
11	1039	23
0	6	7
1	11	7
2	15	7
3	22	7
4	32	7
5	64	7
6	122	7
7	210	7
8	295	7
9	401	7
10	479	7
11	485	7
0	485	7

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

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

explain169.0ms (1.4%)

FPErrors

Click to see full error table

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

Results

77.0ms	106×	2	valid
37.0ms	184×	1	valid
27.0ms	222×	0	valid

Compiler

Compiled 48 to 20 computations (58.3% saved)

Precisions

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

ival-sqrt: 28.0ms (49.3% of total)

backward-pass: 15.0ms (26.4% of total)

ival-add: 8.0ms (14.1% of total)

ival-sub: 5.0ms (8.8% of total)

const: 1.0ms (1.8% of total)

eval0.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	46.1%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify24.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

124×	`fnmadd-define`
122×	`sum3-define`
80×	`fma-lowering-fma.f32`
80×	`fnmsub-define`
80×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	18
1	11	18
2	15	18
3	22	18
4	32	18
5	64	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize66.0ms (0.5%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	46.1%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

18.0ms	53×	2	valid
18.0ms	111×	0	valid
17.0ms	92×	1	valid

Compiler

Compiled 20 to 7 computations (65% saved)

Precisions

Click to see histograms. Total time spent on operations: 21.0ms

backward-pass: 8.0ms (37.3% of total)

ival-sqrt: 7.0ms (32.6% of total)

ival-add: 3.0ms (14% of total)

ival-sub: 2.0ms (9.3% of total)

const: 1.0ms (4.7% of total)

series5.0ms (0%)

Counts

4 → 48

Calls

Call 1

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

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

Calls

12 calls:

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

rewrite341.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

2088×	`-lowering-.f32`
2088×	`-lowering-.f64`
1794×	`fma-lowering-fma.f32`
1794×	`fma-lowering-fma.f64`
1676×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	39	16
2	303	16
3	3722	16
0	8045	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 220

Calls

Call 1

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

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

simplify296.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

2970×	`-lowering-.f32`
2970×	`-lowering-.f64`
2056×	`+-lowering-+.f64`
2056×	`+-lowering-+.f32`
1514×	`sum3-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	434
1	325	384
2	1039	376
3	3226	373
4	7122	373
0	8132	373

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

Outputs
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(+.f64 #s(literal 1 binary64) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(+.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)))))))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (.f64 #s(literal -5/128 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) x)
(* -1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal -1/16 binary64)))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(/.f64 (+.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal -1/16 binary64)))) (.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) #s(literal 5/128 binary64))) x)
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(+ 1 (* x (+ 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 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(.f64 x (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(.f64 x (+.f64 (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/2 binary64))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -1/2 binary64)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 x (-.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))))
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)
(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)

eval58.0ms (0.5%)

Compiler: Compiled 5806 to 837 computations (85.6% saved)

prune57.0ms (0.5%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	260	8	268
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	260	9	269

Accuracy

100.0%

Counts

269 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	57.6%	(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
▶	48.1%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
▶	46.0%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))
	46.0%	(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 x))
▶	44.9%	(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x))
✓	46.1%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	42.8%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
	44.9%	(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64)))
▶	59.5%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 176 to 130 computations (26.1% saved)

simplify154.0ms (1.3%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

2238×	`sum3-define`
1928×	`fmsub-define`
1810×	`fmm-def`
1808×	`fnmadd-define`
1724×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	20	112
1	43	110
2	82	106
3	146	105
4	274	105
5	505	105
6	953	105
7	1687	105
8	2382	105
9	3106	105
10	5606	105
0	8030	105

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize322.0ms (2.6%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))
✓	accuracy	100.0%	(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
✓	accuracy	99.7%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
✓	accuracy	47.8%	(+.f64 x (-.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
✓	accuracy	46.1%	(-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))

Results

161.0ms	93×	1	valid
62.0ms	51×	2	valid
55.0ms	112×	0	valid

Compiler

Compiled 133 to 21 computations (84.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 79.0ms

ival-pow: 19.0ms (24.2% of total)

backward-pass: 15.0ms (19.1% of total)

ival-div: 12.0ms (15.3% of total)

ival-sub: 9.0ms (11.5% of total)

ival-add: 9.0ms (11.5% of total)

ival-sqrt: 7.0ms (8.9% of total)

ival-mult: 6.0ms (7.6% of total)

const: 1.0ms (1.3% of total)

series16.0ms (0.1%)

Counts

16 → 192

Calls

Call 1

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

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

48 calls:

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

rewrite1.6s (12.8%)

Algorithm

1×	batch-egg-rewrite

Rules

3752×	`/-lowering-/.f32`
3752×	`/-lowering-/.f64`
3558×	`-lowering-.f32`
3558×	`-lowering-.f64`
1954×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	20	80
1	156	76
2	1357	76
0	8647	76

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 904

Calls

Call 1

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

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

simplify358.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

3744×	`+-lowering-+.f64`
3744×	`+-lowering-+.f32`
3430×	`-lowering-.f32`
3430×	`-lowering-.f64`
1412×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	310	1965
1	1004	1678
2	3729	1666
0	8245	1666

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

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

Outputs
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(sqrt (/ 1 x))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(/ 1 x)
(/.f64 #s(literal 1 binary64) x)
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(* -1 (sqrt x))
(-.f64 #s(literal 0 binary64) (sqrt.f64 x))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) x)))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) x)))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) x)))
(* (sqrt x) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 x))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) x)))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) x)))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 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 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(+.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)))
(- (+ 1 (* 1/2 x)) (sqrt x))
(+.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)))
(- (+ 1 (* 1/2 x)) (sqrt x))
(+.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)))
(* x (- 1/2 (sqrt (/ 1 x))))
(*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(+.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(+.f64 #s(literal 1 binary64) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))) (sqrt x))
(+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x)))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))) x)
(/ (+ (* -1/8 (sqrt (/ 1 x))) (+ (* -5/128 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))))) x)
(/.f64 (+.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (.f64 #s(literal -5/128 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) x)
(* -1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (neg.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))) x)
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x)))) x))
(/.f64 (+.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (+ (* -5/128 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 6)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))))) x))
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64)) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (+.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (/.f64 (.f64 #s(literal -5/128 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(/ 1 (- 1 (sqrt x)))
(/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+ (* -1/2 (/ x (pow (- 1 (sqrt x)) 2))) (/ 1 (- 1 (sqrt x))))
(+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (- 1 (sqrt x)) 2))))) (/ 1 (- 1 (sqrt x))))
(+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) (.f64 x (+.f64 (.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (- 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (- 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3)))) (- 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (- 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (- 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (- 1 (sqrt x)) 2))))) (/ 1 (- 1 (sqrt x))))
(+.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) (.f64 x (+.f64 (.f64 x (-.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)))) (.f64 x (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))) (/.f64 (.f64 #s(literal 1/2 binary64) (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))))) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))))))
(* 2 (sqrt x))
(*.f64 #s(literal 2 binary64) (sqrt.f64 x))
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64))))
(* x (- (+ (* -1 (/ (+ (* -1/8 (sqrt (pow x 3))) (* 1/4 (sqrt (pow x 3)))) (pow x 4))) (* 2 (sqrt (/ 1 x)))) (* -1/2 (sqrt (/ 1 (pow x 3))))))
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(* -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 #s(literal 0 binary64) (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (.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)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
(.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (/.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))))))

eval260.0ms (2.1%)

Compiler: Compiled 29222 to 2831 computations (90.3% saved)

prune477.0ms (3.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	1211	11	1222
Fresh	3	0	3
Picked	4	1	5
Done	0	1	1
Total	1218	13	1231

Accuracy

100.0%

Counts

1231 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	57.6%	(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
▶	44.6%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.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.f64 x)))
	44.4%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 x)))
▶	44.7%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x)))
▶	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
▶	52.7%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	59.3%	(/.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))))
▶	59.4%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	46.1%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	42.8%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
	44.9%	(+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) #s(literal 1 binary64))
	59.6%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
	55.5%	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))

Compiler

Compiled 291 to 212 computations (27.1% saved)

simplify166.0ms (1.4%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

1896×	`fma-lowering-fma.f32`
1896×	`fma-lowering-fma.f64`
1894×	`fma-define`
1748×	`fnmadd-define`
1232×	`fnmsub-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	27	180
1	66	166
2	166	158
3	351	156
4	760	156
5	1450	156
6	2549	156
7	4811	156
8	6421	156
0	8051	156

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize283.0ms (2.3%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))
✓	accuracy	99.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
✓	accuracy	99.0%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.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.f64 x)))
✓	accuracy	47.8%	(+.f64 x (-.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.9%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x)))
✓	accuracy	47.8%	(+.f64 x (-.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))
✓	accuracy	100.0%	(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))

Results

172.0ms	133×	1	valid
51.0ms	123×	0	valid

Compiler

Compiled 199 to 28 computations (85.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 90.0ms

backward-pass: 30.0ms (33.3% of total)

ival-add: 19.0ms (21.1% of total)

ival-div: 14.0ms (15.5% of total)

ival-pow: 10.0ms (11.1% of total)

ival-mult: 9.0ms (10% of total)

ival-sqrt: 4.0ms (4.4% of total)

ival-sub: 2.0ms (2.2% of total)

const: 1.0ms (1.1% of total)

series11.0ms (0.1%)

Counts

17 → 204

Calls

Call 1

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

Outputs
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)>
#<alt (/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)>
#<alt (* -1/2 (sqrt (/ 1 x)))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))>
#<alt (* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))>
#<alt (* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) 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))))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 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)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (* 1/2 (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 (+ 1 (sqrt x)))>
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (sqrt (/ 1 x))>
#<alt (/ (- (sqrt x) 1) x)>
#<alt (/ (- (+ (sqrt x) (sqrt (/ 1 x))) 1) x)>
#<alt (/ (- (sqrt x) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (/ 1 x)))) x)>
#<alt (* -1 (sqrt (/ 1 x)))>
#<alt (* -1 (/ (- (sqrt x) (/ 1 (pow (sqrt -1) 2))) x))>
#<alt (* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x))>
#<alt (* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (/ (- (/ x (pow (sqrt -1) 4)) (* -1 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (sqrt x))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (/ 1 x)))>
#<alt (* x (+ (sqrt (/ 1 x)) (/ 1 x)))>
#<alt (* x (+ (sqrt (/ 1 x)) (/ 1 x)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (* 1/4 (/ x (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* -1/8 (/ x (pow (+ 1 (sqrt x)) 4))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (/ 1 (* x (+ 1/2 (sqrt (/ 1 x)))))>
#<alt (/ (- (/ 1 (+ 1/2 (sqrt (/ 1 x)))) (/ 1 (* x (pow (+ 1/2 (sqrt (/ 1 x))) 2)))) x)>
#<alt (/ (- (+ (/ 1 (* (pow x 2) (pow (+ 1/2 (sqrt (/ 1 x))) 3))) (/ 1 (+ 1/2 (sqrt (/ 1 x))))) (/ 1 (* x (pow (+ 1/2 (sqrt (/ 1 x))) 2)))) x)>
#<alt (/ (- (+ (/ 1 (* (pow x 2) (pow (+ 1/2 (sqrt (/ 1 x))) 3))) (/ 1 (+ 1/2 (sqrt (/ 1 x))))) (+ (/ 1 (* x (pow (+ 1/2 (sqrt (/ 1 x))) 2))) (/ 1 (* (pow x 3) (pow (+ 1/2 (sqrt (/ 1 x))) 4))))) x)>
#<alt (/ -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))>
#<alt (* -1 (/ (+ (/ 1 (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 2))) (/ 1 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2))) x))>
#<alt (* -1 (/ (+ (/ 1 (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 2))) (+ (/ 1 (* (pow x 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 3))) (/ 1 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (+ (/ 1 (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 4))) (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 3))) x)) (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 2))) x)) (/ 1 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 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 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (+ (sqrt x) (* 1/2 x)))>
#<alt (+ 1 (+ (sqrt x) (* 1/2 x)))>
#<alt (+ 1 (+ (sqrt x) (* 1/2 x)))>
#<alt (* x (+ 1/2 (sqrt (/ 1 x))))>
#<alt (* x (+ 1/2 (+ (sqrt (/ 1 x)) (/ 1 x))))>
#<alt (* x (+ 1/2 (+ (sqrt (/ 1 x)) (/ 1 x))))>
#<alt (* x (+ 1/2 (+ (sqrt (/ 1 x)) (/ 1 x))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (+ 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (+ 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (+ 1/2 (/ 1 x)))))>
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (/ 16 (pow x 3))>
#<alt (/ (+ 16 (* 32 (/ 1 x))) (pow x 3))>
#<alt (/ (- (+ 16 (+ (* 32 (/ 1 x)) (/ 64 (pow x 2)))) (* 256 (/ (+ 1/2 (sqrt (/ 1 x))) (pow x 2)))) (pow x 3))>
#<alt (/ (- (+ 16 (+ (* -1 (/ (+ 256 (+ (* -2 (- 64 (* 256 (+ 1/2 (sqrt (/ 1 x)))))) (* 512 (+ 1/2 (sqrt (/ 1 x)))))) (pow x 3))) (+ (* 32 (/ 1 x)) (/ 64 (pow x 2))))) (* 256 (/ (+ 1/2 (sqrt (/ 1 x))) (pow x 2)))) (pow x 3))>
#<alt (/ 16 (pow x 3))>
#<alt (/ (+ 16 (* 32 (/ 1 x))) (pow x 3))>
#<alt (* -1 (/ (- (* -1 (/ (+ 32 (+ (* 256 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) x)) (* 64 (/ 1 x)))) x)) 16) (pow x 3)))>
#<alt (* -1 (/ (- (* -1 (/ (+ 32 (* -1 (/ (- (+ (* -512 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) x)) (+ (* -2 (/ (+ 64 (* 256 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2))) x)) (* 256 (/ 1 x)))) (+ 64 (* 256 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))) x))) x)) 16) (pow x 3)))>
#<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 (* 1/16 (pow x 3))>
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/16 (+ (sqrt (/ 1 (pow x 5))) (/ 1/2 (pow x 2)))) (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/16 (+ (sqrt (/ 1 (pow x 5))) (+ (/ 1/2 (pow x 2)) (/ 1 (pow x 3))))) (* 1/8 (/ 1 x))))>
#<alt (* 1/16 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) x)) 1/8) x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (+ 1/2 (/ 1 x))) x)) 1/8) x)) 1/16)))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/8 x)))>
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))>
#<alt (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))>
#<alt (* 1/16 (pow x 3))>
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))>
#<alt (* 1/16 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))>
#<alt (* -1/8 x)>
#<alt (* x (- (* 1/16 x) 1/8))>
#<alt (* x (- (* 1/16 x) 1/8))>
#<alt (* x (- (* 1/16 x) 1/8))>
#<alt (* 1/16 (pow x 2))>
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* 1/16 (pow x 2))>
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))>

Calls

51 calls:

Time	Variable		Point	Expression
1.0ms	x	@	-inf	(/ (+ x (- 1 x)) (+ (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (sqrt x)))
1.0ms	x	@	-inf	(/ 1/2 (sqrt x))
1.0ms	x	@	-inf	(/ (+ x (- 1 x)) (+ (+ 1 (* 1/2 x)) (sqrt x)))
1.0ms	x	@	inf	(/ (+ x (- 1 x)) (+ (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (sqrt x)))
1.0ms	x	@	-inf	(/ 1 (+ 1 (sqrt x)))

rewrite376.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3318×	`-lowering-.f32`
3318×	`-lowering-.f64`
2002×	`fma-lowering-fma.f32`
2002×	`fma-lowering-fma.f64`
1996×	`/-lowering-/.f32`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	122
1	228	115
2	2180	115
0	8285	115

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 596

Calls

Call 1

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

Outputs
(exp.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64)))
(neg.f64 (/.f64 #s(literal -1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) #s(literal -1 binary64))
(pow.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1/2 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1/2 binary64))
(pow.f64 (exp.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64)))
(*.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1/2 binary64)) (pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal -1/2 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)))))) #s(literal -1 binary64)))
(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
(+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(exp.f64 (neg.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64))))
(-.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (/.f64 x (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(fma.f64 #s(literal 1 binary64) (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(fma.f64 (sqrt.f64 x) #s(literal 1 binary64) (sqrt.f64 (+.f64 #s(literal 1 binary64) 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 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1 binary64))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (*.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 x (-.f64 #s(literal 1 binary64) x))) (neg.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64))
(/.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))))
(/.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 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 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)))))))
(/.f64 (neg.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))))))
(/.f64 (-.f64 x (+.f64 #s(literal 1 binary64) x)) (-.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) (.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) x)) (*.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(pow.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x))))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) (+.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal -1 binary64))
(*.f64 (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 1 binary64))
(*.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (/.f64 #s(literal 1 binary64) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))))
(.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 x (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)))))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log1p.f64 x)))
(exp.f64 (*.f64 (log.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (log.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64)))
(exp.f64 (.f64 (.f64 (log1p.f64 x) #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log1p.f64 x) #s(literal 1/4 binary64)) (.f64 (log1p.f64 x) #s(literal 1/4 binary64))))
(hypot.f64 #s(literal 1 binary64) (sqrt.f64 x))
(fabs.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))
(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (+.f64 x #s(literal -1 binary64)) (+.f64 (*.f64 x x) #s(literal -1 binary64)))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x))))
(/.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (+.f64 #s(literal 1 binary64) (-.f64 (*.f64 x x) x))))
(/.f64 (pow.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)) #s(literal 1/2 binary64)) (pow.f64 (+.f64 x #s(literal -1 binary64)) #s(literal 1/2 binary64)))
(/.f64 (sqrt.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (sqrt.f64 (-.f64 #s(literal 1 binary64) x)))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (sqrt.f64 (neg.f64 (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)))))
(/.f64 (sqrt.f64 (neg.f64 (+.f64 (*.f64 x x) #s(literal -1 binary64)))) (sqrt.f64 (neg.f64 (+.f64 x #s(literal -1 binary64)))))
(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) #s(literal 1 binary64))
(pow.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (*.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64))
(pow.f64 (exp.f64 #s(literal 1/2 binary64)) (log1p.f64 x))
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(fma.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) x (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (*.f64 x #s(literal 1/2 binary64)))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))))) (+.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (-.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))))
(/.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
(/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) #s(literal 1/2 binary64)))))
(/.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))) (-.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))
(/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))) x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) #s(literal 1/2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) x) (-.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))
(.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)))))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) x)
(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))
(.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) x)
(+.f64 (.f64 x #s(literal -1/8 binary64)) (.f64 #s(literal 1/16 binary64) (*.f64 x x)))
(+.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (*.f64 x #s(literal -1/8 binary64)))
(fma.f64 x #s(literal -1/8 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x x)))
(fma.f64 x (.f64 x #s(literal 1/16 binary64)) (.f64 x #s(literal -1/8 binary64)))
(fma.f64 #s(literal -1/8 binary64) x (.f64 #s(literal 1/16 binary64) (.f64 x x)))
(fma.f64 #s(literal 1/16 binary64) (.f64 x x) (.f64 x #s(literal -1/8 binary64)))
(fma.f64 (.f64 x #s(literal 1/16 binary64)) x (.f64 x #s(literal -1/8 binary64)))
(fma.f64 (.f64 x x) #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64)))
(/.f64 (+.f64 (.f64 #s(literal -1/512 binary64) (.f64 x (.f64 x x))) (.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/4096 binary64)) (.f64 x (.f64 x x)))) (+.f64 (.f64 (.f64 x #s(literal -1/8 binary64)) (.f64 x #s(literal -1/8 binary64))) (-.f64 (.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (.f64 #s(literal 1/16 binary64) (.f64 x x))) (.f64 (.f64 x #s(literal -1/8 binary64)) (.f64 #s(literal 1/16 binary64) (*.f64 x x))))))
(/.f64 (-.f64 (.f64 (.f64 x #s(literal -1/8 binary64)) (.f64 x #s(literal -1/8 binary64))) (.f64 (.f64 #s(literal 1/16 binary64) (.f64 x x)) (.f64 #s(literal 1/16 binary64) (.f64 x x)))) (-.f64 (.f64 x #s(literal -1/8 binary64)) (.f64 #s(literal 1/16 binary64) (*.f64 x x))))
(/.f64 (.f64 x (+.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/4096 binary64)))) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x #s(literal 1/16 binary64)) (-.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))))
(/.f64 (.f64 x (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal 1/256 binary64)))) (+.f64 #s(literal -1/8 binary64) (.f64 #s(literal -1/16 binary64) x)))
(/.f64 (.f64 (+.f64 #s(literal -1/512 binary64) (.f64 (.f64 x (.f64 x x)) #s(literal 1/4096 binary64))) x) (+.f64 #s(literal 1/64 binary64) (.f64 (.f64 x #s(literal 1/16 binary64)) (-.f64 (*.f64 x #s(literal 1/16 binary64)) #s(literal -1/8 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/64 binary64) (.f64 (.f64 x x) #s(literal 1/256 binary64))) x) (+.f64 #s(literal -1/8 binary64) (.f64 #s(literal -1/16 binary64) x)))
(.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))
(.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) x)

simplify259.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

4260×	`-lowering-.f32`
4260×	`-lowering-.f64`
2054×	`+-lowering-+.f64`
2054×	`+-lowering-+.f32`
1642×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	407	2250
1	1307	1972
2	4496	1934
0	8310	1934

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
(/ 1 (+ 1 (sqrt x)))
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))
(+ 1 (sqrt x))
(+ 1 (+ (sqrt x) (* 1/2 x)))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))
(* 2 (sqrt x))
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* 1/2 (sqrt (/ 1 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)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (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 (sqrt x)))
(/ 1 (+ 1 (sqrt x)))
(/ 1 (+ 1 (sqrt x)))
(/ 1 (+ 1 (sqrt x)))
(sqrt (/ 1 x))
(/ (- (sqrt x) 1) x)
(/ (- (+ (sqrt x) (sqrt (/ 1 x))) 1) x)
(/ (- (sqrt x) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (/ 1 x)))) x)
(* -1 (sqrt (/ 1 x)))
(* -1 (/ (- (sqrt x) (/ 1 (pow (sqrt -1) 2))) x))
(* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x))
(* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (/ (- (/ x (pow (sqrt -1) 4)) (* -1 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x))
(+ 1 (sqrt x))
(+ 1 (sqrt x))
(+ 1 (sqrt x))
(+ 1 (sqrt x))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(/ 1 (+ 1 (sqrt x)))
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* 1/4 (/ x (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* x (+ (* -1/8 (/ x (pow (+ 1 (sqrt x)) 4))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(/ 1 (* x (+ 1/2 (sqrt (/ 1 x)))))
(/ (- (/ 1 (+ 1/2 (sqrt (/ 1 x)))) (/ 1 (* x (pow (+ 1/2 (sqrt (/ 1 x))) 2)))) x)
(/ (- (+ (/ 1 (* (pow x 2) (pow (+ 1/2 (sqrt (/ 1 x))) 3))) (/ 1 (+ 1/2 (sqrt (/ 1 x))))) (/ 1 (* x (pow (+ 1/2 (sqrt (/ 1 x))) 2)))) x)
(/ (- (+ (/ 1 (* (pow x 2) (pow (+ 1/2 (sqrt (/ 1 x))) 3))) (/ 1 (+ 1/2 (sqrt (/ 1 x))))) (+ (/ 1 (* x (pow (+ 1/2 (sqrt (/ 1 x))) 2))) (/ 1 (* (pow x 3) (pow (+ 1/2 (sqrt (/ 1 x))) 4))))) x)
(/ -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))
(* -1 (/ (+ (/ 1 (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 2))) (/ 1 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2))) x))
(* -1 (/ (+ (/ 1 (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 2))) (+ (/ 1 (* (pow x 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 3))) (/ 1 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))) x))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (+ (/ 1 (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 4))) (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 3))) x)) (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 2))) x)) (/ 1 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2))) x))
1
1
1
1
1
1
1
1
1
1
1
1
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(+ 1 (sqrt x))
(+ 1 (+ (sqrt x) (* 1/2 x)))
(+ 1 (+ (sqrt x) (* 1/2 x)))
(+ 1 (+ (sqrt x) (* 1/2 x)))
(* x (+ 1/2 (sqrt (/ 1 x))))
(* x (+ 1/2 (+ (sqrt (/ 1 x)) (/ 1 x))))
(* x (+ 1/2 (+ (sqrt (/ 1 x)) (/ 1 x))))
(* x (+ 1/2 (+ (sqrt (/ 1 x)) (/ 1 x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (+ 1/2 (/ 1 x)))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (+ 1/2 (/ 1 x)))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (+ 1/2 (/ 1 x)))))
(/ 1 (+ 1 (sqrt x)))
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(/ 16 (pow x 3))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 3))
(/ (- (+ 16 (+ (* 32 (/ 1 x)) (/ 64 (pow x 2)))) (* 256 (/ (+ 1/2 (sqrt (/ 1 x))) (pow x 2)))) (pow x 3))
(/ (- (+ 16 (+ (* -1 (/ (+ 256 (+ (* -2 (- 64 (* 256 (+ 1/2 (sqrt (/ 1 x)))))) (* 512 (+ 1/2 (sqrt (/ 1 x)))))) (pow x 3))) (+ (* 32 (/ 1 x)) (/ 64 (pow x 2))))) (* 256 (/ (+ 1/2 (sqrt (/ 1 x))) (pow x 2)))) (pow x 3))
(/ 16 (pow x 3))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 3))
(* -1 (/ (- (* -1 (/ (+ 32 (+ (* 256 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) x)) (* 64 (/ 1 x)))) x)) 16) (pow x 3)))
(* -1 (/ (- (* -1 (/ (+ 32 (* -1 (/ (- (+ (* -512 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) x)) (+ (* -2 (/ (+ 64 (* 256 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2))) x)) (* 256 (/ 1 x)))) (+ 64 (* 256 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))) x))) x)) 16) (pow x 3)))
(+ 1 (sqrt x))
(+ 1 (+ (sqrt x) (* 1/2 x)))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))
(* 1/16 (pow x 3))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (+ (sqrt (/ 1 (pow x 5))) (/ 1/2 (pow x 2)))) (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (+ (sqrt (/ 1 (pow x 5))) (+ (/ 1/2 (pow x 2)) (/ 1 (pow x 3))))) (* 1/8 (/ 1 x))))
(* 1/16 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) x)) 1/8) x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (+ 1/2 (/ 1 x))) x)) 1/8) x)) 1/16)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* 1/16 (pow x 3))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(* 1/16 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
(* -1/8 x)
(* x (- (* 1/16 x) 1/8))
(* x (- (* 1/16 x) 1/8))
(* x (- (* 1/16 x) 1/8))
(* 1/16 (pow x 2))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(* 1/16 (pow x 2))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))

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

eval131.0ms (1.1%)

Compiler: Compiled 31861 to 2807 computations (91.2% saved)

prune144.0ms (1.2%)

Pruning

19 alts after pruning (15 fresh and 4 done)

	Pruned	Kept	Total
New	984	12	996
Fresh	3	3	6
Picked	3	2	5
Done	0	2	2
Total	990	19	1009

Accuracy

100.0%

Counts

1009 → 19

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	4.3%	(/.f64 (/.f64 #s(literal 16 binary64) (*.f64 x x)) x)
	57.6%	(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
▶	43.1%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))))
▶	2.7%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
	4.0%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x))))
	4.2%	(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (.f64 x (.f64 x x)))
	44.9%	(/.f64 #s(literal 1 binary64) (+.f64 (+.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.f64 x)))
	44.1%	(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 x)))
▶	46.3%	(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x)))
▶	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
✓	52.7%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	59.3%	(/.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))))
	59.2%	(/.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)))
✓	59.4%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
	55.5%	(/.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
✓	46.1%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	42.8%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
	44.9%	(+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) #s(literal 1 binary64))
	59.6%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))

Compiler

Compiled 511 to 321 computations (37.2% saved)

simplify187.0ms (1.5%)

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	384	(.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal 1 binary64))
✓	cost-diff	640	(+.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))))
✓	cost-diff	1024	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64)))
✓	cost-diff	1408	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))))
✓	cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	0	(+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x)))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) x)
✓	cost-diff	128	(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
✓	cost-diff	256	(+.f64 x (-.f64 #s(literal 1 binary64) x))
✓	cost-diff	384	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(/.f64 #s(literal 16 binary64) (*.f64 x x))
✓	cost-diff	0	(/.f64 (/.f64 #s(literal 16 binary64) (*.f64 x x)) x)
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))

Rules

2768×	`-lowering-.f32`
2768×	`-lowering-.f64`
2140×	`+-lowering-+.f64`
2140×	`+-lowering-+.f32`
1288×	`--lowering--.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	41	354
1	129	334
2	503	324
3	2342	305
4	7678	304
0	8226	304

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

Inputs
(/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))
1
(+ (sqrt (+ 1 x)) (sqrt x))
(sqrt (+ 1 x))
(+ 1 x)
x
(sqrt x)
(/ (/ 16 (* x x)) x)
(/ 16 (* x x))
16
(* x x)
x
(/ (+ x (- 1 x)) (* (* x (* x x)) (+ 1/16 (/ -1/8 x))))
(+ x (- 1 x))
x
(- 1 x)
1
(* (* x (* x x)) (+ 1/16 (/ -1/8 x)))
(* x (* x x))
(* x x)
(+ 1/16 (/ -1/8 x))
1/16
(/ -1/8 x)
-1/8
(/ 1 (+ (+ 1 (* x 1/2)) (sqrt x)))
1
(+ (+ 1 (* x 1/2)) (sqrt x))
(+ 1 (* x 1/2))
(* x 1/2)
x
1/2
(sqrt x)
(/ (+ x (- 1 x)) (/ (+ (* (- (* (* x x) 1/4) (* (* x (* x (+ -1/8 (* x 1/16)))) (* x (* x (+ -1/8 (* x 1/16)))))) 1) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) (+ 1 (sqrt x)))) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) 1)))
(+ x (- 1 x))
x
(- 1 x)
1
(/ (+ (* (- (* (* x x) 1/4) (* (* x (* x (+ -1/8 (* x 1/16)))) (* x (* x (+ -1/8 (* x 1/16)))))) 1) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) (+ 1 (sqrt x)))) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) 1))
(+ (* (- (* (* x x) 1/4) (* (* x (* x (+ -1/8 (* x 1/16)))) (* x (* x (+ -1/8 (* x 1/16)))))) 1) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) (+ 1 (sqrt x))))
(* (- (* (* x x) 1/4) (* (* x (* x (+ -1/8 (* x 1/16)))) (* x (* x (+ -1/8 (* x 1/16)))))) 1)
(- (* (* x x) 1/4) (* (* x (* x (+ -1/8 (* x 1/16)))) (* x (* x (+ -1/8 (* x 1/16))))))
(* (* x x) 1/4)
(* x x)
1/4
(* (* x (* x (+ -1/8 (* x 1/16)))) (* x (* x (+ -1/8 (* x 1/16)))))
(* x (* x (+ -1/8 (* x 1/16))))
(* x (+ -1/8 (* x 1/16)))
(+ -1/8 (* x 1/16))
-1/8
(* x 1/16)
1/16
(* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) (+ 1 (sqrt x)))
(- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16)))))
(* x 1/2)
1/2
(+ 1 (sqrt x))
(sqrt x)
(* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) 1)

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

localize411.0ms (3.4%)

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.0%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))))
✓	accuracy	73.4%	(-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))
✓	accuracy	61.5%	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64)))
✓	accuracy	47.8%	(+.f64 x (-.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.9%	(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x)))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	99.0%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
✓	accuracy	93.6%	(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
✓	accuracy	47.8%	(+.f64 x (-.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(/.f64 (/.f64 #s(literal 16 binary64) (*.f64 x x)) x)
✓	accuracy	99.0%	(/.f64 #s(literal 16 binary64) (*.f64 x x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 #s(literal 1 binary64) x))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))

Results

205.0ms	133×	1	valid
85.0ms	123×	0	valid

Compiler

Compiled 481 to 42 computations (91.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 110.0ms

ival-mult: 28.0ms (25.4% of total)

ival-div: 22.0ms (20% of total)

backward-pass: 22.0ms (20% of total)

ival-add: 18.0ms (16.4% of total)

ival-sqrt: 12.0ms (10.9% of total)

ival-sub: 6.0ms (5.5% of total)

const: 2.0ms (1.8% of total)

series19.0ms (0.2%)

Counts

22 → 264

Calls

Call 1

Inputs
#<alt (/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))>
#<alt (+ (sqrt (+ 1 x)) (sqrt x))>
#<alt (sqrt (+ 1 x))>
#<alt (+ 1 x)>
#<alt (/ (/ 16 (* x x)) x)>
#<alt (/ 16 (* x x))>
#<alt (* x x)>
#<alt (/ (+ x (- 1 x)) (* (* x (* x x)) (+ 1/16 (/ -1/8 x))))>
#<alt (+ x (- 1 x))>
#<alt (* (* x (* x x)) (+ 1/16 (/ -1/8 x)))>
#<alt (- 1 x)>
#<alt (/ 1 (+ (+ 1 (* x 1/2)) (sqrt x)))>
#<alt (+ (+ 1 (* x 1/2)) (sqrt x))>
#<alt (+ 1 (* x 1/2))>
#<alt (* x 1/2)>
#<alt (/ (+ x (- 1 x)) (/ (+ (* (- (* (* x x) 1/4) (* (* x (* x (+ -1/8 (* x 1/16)))) (* x (* x (+ -1/8 (* x 1/16)))))) 1) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) (+ 1 (sqrt x)))) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) 1)))>
#<alt (/ (+ (* (- (* (* x x) 1/4) (* (* x (* x (+ -1/8 (* x 1/16)))) (* x (* x (+ -1/8 (* x 1/16)))))) 1) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) (+ 1 (sqrt x)))) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) 1))>
#<alt (+ (* (- (* (* x x) 1/4) (* (* x (* x (+ -1/8 (* x 1/16)))) (* x (* x (+ -1/8 (* x 1/16)))))) 1) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) (+ 1 (sqrt x))))>
#<alt (* (- (* (* x x) 1/4) (* (* x (* x (+ -1/8 (* x 1/16)))) (* x (* x (+ -1/8 (* x 1/16)))))) 1)>
#<alt (sqrt x)>
#<alt (* x (* x x))>
#<alt (- (* (* x x) 1/4) (* (* x (* x (+ -1/8 (* x 1/16)))) (* x (* x (+ -1/8 (* x 1/16))))))>

Outputs
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)>
#<alt (/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)>
#<alt (* -1/2 (sqrt (/ 1 x)))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))>
#<alt (* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))>
#<alt (* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) 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))))))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt 1>
#<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 (/ 16 (pow x 3))>
#<alt (/ 16 (pow x 3))>
#<alt (/ 16 (pow x 3))>
#<alt (/ 16 (pow x 3))>
#<alt (/ 16 (pow x 3))>
#<alt (/ 16 (pow x 3))>
#<alt (/ 16 (pow x 3))>
#<alt (/ 16 (pow x 3))>
#<alt (/ 16 (pow x 3))>
#<alt (/ 16 (pow x 3))>
#<alt (/ 16 (pow x 3))>
#<alt (/ 16 (pow x 3))>
#<alt (/ 16 (pow x 2))>
#<alt (/ 16 (pow x 2))>
#<alt (/ 16 (pow x 2))>
#<alt (/ 16 (pow x 2))>
#<alt (/ 16 (pow x 2))>
#<alt (/ 16 (pow x 2))>
#<alt (/ 16 (pow x 2))>
#<alt (/ 16 (pow x 2))>
#<alt (/ 16 (pow x 2))>
#<alt (/ 16 (pow x 2))>
#<alt (/ 16 (pow x 2))>
#<alt (/ 16 (pow x 2))>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (pow x 2)>
#<alt (/ -8 (pow x 2))>
#<alt (/ (- (* -4 x) 8) (pow x 2))>
#<alt (/ (- (* x (- (* -2 x) 4)) 8) (pow x 2))>
#<alt (/ (- (* x (- (* x (- (* -1 x) 2)) 4)) 8) (pow x 2))>
#<alt (/ 16 (pow x 3))>
#<alt (/ (+ 16 (* 32 (/ 1 x))) (pow x 3))>
#<alt (/ (+ 16 (+ (* 32 (/ 1 x)) (/ 64 (pow x 2)))) (pow x 3))>
#<alt (/ (+ 16 (+ (* 32 (/ 1 x)) (+ (* 128 (/ 1 (pow x 3))) (/ 64 (pow x 2))))) (pow x 3))>
#<alt (/ 16 (pow x 3))>
#<alt (/ (+ 16 (* 32 (/ 1 x))) (pow x 3))>
#<alt (* -1 (/ (- (* -1 (/ (+ 32 (* 64 (/ 1 x))) x)) 16) (pow x 3)))>
#<alt (* -1 (/ (- (* -1 (/ (+ 32 (+ (* 64 (/ 1 x)) (/ 128 (pow x 2)))) x)) 16) (pow x 3)))>
#<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 (* -1/8 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/16 x) 1/8))>
#<alt (* (pow x 2) (- (* 1/16 x) 1/8))>
#<alt (* (pow x 2) (- (* 1/16 x) 1/8))>
#<alt (* 1/16 (pow x 3))>
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* 1/16 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (* 1/4 (/ x (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* -1/8 (/ x (pow (+ 1 (sqrt x)) 4))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (/ 1 (* x (+ 1/2 (sqrt (/ 1 x)))))>
#<alt (/ (- (/ 1 (+ 1/2 (sqrt (/ 1 x)))) (/ 1 (* x (pow (+ 1/2 (sqrt (/ 1 x))) 2)))) x)>
#<alt (/ (- (+ (/ 1 (* (pow x 2) (pow (+ 1/2 (sqrt (/ 1 x))) 3))) (/ 1 (+ 1/2 (sqrt (/ 1 x))))) (/ 1 (* x (pow (+ 1/2 (sqrt (/ 1 x))) 2)))) x)>
#<alt (/ (- (+ (/ 1 (* (pow x 2) (pow (+ 1/2 (sqrt (/ 1 x))) 3))) (/ 1 (+ 1/2 (sqrt (/ 1 x))))) (+ (/ 1 (* x (pow (+ 1/2 (sqrt (/ 1 x))) 2))) (/ 1 (* (pow x 3) (pow (+ 1/2 (sqrt (/ 1 x))) 4))))) x)>
#<alt (/ -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))>
#<alt (* -1 (/ (+ (/ 1 (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 2))) (/ 1 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2))) x))>
#<alt (* -1 (/ (+ (/ 1 (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 2))) (+ (/ 1 (* (pow x 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 3))) (/ 1 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (- (* -1 (/ (+ (/ 1 (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 4))) (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 3))) x)) (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 2))) x)) (/ 1 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2))) x))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (+ (sqrt x) (* 1/2 x)))>
#<alt (+ 1 (+ (sqrt x) (* 1/2 x)))>
#<alt (+ 1 (+ (sqrt x) (* 1/2 x)))>
#<alt (* x (+ 1/2 (sqrt (/ 1 x))))>
#<alt (* x (+ 1/2 (+ (sqrt (/ 1 x)) (/ 1 x))))>
#<alt (* x (+ 1/2 (+ (sqrt (/ 1 x)) (/ 1 x))))>
#<alt (* x (+ 1/2 (+ (sqrt (/ 1 x)) (/ 1 x))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (+ 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (+ 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (+ 1/2 (/ 1 x)))))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* 1/2 x))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* x (+ 1/2 (/ 1 x)))>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (* 1/2 x)>
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (+ (* x (- (* 1/4 (/ 1 (+ 1 (sqrt x)))) (* 2 (/ (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (+ (* 1/4 (/ 1 (+ 1 (sqrt x)))) (* x (- (* 1/8 (/ 1 (+ 1 (sqrt x)))) (+ (* 1/8 (/ 1 (+ 1 (sqrt x)))) (* 2 (/ (* (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (- (* 1/4 (/ 1 (+ 1 (sqrt x)))) (* 2 (/ (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x)))))))) (* 2 (/ (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (+ (* 1/4 (/ 1 (+ 1 (sqrt x)))) (* x (- (* x (- (* 1/32 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* -1/8 (- (* 1/4 (/ 1 (+ 1 (sqrt x)))) (* 2 (/ (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (pow (+ 1 (sqrt x)) 2))))) (* 2 (/ (* (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (- (* 1/8 (/ 1 (+ 1 (sqrt x)))) (+ (* 1/8 (/ 1 (+ 1 (sqrt x)))) (* 2 (/ (* (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (- (* 1/4 (/ 1 (+ 1 (sqrt x)))) (* 2 (/ (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x))))))) (+ 1 (sqrt x))))))) (* 2 (/ (* (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (- (* 1/4 (/ 1 (+ 1 (sqrt x)))) (* 2 (/ (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x))))))) (* 2 (/ (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (/ 16 (pow x 3))>
#<alt (/ (+ 16 (* 32 (/ 1 x))) (pow x 3))>
#<alt (/ (+ 16 (+ (* 4096 (/ (- (* -1/16 (sqrt (/ 1 x))) 1/64) (pow x 2))) (* 32 (/ 1 x)))) (pow x 3))>
#<alt (/ (- (+ 16 (+ (* -1 (/ (+ (* -16384 (- (* -1/16 (sqrt (/ 1 x))) 1/64)) (+ (* -8192 (- (* -1/16 (sqrt (/ 1 x))) 1/64)) (* -4096 (- (* 1/8 (sqrt (/ 1 x))) 1/16)))) (pow x 3))) (* 32 (/ 1 x)))) (* -4096 (/ (- (* -1/16 (sqrt (/ 1 x))) 1/64) (pow x 2)))) (pow x 3))>
#<alt (/ 16 (pow x 3))>
#<alt (/ (+ 16 (* 32 (/ 1 x))) (pow x 3))>
#<alt (* -1 (/ (- (* -1 (/ (+ 32 (* 4096 (/ (- (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 1/64) x))) x)) 16) (pow x 3)))>
#<alt (* -1 (/ (- (* -1 (/ (+ 32 (* -1 (/ (+ (* -4096 (- (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 1/64)) (* -1 (/ (+ (* 4096 (- (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 1/16)) (+ (* 8192 (- (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 1/64)) (* 16384 (- (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 1/64)))) x))) x))) x)) 16) (pow x 3)))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (+ (sqrt x) (* x (- (* 2 (+ 1/4 (* 1/8 (+ 1 (sqrt x))))) (* 1/4 (+ 1 (sqrt x)))))))>
#<alt (+ 1 (+ (sqrt x) (* x (- (+ (* -1/4 (* x (- (* 2 (+ 1/4 (* 1/8 (+ 1 (sqrt x))))) (* 1/4 (+ 1 (sqrt x)))))) (* 2 (+ 1/4 (* 1/8 (+ 1 (sqrt x)))))) (* 1/4 (+ 1 (sqrt x)))))))>
#<alt (+ 1 (+ (sqrt x) (* x (- (+ (* 2 (+ 1/4 (* 1/8 (+ 1 (sqrt x))))) (* x (- (* -1 (* x (+ 1/32 (+ (* -1/8 (- (* 2 (+ 1/4 (* 1/8 (+ 1 (sqrt x))))) (* 1/4 (+ 1 (sqrt x))))) (* -1/16 (- (* 2 (+ 1/4 (* 1/8 (+ 1 (sqrt x))))) (* 1/4 (+ 1 (sqrt x))))))))) (* 1/4 (- (* 2 (+ 1/4 (* 1/8 (+ 1 (sqrt x))))) (* 1/4 (+ 1 (sqrt x)))))))) (* 1/4 (+ 1 (sqrt x)))))))>
#<alt (* 1/16 (pow x 3))>
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/16 (+ (* -16 (/ (- (* -1/16 (sqrt (/ 1 x))) 1/64) (pow x 2))) (/ 1/4 (pow x 2)))) (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/16 (+ (* -16 (/ (- (* -1/16 (sqrt (/ 1 x))) 1/64) (pow x 2))) (+ (* -16 (/ (- (* 1/8 (sqrt (/ 1 x))) 1/16) (pow x 3))) (/ 1/4 (pow x 2))))) (+ (* -2 (/ (+ 1/4 (* -16 (- (* -1/16 (sqrt (/ 1 x))) 1/64))) (pow x 3))) (+ (* 1/8 (/ 1 x)) (/ 1 (pow x 3))))))>
#<alt (* 1/16 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* -16 (/ (- (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 1/64) x)) (* 1/4 (/ 1 x))) 1/8) x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (+ 1/4 (* -16 (- (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 1/64)))) (+ (* 16 (/ (- (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 1/16) x)) (/ 1 x))) (* 2 (/ (+ 1/4 (* -16 (- (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 1/64))) x))) x)) 1/8) x)) 1/16)))>
#<alt (* 1/2 (* x (+ 1 (sqrt x))))>
#<alt (* x (+ (* 1/2 (+ 1 (sqrt x))) (* x (+ 1/4 (* 1/8 (+ 1 (sqrt x)))))))>
#<alt (* x (+ (* 1/2 (+ 1 (sqrt x))) (* x (+ 1/4 (+ (* -1/16 (* x (+ 1 (sqrt x)))) (* 1/8 (+ 1 (sqrt x))))))))>
#<alt (* x (+ (* 1/2 (+ 1 (sqrt x))) (* x (+ 1/4 (+ (* 1/8 (+ 1 (sqrt x))) (* x (+ (* -1/16 (+ 1 (sqrt x))) (* -1/64 x))))))))>
#<alt (* -1/256 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/64 (/ 1 x)) 1/256))>
#<alt (* (pow x 6) (- (+ (* -1/16 (sqrt (/ 1 (pow x 5)))) (* 1/64 (/ 1 x))) (+ 1/256 (/ 1/64 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ (* -1/16 (sqrt (/ 1 (pow x 5)))) (+ (* 1/8 (sqrt (/ 1 (pow x 7)))) (* 1/64 (/ 1 x)))) (+ 1/256 (+ (/ 1/64 (pow x 2)) (* 1/16 (/ 1 (pow x 3)))))))>
#<alt (* -1/256 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/64 (/ 1 x)) 1/256))>
#<alt (* (pow x 6) (- (* -1 (/ (- (* -1 (/ (- (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 1/64) x)) 1/64) x)) 1/256))>
#<alt (* (pow x 6) (- (* -1 (/ (- (* -1 (/ (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ 1/64 (* 1/16 (/ 1 x)))) x)) 1/64) x)) 1/256))>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (+ 1/4 (* -1/64 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/64 x) 1/64))))>
#<alt (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* x (+ 1/64 (* -1/256 x))) 1/64))))>
#<alt (* -1/256 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/64 (/ 1 x)) 1/256))>
#<alt (* (pow x 6) (- (* 1/64 (/ 1 x)) (+ 1/256 (/ 1/64 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ (* 1/64 (/ 1 x)) (* 1/4 (/ 1 (pow x 4)))) (+ 1/256 (/ 1/64 (pow x 2)))))>
#<alt (* -1/256 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/64 (/ 1 x)) 1/256))>
#<alt (* (pow x 6) (- (* -1 (/ (- (* 1/64 (/ 1 x)) 1/64) x)) 1/256))>
#<alt (* (pow x 6) (- (* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/64) x)) 1/64) x)) 1/256))>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (sqrt x)>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (pow x 3)>
#<alt (* 1/4 (pow x 2))>
#<alt (* (pow x 2) (+ 1/4 (* -1/64 (pow x 2))))>
#<alt (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/64 x) 1/64))))>
#<alt (* (pow x 2) (+ 1/4 (* (pow x 2) (- (* x (+ 1/64 (* -1/256 x))) 1/64))))>
#<alt (* -1/256 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/64 (/ 1 x)) 1/256))>
#<alt (* (pow x 6) (- (* 1/64 (/ 1 x)) (+ 1/256 (/ 1/64 (pow x 2)))))>
#<alt (* (pow x 6) (- (+ (* 1/64 (/ 1 x)) (* 1/4 (/ 1 (pow x 4)))) (+ 1/256 (/ 1/64 (pow x 2)))))>
#<alt (* -1/256 (pow x 6))>
#<alt (* (pow x 6) (- (* 1/64 (/ 1 x)) 1/256))>
#<alt (* (pow x 6) (- (* -1 (/ (- (* 1/64 (/ 1 x)) 1/64) x)) 1/256))>
#<alt (* (pow x 6) (- (* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/64) x)) 1/64) x)) 1/256))>

Calls

66 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))
1.0ms	x	@	0	(/ (+ x (- 1 x)) (/ (+ (* (- (* (* x x) 1/4) (* (* x (* x (+ -1/8 (* x 1/16)))) (* x (* x (+ -1/8 (* x 1/16)))))) 1) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) (+ 1 (sqrt x)))) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) 1)))
1.0ms	x	@	-inf	(/ (+ x (- 1 x)) (/ (+ (* (- (* (* x x) 1/4) (* (* x (* x (+ -1/8 (* x 1/16)))) (* x (* x (+ -1/8 (* x 1/16)))))) 1) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) (+ 1 (sqrt x)))) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) 1)))
1.0ms	x	@	inf	(/ (+ x (- 1 x)) (/ (+ (* (- (* (* x x) 1/4) (* (* x (* x (+ -1/8 (* x 1/16)))) (* x (* x (+ -1/8 (* x 1/16)))))) 1) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) (+ 1 (sqrt x)))) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) 1)))
1.0ms	x	@	0	(/ (/ 16 (* x x)) x)

rewrite333.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

2948×	`-lowering-.f32`
2948×	`-lowering-.f64`
1560×	`sum4-define`
1422×	`pow-lowering-pow.f64`
1422×	`pow-lowering-pow.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	239
1	327	225
2	3334	221
0	8238	221

Stop Event

1×	iter limit
1×	node limit

Counts

22 → 583

Calls

Call 1

Inputs
(/ 1 (+ (sqrt (+ 1 x)) (sqrt x)))
(+ (sqrt (+ 1 x)) (sqrt x))
(sqrt (+ 1 x))
(+ 1 x)
(/ (/ 16 (* x x)) x)
(/ 16 (* x x))
(* x x)
(/ (+ x (- 1 x)) (* (* x (* x x)) (+ 1/16 (/ -1/8 x))))
(+ x (- 1 x))
(* (* x (* x x)) (+ 1/16 (/ -1/8 x)))
(- 1 x)
(/ 1 (+ (+ 1 (* x 1/2)) (sqrt x)))
(+ (+ 1 (* x 1/2)) (sqrt x))
(+ 1 (* x 1/2))
(* x 1/2)
(/ (+ x (- 1 x)) (/ (+ (* (- (* (* x x) 1/4) (* (* x (* x (+ -1/8 (* x 1/16)))) (* x (* x (+ -1/8 (* x 1/16)))))) 1) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) (+ 1 (sqrt x)))) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) 1)))
(/ (+ (* (- (* (* x x) 1/4) (* (* x (* x (+ -1/8 (* x 1/16)))) (* x (* x (+ -1/8 (* x 1/16)))))) 1) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) (+ 1 (sqrt x)))) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) 1))
(+ (* (- (* (* x x) 1/4) (* (* x (* x (+ -1/8 (* x 1/16)))) (* x (* x (+ -1/8 (* x 1/16)))))) 1) (* (- (* x 1/2) (* x (* x (+ -1/8 (* x 1/16))))) (+ 1 (sqrt x))))
(* (- (* (* x x) 1/4) (* (* x (* x (+ -1/8 (* x 1/16)))) (* x (* x (+ -1/8 (* x 1/16)))))) 1)
(sqrt x)
(* x (* x x))
(- (* (* x x) 1/4) (* (* x (* x (+ -1/8 (* x 1/16)))) (* x (* x (+ -1/8 (* x 1/16))))))

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

simplify343.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

4296×	`-lowering-.f32`
4296×	`-lowering-.f64`
3140×	`+-lowering-+.f64`
3140×	`+-lowering-+.f32`
1538×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	591	3181
1	1920	2743
2	6670	2728
0	8418	2728

Stop Event

1×	iter limit
1×	node limit

Counts

264 → 264

Calls

Call 1

Inputs
(/ 1 (+ 1 (sqrt x)))
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))
(+ 1 (sqrt x))
(+ 1 (+ (sqrt x) (* 1/2 x)))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))
(* 2 (sqrt x))
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
1
(+ 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)))
(/ 16 (pow x 3))
(/ 16 (pow x 3))
(/ 16 (pow x 3))
(/ 16 (pow x 3))
(/ 16 (pow x 3))
(/ 16 (pow x 3))
(/ 16 (pow x 3))
(/ 16 (pow x 3))
(/ 16 (pow x 3))
(/ 16 (pow x 3))
(/ 16 (pow x 3))
(/ 16 (pow x 3))
(/ 16 (pow x 2))
(/ 16 (pow x 2))
(/ 16 (pow x 2))
(/ 16 (pow x 2))
(/ 16 (pow x 2))
(/ 16 (pow x 2))
(/ 16 (pow x 2))
(/ 16 (pow x 2))
(/ 16 (pow x 2))
(/ 16 (pow x 2))
(/ 16 (pow x 2))
(/ 16 (pow x 2))
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(/ -8 (pow x 2))
(/ (- (* -4 x) 8) (pow x 2))
(/ (- (* x (- (* -2 x) 4)) 8) (pow x 2))
(/ (- (* x (- (* x (- (* -1 x) 2)) 4)) 8) (pow x 2))
(/ 16 (pow x 3))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 3))
(/ (+ 16 (+ (* 32 (/ 1 x)) (/ 64 (pow x 2)))) (pow x 3))
(/ (+ 16 (+ (* 32 (/ 1 x)) (+ (* 128 (/ 1 (pow x 3))) (/ 64 (pow x 2))))) (pow x 3))
(/ 16 (pow x 3))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 3))
(* -1 (/ (- (* -1 (/ (+ 32 (* 64 (/ 1 x))) x)) 16) (pow x 3)))
(* -1 (/ (- (* -1 (/ (+ 32 (+ (* 64 (/ 1 x)) (/ 128 (pow x 2)))) x)) 16) (pow x 3)))
1
1
1
1
1
1
1
1
1
1
1
1
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/16 x) 1/8))
(* (pow x 2) (- (* 1/16 x) 1/8))
(* (pow x 2) (- (* 1/16 x) 1/8))
(* 1/16 (pow x 3))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* 1/16 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(/ 1 (+ 1 (sqrt x)))
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* 1/4 (/ x (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* x (+ (* -1/8 (/ x (pow (+ 1 (sqrt x)) 4))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(/ 1 (* x (+ 1/2 (sqrt (/ 1 x)))))
(/ (- (/ 1 (+ 1/2 (sqrt (/ 1 x)))) (/ 1 (* x (pow (+ 1/2 (sqrt (/ 1 x))) 2)))) x)
(/ (- (+ (/ 1 (* (pow x 2) (pow (+ 1/2 (sqrt (/ 1 x))) 3))) (/ 1 (+ 1/2 (sqrt (/ 1 x))))) (/ 1 (* x (pow (+ 1/2 (sqrt (/ 1 x))) 2)))) x)
(/ (- (+ (/ 1 (* (pow x 2) (pow (+ 1/2 (sqrt (/ 1 x))) 3))) (/ 1 (+ 1/2 (sqrt (/ 1 x))))) (+ (/ 1 (* x (pow (+ 1/2 (sqrt (/ 1 x))) 2))) (/ 1 (* (pow x 3) (pow (+ 1/2 (sqrt (/ 1 x))) 4))))) x)
(/ -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))
(* -1 (/ (+ (/ 1 (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 2))) (/ 1 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2))) x))
(* -1 (/ (+ (/ 1 (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 2))) (+ (/ 1 (* (pow x 2) (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 3))) (/ 1 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))) x))
(* -1 (/ (+ (* -1 (/ (- (* -1 (/ (+ (/ 1 (* x (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 4))) (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 3))) x)) (/ 1 (pow (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) 2))) x)) (/ 1 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2))) x))
(+ 1 (sqrt x))
(+ 1 (+ (sqrt x) (* 1/2 x)))
(+ 1 (+ (sqrt x) (* 1/2 x)))
(+ 1 (+ (sqrt x) (* 1/2 x)))
(* x (+ 1/2 (sqrt (/ 1 x))))
(* x (+ 1/2 (+ (sqrt (/ 1 x)) (/ 1 x))))
(* x (+ 1/2 (+ (sqrt (/ 1 x)) (/ 1 x))))
(* x (+ 1/2 (+ (sqrt (/ 1 x)) (/ 1 x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (+ 1/2 (/ 1 x)))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (+ 1/2 (/ 1 x)))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (+ 1/2 (/ 1 x)))))
1
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(+ 1 (* 1/2 x))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* x (+ 1/2 (/ 1 x)))
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(* 1/2 x)
(/ 1 (+ 1 (sqrt x)))
(+ (* x (- (* 1/4 (/ 1 (+ 1 (sqrt x)))) (* 2 (/ (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (+ (* 1/4 (/ 1 (+ 1 (sqrt x)))) (* x (- (* 1/8 (/ 1 (+ 1 (sqrt x)))) (+ (* 1/8 (/ 1 (+ 1 (sqrt x)))) (* 2 (/ (* (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (- (* 1/4 (/ 1 (+ 1 (sqrt x)))) (* 2 (/ (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x)))))))) (* 2 (/ (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (+ (* 1/4 (/ 1 (+ 1 (sqrt x)))) (* x (- (* x (- (* 1/32 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* -1/8 (- (* 1/4 (/ 1 (+ 1 (sqrt x)))) (* 2 (/ (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (pow (+ 1 (sqrt x)) 2))))) (* 2 (/ (* (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (- (* 1/8 (/ 1 (+ 1 (sqrt x)))) (+ (* 1/8 (/ 1 (+ 1 (sqrt x)))) (* 2 (/ (* (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (- (* 1/4 (/ 1 (+ 1 (sqrt x)))) (* 2 (/ (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x))))))) (+ 1 (sqrt x))))))) (* 2 (/ (* (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (- (* 1/4 (/ 1 (+ 1 (sqrt x)))) (* 2 (/ (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (pow (+ 1 (sqrt x)) 2))))) (+ 1 (sqrt x))))))) (* 2 (/ (+ 1/4 (* 1/8 (+ 1 (sqrt x)))) (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(/ 16 (pow x 3))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 3))
(/ (+ 16 (+ (* 4096 (/ (- (* -1/16 (sqrt (/ 1 x))) 1/64) (pow x 2))) (* 32 (/ 1 x)))) (pow x 3))
(/ (- (+ 16 (+ (* -1 (/ (+ (* -16384 (- (* -1/16 (sqrt (/ 1 x))) 1/64)) (+ (* -8192 (- (* -1/16 (sqrt (/ 1 x))) 1/64)) (* -4096 (- (* 1/8 (sqrt (/ 1 x))) 1/16)))) (pow x 3))) (* 32 (/ 1 x)))) (* -4096 (/ (- (* -1/16 (sqrt (/ 1 x))) 1/64) (pow x 2)))) (pow x 3))
(/ 16 (pow x 3))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 3))
(* -1 (/ (- (* -1 (/ (+ 32 (* 4096 (/ (- (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 1/64) x))) x)) 16) (pow x 3)))
(* -1 (/ (- (* -1 (/ (+ 32 (* -1 (/ (+ (* -4096 (- (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 1/64)) (* -1 (/ (+ (* 4096 (- (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 1/16)) (+ (* 8192 (- (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 1/64)) (* 16384 (- (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 1/64)))) x))) x))) x)) 16) (pow x 3)))
(+ 1 (sqrt x))
(+ 1 (+ (sqrt x) (* x (- (* 2 (+ 1/4 (* 1/8 (+ 1 (sqrt x))))) (* 1/4 (+ 1 (sqrt x)))))))
(+ 1 (+ (sqrt x) (* x (- (+ (* -1/4 (* x (- (* 2 (+ 1/4 (* 1/8 (+ 1 (sqrt x))))) (* 1/4 (+ 1 (sqrt x)))))) (* 2 (+ 1/4 (* 1/8 (+ 1 (sqrt x)))))) (* 1/4 (+ 1 (sqrt x)))))))
(+ 1 (+ (sqrt x) (* x (- (+ (* 2 (+ 1/4 (* 1/8 (+ 1 (sqrt x))))) (* x (- (* -1 (* x (+ 1/32 (+ (* -1/8 (- (* 2 (+ 1/4 (* 1/8 (+ 1 (sqrt x))))) (* 1/4 (+ 1 (sqrt x))))) (* -1/16 (- (* 2 (+ 1/4 (* 1/8 (+ 1 (sqrt x))))) (* 1/4 (+ 1 (sqrt x))))))))) (* 1/4 (- (* 2 (+ 1/4 (* 1/8 (+ 1 (sqrt x))))) (* 1/4 (+ 1 (sqrt x)))))))) (* 1/4 (+ 1 (sqrt x)))))))
(* 1/16 (pow x 3))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (+ (* -16 (/ (- (* -1/16 (sqrt (/ 1 x))) 1/64) (pow x 2))) (/ 1/4 (pow x 2)))) (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (+ (* -16 (/ (- (* -1/16 (sqrt (/ 1 x))) 1/64) (pow x 2))) (+ (* -16 (/ (- (* 1/8 (sqrt (/ 1 x))) 1/16) (pow x 3))) (/ 1/4 (pow x 2))))) (+ (* -2 (/ (+ 1/4 (* -16 (- (* -1/16 (sqrt (/ 1 x))) 1/64))) (pow x 3))) (+ (* 1/8 (/ 1 x)) (/ 1 (pow x 3))))))
(* 1/16 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* -16 (/ (- (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 1/64) x)) (* 1/4 (/ 1 x))) 1/8) x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (+ (* -1 (+ 1/4 (* -16 (- (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 1/64)))) (+ (* 16 (/ (- (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 1/16) x)) (/ 1 x))) (* 2 (/ (+ 1/4 (* -16 (- (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 1/64))) x))) x)) 1/8) x)) 1/16)))
(* 1/2 (* x (+ 1 (sqrt x))))
(* x (+ (* 1/2 (+ 1 (sqrt x))) (* x (+ 1/4 (* 1/8 (+ 1 (sqrt x)))))))
(* x (+ (* 1/2 (+ 1 (sqrt x))) (* x (+ 1/4 (+ (* -1/16 (* x (+ 1 (sqrt x)))) (* 1/8 (+ 1 (sqrt x))))))))
(* x (+ (* 1/2 (+ 1 (sqrt x))) (* x (+ 1/4 (+ (* 1/8 (+ 1 (sqrt x))) (* x (+ (* -1/16 (+ 1 (sqrt x))) (* -1/64 x))))))))
(* -1/256 (pow x 6))
(* (pow x 6) (- (* 1/64 (/ 1 x)) 1/256))
(* (pow x 6) (- (+ (* -1/16 (sqrt (/ 1 (pow x 5)))) (* 1/64 (/ 1 x))) (+ 1/256 (/ 1/64 (pow x 2)))))
(* (pow x 6) (- (+ (* -1/16 (sqrt (/ 1 (pow x 5)))) (+ (* 1/8 (sqrt (/ 1 (pow x 7)))) (* 1/64 (/ 1 x)))) (+ 1/256 (+ (/ 1/64 (pow x 2)) (* 1/16 (/ 1 (pow x 3)))))))
(* -1/256 (pow x 6))
(* (pow x 6) (- (* 1/64 (/ 1 x)) 1/256))
(* (pow x 6) (- (* -1 (/ (- (* -1 (/ (- (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) 1/64) x)) 1/64) x)) 1/256))
(* (pow x 6) (- (* -1 (/ (- (* -1 (/ (- (+ (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/16 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) (+ 1/64 (* 1/16 (/ 1 x)))) x)) 1/64) x)) 1/256))
(* 1/4 (pow x 2))
(* (pow x 2) (+ 1/4 (* -1/64 (pow x 2))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/64 x) 1/64))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* x (+ 1/64 (* -1/256 x))) 1/64))))
(* -1/256 (pow x 6))
(* (pow x 6) (- (* 1/64 (/ 1 x)) 1/256))
(* (pow x 6) (- (* 1/64 (/ 1 x)) (+ 1/256 (/ 1/64 (pow x 2)))))
(* (pow x 6) (- (+ (* 1/64 (/ 1 x)) (* 1/4 (/ 1 (pow x 4)))) (+ 1/256 (/ 1/64 (pow x 2)))))
(* -1/256 (pow x 6))
(* (pow x 6) (- (* 1/64 (/ 1 x)) 1/256))
(* (pow x 6) (- (* -1 (/ (- (* 1/64 (/ 1 x)) 1/64) x)) 1/256))
(* (pow x 6) (- (* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/64) x)) 1/64) x)) 1/256))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(* 1/4 (pow x 2))
(* (pow x 2) (+ 1/4 (* -1/64 (pow x 2))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/64 x) 1/64))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* x (+ 1/64 (* -1/256 x))) 1/64))))
(* -1/256 (pow x 6))
(* (pow x 6) (- (* 1/64 (/ 1 x)) 1/256))
(* (pow x 6) (- (* 1/64 (/ 1 x)) (+ 1/256 (/ 1/64 (pow x 2)))))
(* (pow x 6) (- (+ (* 1/64 (/ 1 x)) (* 1/4 (/ 1 (pow x 4)))) (+ 1/256 (/ 1/64 (pow x 2)))))
(* -1/256 (pow x 6))
(* (pow x 6) (- (* 1/64 (/ 1 x)) 1/256))
(* (pow x 6) (- (* -1 (/ (- (* 1/64 (/ 1 x)) 1/64) x)) 1/256))
(* (pow x 6) (- (* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/64) x)) 1/64) x)) 1/256))

Outputs
(/ 1 (+ 1 (sqrt x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (.f64 x (+.f64 (.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (.f64 x (+.f64 (.f64 x (-.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)))) (.f64 x (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))) (/.f64 (.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))))))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (-.f64 (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))) x)
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)
(/.f64 (-.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))))) (+.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/16 binary64)))) x)
(* -1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) x))
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))
(/.f64 (+.f64 (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))
(/.f64 (+.f64 (+.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (.f64 (/.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 binary64))) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 x #s(literal 1/2 binary64))))
(+ 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 (sqrt.f64 x) (+.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))))))))
(* 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 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* 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 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
(.f64 x (+.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64))))))))
(* -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 #s(literal 1 binary64) (.f64 x (.f64 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 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (-.f64 #s(literal 0 binary64) x))
(* -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 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (*.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (-.f64 #s(literal 0 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(+ 1 (* x (+ 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 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(.f64 x (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))
(* 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 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(* -1 (* x (+ (* 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 -1 binary64))) (-.f64 #s(literal 0 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 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) (*.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 (.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 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1 binary64)) (.f64 #s(literal 1/16 binary64) (/.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))))))) (-.f64 #s(literal 0 binary64) x))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
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(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/256 binary64) (/.f64 #s(literal 1/64 binary64) x)))
(* (pow x 6) (- (* -1 (/ (- (* 1/64 (/ 1 x)) 1/64) x)) 1/256))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/256 binary64) (/.f64 (+.f64 #s(literal -1/64 binary64) (/.f64 #s(literal 1/64 binary64) x)) (-.f64 #s(literal 0 binary64) x))))
(* (pow x 6) (- (* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/64) x)) 1/64) x)) 1/256))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/256 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal -1/64 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal -1/64 binary64)) x))) 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)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1 binary64) (sqrt.f64 x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(pow x 3)
(.f64 x (.f64 x x))
(* 1/4 (pow x 2))
(.f64 #s(literal 1/4 binary64) (.f64 x x))
(* (pow x 2) (+ 1/4 (* -1/64 (pow x 2))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/64 binary64))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* 1/64 x) 1/64))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/64 binary64) (*.f64 x #s(literal 1/64 binary64))))))
(* (pow x 2) (+ 1/4 (* (pow x 2) (- (* x (+ 1/64 (* -1/256 x))) 1/64))))
(.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (+.f64 #s(literal -1/64 binary64) (.f64 x (+.f64 #s(literal 1/64 binary64) (.f64 x #s(literal -1/256 binary64))))))))
(* -1/256 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/256 binary64))
(* (pow x 6) (- (* 1/64 (/ 1 x)) 1/256))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/256 binary64) (/.f64 #s(literal 1/64 binary64) x)))
(* (pow x 6) (- (* 1/64 (/ 1 x)) (+ 1/256 (/ 1/64 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (-.f64 #s(literal -1/256 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 x x)))))
(* (pow x 6) (- (+ (* 1/64 (/ 1 x)) (* 1/4 (/ 1 (pow x 4)))) (+ 1/256 (/ 1/64 (pow x 2)))))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 (/.f64 #s(literal 1/64 binary64) x) (-.f64 (/.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (.f64 x x)) x)) (+.f64 #s(literal 1/256 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 x x))))))
(* -1/256 (pow x 6))
(*.f64 (pow.f64 x #s(literal 6 binary64)) #s(literal -1/256 binary64))
(* (pow x 6) (- (* 1/64 (/ 1 x)) 1/256))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/256 binary64) (/.f64 #s(literal 1/64 binary64) x)))
(* (pow x 6) (- (* -1 (/ (- (* 1/64 (/ 1 x)) 1/64) x)) 1/256))
(*.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/256 binary64) (/.f64 (+.f64 #s(literal -1/64 binary64) (/.f64 #s(literal 1/64 binary64) x)) (-.f64 #s(literal 0 binary64) x))))
(* (pow x 6) (- (* -1 (/ (- (* -1 (/ (- (* 1/4 (/ 1 (pow x 2))) 1/64) x)) 1/64) x)) 1/256))
(.f64 (pow.f64 x #s(literal 6 binary64)) (+.f64 #s(literal -1/256 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal -1/64 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 (/.f64 #s(literal 1/4 binary64) (.f64 x x)) #s(literal -1/64 binary64)) x))) x))))

eval164.0ms (1.3%)

Compiler: Compiled 47182 to 2785 computations (94.1% saved)

prune493.0ms (4%)

Pruning

28 alts after pruning (21 fresh and 7 done)

	Pruned	Kept	Total
New	1028	13	1041
Fresh	2	8	10
Picked	2	3	5
Done	0	4	4
Total	1032	28	1060

Accuracy

100.0%

Counts

1060 → 28

Alt Table

Click to see full alt table

Status	Accuracy	Program
	4.3%	(/.f64 (/.f64 (/.f64 #s(literal 16 binary64) x) x) x)
	4.3%	(/.f64 (/.f64 #s(literal 16 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x x)))) x)
✓	4.3%	(/.f64 (/.f64 #s(literal 16 binary64) (*.f64 x x)) x)
	4.3%	(/.f64 (/.f64 #s(literal 16 binary64) x) (*.f64 x x))
	4.3%	(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 16 binary64) x))) x)
	57.6%	(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
	43.3%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/64 binary64)))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))))
	3.3%	(/.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
	4.2%	(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (.f64 x (.f64 x x)))
	4.3%	(/.f64 (*.f64 (/.f64 #s(literal 16 binary64) x) (/.f64 #s(literal 1 binary64) x)) x)
	4.3%	(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
	44.9%	(/.f64 #s(literal 1 binary64) (+.f64 (+.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.f64 x)))
	44.1%	(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 x)))
✓	46.3%	(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x)))
	63.5%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (+.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))) (sqrt.f64 x)))
✓	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
✓	52.7%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	3.0%	(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
	59.2%	(/.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)))
✓	59.4%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
	55.5%	(/.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
	2.2%	(/.f64 #s(literal -8 binary64) (*.f64 x x))
✓	46.1%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	42.8%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
	44.9%	(+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) #s(literal 1 binary64))
	59.6%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
	4.3%	(.f64 (/.f64 #s(literal 16 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) x))
	4.3%	(.f64 #s(literal 16 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))

Compiler

Compiled 916 to 377 computations (58.8% saved)

regimes30.0ms (0.2%)

Counts

45 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal -8 binary64) (*.f64 x x))
(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
(/.f64 (/.f64 #s(literal 16 binary64) x) (*.f64 x x))
(/.f64 (/.f64 #s(literal 16 binary64) (*.f64 x x)) x)
(/.f64 (/.f64 (/.f64 #s(literal 16 binary64) x) x) x)
(.f64 #s(literal 16 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))
(.f64 (/.f64 #s(literal 16 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 (/.f64 #s(literal 16 binary64) x) (/.f64 #s(literal 1 binary64) x)) x)
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 16 binary64) x))) x)
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (.f64 x (.f64 x x)))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x))))
(/.f64 (/.f64 #s(literal 16 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x x)))) x)
(/.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) #s(literal 1 binary64))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (+.f64 (+.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.f64 x)))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.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.f64 x)))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/64 binary64)))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))))
(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(/.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
(/.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
(-.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (+.f64 x #s(literal 1 binary64))))) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 2 binary64)))))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (+.f64 (*.f64 x x) (-.f64 #s(literal 1 binary64) x)))) (sqrt.f64 x)))

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

Calls

2 calls:

14.0ms	x
10.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
99.7%	1	`x`
99.7%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes22.0ms (0.2%)

Counts

35 → 2

Calls

Call 1

Inputs
(/.f64 #s(literal -8 binary64) (*.f64 x x))
(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
(/.f64 (/.f64 #s(literal 16 binary64) x) (*.f64 x x))
(/.f64 (/.f64 #s(literal 16 binary64) (*.f64 x x)) x)
(/.f64 (/.f64 (/.f64 #s(literal 16 binary64) x) x) x)
(.f64 #s(literal 16 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))
(.f64 (/.f64 #s(literal 16 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 (/.f64 #s(literal 16 binary64) x) (/.f64 #s(literal 1 binary64) x)) x)
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 16 binary64) x))) x)
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (.f64 x (.f64 x x)))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x))))
(/.f64 (/.f64 #s(literal 16 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x x)))) x)
(/.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) #s(literal 1 binary64))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (+.f64 (+.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.f64 x)))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.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.f64 x)))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/64 binary64)))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))))
(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(/.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
(/.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64)))

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

Calls

2 calls:

10.0ms	x
9.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
99.3%	2	`x`
99.3%	2	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes11.0ms (0.1%)

Counts

32 → 2

Calls

Call 1

Inputs
(/.f64 #s(literal -8 binary64) (*.f64 x x))
(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
(/.f64 (/.f64 #s(literal 16 binary64) x) (*.f64 x x))
(/.f64 (/.f64 #s(literal 16 binary64) (*.f64 x x)) x)
(/.f64 (/.f64 (/.f64 #s(literal 16 binary64) x) x) x)
(.f64 #s(literal 16 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))
(.f64 (/.f64 #s(literal 16 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 (/.f64 #s(literal 16 binary64) x) (/.f64 #s(literal 1 binary64) x)) x)
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 16 binary64) x))) x)
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (.f64 x (.f64 x x)))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x))))
(/.f64 (/.f64 #s(literal 16 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x x)))) x)
(/.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) #s(literal 1 binary64))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (+.f64 (+.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.f64 x)))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 x)))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (+.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.f64 x)))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) #s(literal -1/64 binary64)))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (/.f64 (+.f64 (.f64 (-.f64 (.f64 (.f64 x x) #s(literal 1/4 binary64)) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) #s(literal 1 binary64)) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))) (.f64 (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))))
(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))

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

Calls

1 calls:

9.0ms

Results

Accuracy	Segments	Branch
98.9%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes28.0ms (0.2%)

Counts

21 → 2

Calls

Call 1

Inputs
(/.f64 #s(literal -8 binary64) (*.f64 x x))
(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
(/.f64 (/.f64 #s(literal 16 binary64) x) (*.f64 x x))
(/.f64 (/.f64 #s(literal 16 binary64) (*.f64 x x)) x)
(/.f64 (/.f64 (/.f64 #s(literal 16 binary64) x) x) x)
(.f64 #s(literal 16 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))
(.f64 (/.f64 #s(literal 16 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 (/.f64 #s(literal 16 binary64) x) (/.f64 #s(literal 1 binary64) x)) x)
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 16 binary64) x))) x)
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (.f64 x (.f64 x x)))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x))))
(/.f64 (/.f64 #s(literal 16 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x x)))) x)
(/.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64)))

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

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
98.9%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes8.0ms (0.1%)

Counts

20 → 2

Calls

Call 1

Inputs
(/.f64 #s(literal -8 binary64) (*.f64 x x))
(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
(/.f64 (/.f64 #s(literal 16 binary64) x) (*.f64 x x))
(/.f64 (/.f64 #s(literal 16 binary64) (*.f64 x x)) x)
(/.f64 (/.f64 (/.f64 #s(literal 16 binary64) x) x) x)
(.f64 #s(literal 16 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))
(.f64 (/.f64 #s(literal 16 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 (/.f64 #s(literal 16 binary64) x) (/.f64 #s(literal 1 binary64) x)) x)
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 16 binary64) x))) x)
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (.f64 x (.f64 x x)))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x))))
(/.f64 (/.f64 #s(literal 16 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x x)))) x)
(/.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))

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

Calls

1 calls:

6.0ms

Results

Accuracy	Segments	Branch
98.7%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes7.0ms (0.1%)

Counts

17 → 2

Calls

Call 1

Inputs
(/.f64 #s(literal -8 binary64) (*.f64 x x))
(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
(/.f64 (/.f64 #s(literal 16 binary64) x) (*.f64 x x))
(/.f64 (/.f64 #s(literal 16 binary64) (*.f64 x x)) x)
(/.f64 (/.f64 (/.f64 #s(literal 16 binary64) x) x) x)
(.f64 #s(literal 16 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))
(.f64 (/.f64 #s(literal 16 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 (/.f64 #s(literal 16 binary64) x) (/.f64 #s(literal 1 binary64) x)) x)
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 16 binary64) x))) x)
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (.f64 x (.f64 x x)))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x))))
(/.f64 (/.f64 #s(literal 16 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x x)))) x)
(/.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
98.5%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes7.0ms (0.1%)

Counts

16 → 2

Calls

Call 1

Inputs
(/.f64 #s(literal -8 binary64) (*.f64 x x))
(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
(/.f64 (/.f64 #s(literal 16 binary64) x) (*.f64 x x))
(/.f64 (/.f64 #s(literal 16 binary64) (*.f64 x x)) x)
(/.f64 (/.f64 (/.f64 #s(literal 16 binary64) x) x) x)
(.f64 #s(literal 16 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))
(.f64 (/.f64 #s(literal 16 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 (/.f64 #s(literal 16 binary64) x) (/.f64 #s(literal 1 binary64) x)) x)
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 16 binary64) x))) x)
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (.f64 x (.f64 x x)))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x))))
(/.f64 (/.f64 #s(literal 16 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x x)))) x)
(/.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
44.9%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes7.0ms (0.1%)

Counts

15 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal -8 binary64) (*.f64 x x))
(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
(/.f64 (/.f64 #s(literal 16 binary64) x) (*.f64 x x))
(/.f64 (/.f64 #s(literal 16 binary64) (*.f64 x x)) x)
(/.f64 (/.f64 (/.f64 #s(literal 16 binary64) x) x) x)
(.f64 #s(literal 16 binary64) (/.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) x))
(.f64 (/.f64 #s(literal 16 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) x))
(/.f64 (*.f64 (/.f64 #s(literal 16 binary64) x) (/.f64 #s(literal 1 binary64) x)) x)
(/.f64 (/.f64 #s(literal 1 binary64) (/.f64 x (/.f64 #s(literal 16 binary64) x))) x)
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (.f64 x (.f64 x x)))
(/.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x))))
(/.f64 (/.f64 #s(literal 16 binary64) (.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x x)))) x)
(/.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
4.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

2 → 1

Calls

Call 1

Inputs
(/.f64 #s(literal -8 binary64) (*.f64 x x))
(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
4.3%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
2.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	8.100790000753477e-5	0.00035029415516873996

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch17.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	2.303191996415425e-10	1.7289297610666188

Results

10.0ms

160×

valid

Compiler

Compiled 182 to 149 computations (18.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-sqrt: 2.0ms (45.7% of total)

ival-sub: 1.0ms (22.9% of total)

ival-add: 1.0ms (22.9% of total)

const: 0.0ms (0% of total)

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

bsearch17.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	2.303191996415425e-10	1.7289297610666188

Results

10.0ms

160×

valid

Compiler

Compiled 182 to 149 computations (18.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-sqrt: 2.0ms (45.5% of total)

ival-sub: 1.0ms (22.7% of total)

ival-add: 1.0ms (22.7% of total)

const: 0.0ms (0% of total)

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

bsearch18.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
16.0ms	2.303191996415425e-10	1.7289297610666188

Results

11.0ms

160×

valid

Compiler

Compiled 142 to 119 computations (16.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-sqrt: 4.0ms (64.6% of total)

ival-sub: 1.0ms (16.1% of total)

ival-add: 1.0ms (16.1% of total)

const: 0.0ms (0% of total)

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

bsearch31.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
29.0ms	2.303191996415425e-10	1.7289297610666188

Results

24.0ms

160×

valid

Compiler

Compiled 132 to 109 computations (17.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 19.0ms

ival-add: 16.0ms (82.4% of total)

ival-sqrt: 2.0ms (10.3% of total)

ival-sub: 1.0ms (5.2% of total)

const: 0.0ms (0% of total)

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

bsearch23.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	1.7289297610666188	1513501.1443583441

Results

8.0ms

144×

valid

Compiler

Compiled 219 to 162 computations (26% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-sqrt: 2.0ms (52.7% of total)

ival-sub: 1.0ms (26.3% of total)

ival-add: 1.0ms (26.3% of total)

const: 0.0ms (0% of total)

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

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	48	132
1	66	132
2	72	132
3	74	132
4	75	132

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 7378697629483821/73786976294838206464 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(if (<=.f64 x #s(literal 1 binary64)) (+.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) #s(literal 1 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 3242591731706757/9007199254740992 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 3242591731706757/9007199254740992 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(if (<=.f64 x #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))))
(/.f64 (/.f64 #s(literal 16 binary64) x) (*.f64 x x))
(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
(/.f64 #s(literal -8 binary64) (*.f64 x x))

Outputs
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 7378697629483821/73786976294838206464 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 7378697629483821/73786976294838206464 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(if (<=.f64 x #s(literal 1 binary64)) (+.f64 (-.f64 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) #s(literal 1 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 x #s(literal 1/2 binary64)) (sqrt.f64 x))) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 3242591731706757/9007199254740992 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 3242591731706757/9007199254740992 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(if (<=.f64 x #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (+.f64 x #s(literal 1 binary64)) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))))
(if (<=.f64 x #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (+.f64 #s(literal 1 binary64) x) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))))
(/.f64 (/.f64 #s(literal 16 binary64) x) (*.f64 x x))
(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
(/.f64 #s(literal -8 binary64) (*.f64 x x))

soundness3.1s (25.7%)

Rules

4296×	`-lowering-.f32`
4296×	`-lowering-.f64`
4260×	`-lowering-.f32`
4260×	`-lowering-.f64`
3752×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	239
1	327	225
2	3334	221
0	8238	221
0	407	2250
1	1307	1972
2	4496	1934
0	8310	1934
0	310	1965
1	1004	1678
2	3729	1666
0	8245	1666
0	113	434
1	325	384
2	1039	376
3	3226	373
4	7122	373
0	8132	373
0	591	3181
1	1920	2743
2	6670	2728
0	8418	2728
0	20	80
1	156	76
2	1357	76
0	8647	76
0	27	122
1	228	115
2	2180	115
0	8285	115
0	6	16
1	39	16
2	303	16
3	3722	16
0	8045	16

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
1×	iter limit
1×	node limit

Compiler

Compiled 517 to 320 computations (38.1% saved)

preprocess71.0ms (0.6%)

Compiler: Compiled 302 to 116 computations (61.6% saved)

Iter	Nodes	Cost
0	6	18
1	11	18
2	15	18
3	22	18
4	32	18
5	64	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18

Iter	Nodes	Cost
0	6	18
1	11	18
2	15	18
3	22	18
4	32	18
5	64	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18

analyze2.0ms (0%)

sample1.2s (10%)

preprocess42.0ms (0.3%)

explain169.0ms (1.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify24.0ms (0.2%)

localize66.0ms (0.5%)

series5.0ms (0%)

rewrite341.0ms (2.8%)

simplify296.0ms (2.4%)

eval58.0ms (0.5%)

prune57.0ms (0.5%)

simplify154.0ms (1.3%)

localize322.0ms (2.6%)

series16.0ms (0.1%)

rewrite1.6s (12.8%)

simplify358.0ms (2.9%)

eval260.0ms (2.1%)

prune477.0ms (3.9%)

simplify166.0ms (1.4%)

localize283.0ms (2.3%)

series11.0ms (0.1%)

rewrite376.0ms (3.1%)

simplify259.0ms (2.1%)

eval131.0ms (1.1%)

prune144.0ms (1.2%)

simplify187.0ms (1.5%)

localize411.0ms (3.4%)

series19.0ms (0.2%)

rewrite333.0ms (2.7%)

simplify343.0ms (2.8%)

eval164.0ms (1.3%)

prune493.0ms (4%)

regimes30.0ms (0.2%)

regimes22.0ms (0.2%)

regimes11.0ms (0.1%)

regimes28.0ms (0.2%)

regimes8.0ms (0.1%)

regimes7.0ms (0.1%)

regimes7.0ms (0.1%)

regimes7.0ms (0.1%)

regimes2.0ms (0%)

regimes1.0ms (0%)

bsearch0.0ms (0%)

bsearch17.0ms (0.1%)

bsearch17.0ms (0.1%)

bsearch18.0ms (0.1%)

bsearch31.0ms (0.3%)

bsearch23.0ms (0.2%)

simplify14.0ms (0.1%)

soundness3.1s (25.7%)

preprocess71.0ms (0.6%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	6	18
1	11	18
2	15	18
3	22	18
4	32	18
5	64	18
6	122	18
7	210	18
8	295	18
9	401	18
10	479	18
11	485	18
0	485	18