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)

sample1.3s (14.2%)

Results

357.0ms	2400×	1	valid
351.0ms	4198×	0	valid
294.0ms	1658×	2	valid
0.0ms	7×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 665.0ms

ival-sqrt: 295.0ms (44.4% of total)

ival-add: 195.0ms (29.3% of total)

ival-sub: 94.0ms (14.1% of total)

backward-pass: 66.0ms (9.9% of total)

const: 15.0ms (2.3% of total)

Bogosity

preprocess38.0ms (0.4%)

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)))

explain91.0ms (1%)

FPErrors

Click to see full error table

Ground Truth	Example	Underpredictions	Example	Subexpression
138	-	1	(30.69229050516152)	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`
0	-	0	-	`x`
0	-	0	-	`(sqrt.f64 (+.f64 x #s(literal 1 binary64)))`
0	-	0	-	`#s(literal 1 binary64)`
0	-	0	-	`(sqrt.f64 x)`
0	-	0	-	`(+.f64 x #s(literal 1 binary64))`

Results

24.0ms	164×	1	valid
22.0ms	104×	2	valid
15.0ms	244×	0	valid

Compiler

Compiled 48 to 20 computations (58.3% saved)

Precisions

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

ival-sqrt: 13.0ms (38.9% of total)

ival-add: 8.0ms (24% of total)

backward-pass: 6.0ms (18% of total)

ival-sub: 5.0ms (15% of total)

const: 1.0ms (3% 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
▶	50.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify15.0ms (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)

localize44.0ms (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	50.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

16.0ms	52×	2	valid
11.0ms	82×	1	valid
7.0ms	122×	0	valid

Compiler

Compiled 20 to 7 computations (65% saved)

Precisions

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

ival-sqrt: 13.0ms (61.5% of total)

ival-add: 3.0ms (14.2% of total)

backward-pass: 3.0ms (14.2% of total)

ival-sub: 2.0ms (9.5% of total)

const: 1.0ms (4.7% of total)

series6.0ms (0.1%)

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)

rewrite266.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

2378×	`-lowering-.f32`
2378×	`-lowering-.f64`
1782×	`fma-lowering-fma.f32`
1782×	`fma-lowering-fma.f64`
1676×	`fmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	39	16
2	300	16
3	3704	16
0	8338	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 233

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

simplify256.0ms (2.9%)

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	1037	376
3	3221	373
4	7103	373
0	8112	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 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.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))))) (sqrt x))
(+.f64 #s(literal 1 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)))))) (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 #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 (.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 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) 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 #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 #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 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) (/.f64 #s(literal -5/128 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 6 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 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 (.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 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x 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 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 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x 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)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(.f64 x (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/2 binary64)) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (-.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64)) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))))
1
#s(literal 1 binary64)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
(+ 1 x)
(+.f64 #s(literal 1 binary64) x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
x
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(* x (+ 1 (/ 1 x)))
(+.f64 #s(literal 1 binary64) x)
(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)

eval34.0ms (0.4%)

Compiler: Compiled 6005 to 884 computations (85.3% saved)

prune37.0ms (0.4%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	273	8	281
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	273	9	282

Accuracy

100.0%

Counts

282 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	53.3%	(/.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)
	51.5%	(/.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)))
	47.8%	(-.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))
▶	46.5%	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 x))
✓	50.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	46.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
	48.4%	(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64)))
▶	50.5%	(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.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))))))
▶	55.5%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 226 to 158 computations (30.1% saved)

simplify219.0ms (2.4%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) x)
✓	cost-diff	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 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))
✓	cost-diff	384	(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.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))))))
✓	cost-diff	0	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(*.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	cost-diff	0	(+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.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)
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))))
✓	cost-diff	0	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 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

2488×	`--lowering--.f32`
2488×	`--lowering--.f64`
2178×	`+-lowering-+.f64`
2178×	`+-lowering-+.f32`
1978×	`-lowering-.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	201
1	76	188
2	194	178
3	731	177
4	5286	177
0	8610	177

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

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

localize223.0ms (2.5%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	99.5%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))
✓	accuracy	84.5%	(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.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))))))
✓	accuracy	76.7%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))
✓	accuracy	51.2%	(+.f64 x (-.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.7%	(/.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)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
✓	accuracy	100.0%	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 x))
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(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

111.0ms	121×	1	valid
54.0ms	135×	0	valid

Compiler

Compiled 217 to 32 computations (85.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 97.0ms

ival-pow: 25.0ms (25.7% of total)

ival-mult: 18.0ms (18.5% of total)

ival-add: 15.0ms (15.4% of total)

ival-sqrt: 12.0ms (12.4% of total)

ival-div: 9.0ms (9.3% of total)

backward-pass: 9.0ms (9.3% of total)

ival-sub: 8.0ms (8.2% of total)

const: 1.0ms (1% of total)

series17.0ms (0.2%)

Counts

17 → 204

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

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 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))>
#<alt (- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))>
#<alt (* -1/8 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3))))))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))>
#<alt (* -1/8 (pow x 2))>
#<alt (* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8))>
#<alt (* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))>
#<alt (* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))>
#<alt 1>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (* -1/8 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))>
#<alt (* -1/8 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))>
#<alt (* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))>
#<alt (* 1/2 x)>
#<alt (* x (+ 1/2 (* -1/8 x)))>
#<alt (* x (+ 1/2 (* -1/8 x)))>
#<alt (* x (+ 1/2 (* -1/8 x)))>
#<alt (* -1/8 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* -1/8 (pow x 2))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))>
#<alt 1/2>
#<alt (+ 1/2 (* -1/8 x))>
#<alt (+ 1/2 (* -1/8 x))>
#<alt (+ 1/2 (* -1/8 x))>
#<alt (* -1/8 x)>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* x (- (* 1/2 (/ 1 x)) 1/8))>
#<alt (* -1/8 x)>
#<alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))>
#<alt (* -1/8 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (* 1/2 (sqrt x))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))>
#<alt (- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))>
#<alt (- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (* 3/8 (sqrt (/ 1 x)))) x)>
#<alt (/ (- (+ (* -1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3))))))) x)>
#<alt (* 1/2 (* (sqrt (/ 1 x)) (+ 2 (pow (sqrt -1) 2))))>
#<alt (* -1 (/ (+ (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2)))) (* -1/4 (sqrt (/ 1 x)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt -1) 4)))) (+ (* 3/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2)))))) x)) (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))>
#<alt 1>
#<alt (+ 1 (* -1 (* x (+ 3/2 (sqrt x)))))>
#<alt (+ 1 (* x (- (* -1 (* x (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))))) (+ 3/2 (sqrt x)))))>
#<alt (+ 1 (* x (- (* x (- (* x (- 1/16 (+ (* -1 (* (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))) (+ 3/2 (sqrt x)))) (* -3/8 (+ 3/2 (sqrt x)))))) (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))))) (+ 3/2 (sqrt x)))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -3/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))>
#<alt (/ (- (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 3/8 (sqrt (/ 1 x)))) (pow x 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* -9/32 (sqrt (pow x 5))) (* 1/8 (* (sqrt (pow x 3)) (- 1 (* 9/4 x))))) (pow x 4))) (* 1/2 (sqrt x))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3)))))) (pow x 2))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -3/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (pow x 2))>
#<alt (/ (- (+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (* 3/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) (pow x 2))>
#<alt (/ (- (+ (* -1 (/ (- (+ (* -9/32 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (pow (sqrt -1) 2))))) (* -3/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 3))) (* 1/2 (sqrt x))) (* 3/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) (pow x 2))>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 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 (sqrt x)>
#<alt (+ (sqrt x) (* 1/2 (sqrt (pow x 3))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))>
#<alt (* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))>
#<alt (* -1 (* x (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (- (pow (sqrt -1) 2) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))>

Calls

51 calls:

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

rewrite578.0ms (6.5%)

Algorithm

1×	batch-egg-rewrite

Rules

4006×	`-lowering-.f32`
4006×	`-lowering-.f64`
2634×	`+-lowering-+.f64`
2634×	`+-lowering-+.f32`
2408×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	131
1	232	117
2	2319	115
0	9732	115

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 471

Calls

Call 1

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

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

simplify229.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

3588×	`-lowering-.f32`
3588×	`-lowering-.f64`
1512×	`+-lowering-+.f64`
1512×	`+-lowering-+.f32`
1390×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	311	2017
1	982	1657
2	3815	1617
0	8291	1617

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

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 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(* -1/8 (pow x 2))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* -1/8 x)))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
1/2
(+ 1/2 (* -1/8 x))
(+ 1/2 (* -1/8 x))
(+ 1/2 (* -1/8 x))
(* -1/8 x)
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* -1/8 x)
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* 1/2 (sqrt (/ 1 x)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(* -1/8 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(* 1/2 (sqrt x))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(- 1 (sqrt x))
(- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (* 3/8 (sqrt (/ 1 x)))) x)
(/ (- (+ (* -1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3))))))) x)
(* 1/2 (* (sqrt (/ 1 x)) (+ 2 (pow (sqrt -1) 2))))
(* -1 (/ (+ (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2)))) (* -1/4 (sqrt (/ 1 x)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt -1) 4)))) (+ (* 3/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2)))))) x)) (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))
1
(+ 1 (* -1 (* x (+ 3/2 (sqrt x)))))
(+ 1 (* x (- (* -1 (* x (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))))) (+ 3/2 (sqrt x)))))
(+ 1 (* x (- (* x (- (* x (- 1/16 (+ (* -1 (* (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))) (+ 3/2 (sqrt x)))) (* -3/8 (+ 3/2 (sqrt x)))))) (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))))) (+ 3/2 (sqrt x)))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -3/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/ (- (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 3/8 (sqrt (/ 1 x)))) (pow x 2))
(/ (- (+ (* -1 (/ (+ (* -9/32 (sqrt (pow x 5))) (* 1/8 (* (sqrt (pow x 3)) (- 1 (* 9/4 x))))) (pow x 4))) (* 1/2 (sqrt x))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3)))))) (pow x 2))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -3/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (pow x 2))
(/ (- (+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (* 3/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) (pow x 2))
(/ (- (+ (* -1 (/ (- (+ (* -9/32 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (pow (sqrt -1) 2))))) (* -3/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 3))) (* 1/2 (sqrt x))) (* 3/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) (pow x 2))
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))))
(sqrt x)
(+ (sqrt x) (* 1/2 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (- (pow (sqrt -1) 2) (* 1/2 (/ 1 x)))))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))

Outputs
(* 1/2 (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 (*.f64 #s(literal 1/2 binary64) x) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(+.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(* -1/8 (pow x 2))
(.f64 #s(literal -1/8 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(.f64 (.f64 x x) (-.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))))
(* -1/8 (pow x 2))
(.f64 #s(literal -1/8 binary64) (.f64 x x))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8))
(.f64 (.f64 x x) (-.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1/2 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))
(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))
(.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 (/.f64 #s(literal 1/2 binary64) x) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))))
(* -1/8 (pow x 2))
(.f64 #s(literal -1/8 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))
(.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x))))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))
(.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x))))))
(* -1/8 (pow x 2))
(.f64 #s(literal -1/8 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))
(.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x))))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8))
(.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1 binary64) (*.f64 x x))))))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (* -1/8 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* x (+ 1/2 (* -1/8 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* x (+ 1/2 (* -1/8 x)))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* -1/8 (pow x 2))
(.f64 #s(literal -1/8 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* -1/8 (pow x 2))
(.f64 #s(literal -1/8 binary64) (.f64 x x))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
1/2
#s(literal 1/2 binary64)
(+ 1/2 (* -1/8 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
(+ 1/2 (* -1/8 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
(+ 1/2 (* -1/8 x))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
(* -1/8 x)
(*.f64 x #s(literal -1/8 binary64))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(-.f64 #s(literal 0 binary64) (+.f64 (*.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(-.f64 #s(literal 0 binary64) (+.f64 (*.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(-.f64 #s(literal 0 binary64) (+.f64 (*.f64 #s(literal 1/8 binary64) x) #s(literal -1/2 binary64)))
(* -1/8 (sqrt (/ 1 (pow x 3))))
(.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (*.f64 x x))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (*.f64 x x))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (*.f64 x x))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))))
(+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) x)
(* 1/2 (sqrt x))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(* -1 (* x (+ (* 1/8 (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 x (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(* -1/8 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64))
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64))
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64))
(* -1/8 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/8 binary64))
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(+.f64 (.f64 x (+.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x))))) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(+.f64 #s(literal 1 binary64) (-.f64 (.f64 x (+.f64 #s(literal 2 binary64) (+.f64 (.f64 x (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -3/8 binary64))) (.f64 (+.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)))) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x))))) (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)))))) (sqrt.f64 x)))
(- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(+.f64 (.f64 x (+.f64 (.f64 x (-.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -3/8 binary64))) (.f64 (+.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)))) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)))) (.f64 x (+.f64 (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/16 binary64)) (+.f64 (.f64 (+.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)))) #s(literal 3/8 binary64)) (.f64 (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)) (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/2 binary64)) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -3/8 binary64))) (.f64 (+.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)))) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)))))))))) (+.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)))))) (-.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)))
(/ (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (* 3/8 (sqrt (/ 1 x)))) x)
(/.f64 (+.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/16 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -3/8 binary64)))) x)
(/ (- (+ (* -1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3))))))) x)
(/.f64 (+.f64 (+.f64 (+.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 1/16 binary64))) (.f64 #s(literal -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (+.f64 (.f64 #s(literal -3/8 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -3/16 binary64)))) x)
(* 1/2 (* (sqrt (/ 1 x)) (+ 2 (pow (sqrt -1) 2))))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (/ (+ (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2)))) (* -1/4 (sqrt (/ 1 x)))) x))
(/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))
(/.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (/.f64 (+.f64 (/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/16 binary64)) (.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal 3/8 binary64))) x) (.f64 (sqrt.f64 x) #s(literal 1/4 binary64))) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt -1) 4)))) (+ (* 3/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2)))))) x)) (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))
(/.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (/.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/4 binary64)) (/.f64 (-.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/16 binary64)) (.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal -3/8 binary64))) (/.f64 (+.f64 (+.f64 (/.f64 (.f64 (sqrt.f64 x) #s(literal -1/32 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal 3/16 binary64))) (.f64 (sqrt.f64 (.f64 x (*.f64 x x))) #s(literal 3/8 binary64))) x)) x)) x)) (-.f64 #s(literal 0 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* -1 (* x (+ 3/2 (sqrt x)))))
(+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x))))
(+ 1 (* x (- (* -1 (* x (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))))) (+ 3/2 (sqrt x)))))
(+.f64 #s(literal 1 binary64) (.f64 x (-.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (.f64 x (-.f64 #s(literal 3/8 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)) #s(literal 2 binary64)))))))
(+ 1 (* x (- (* x (- (* x (- 1/16 (+ (* -1 (* (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))) (+ 3/2 (sqrt x)))) (* -3/8 (+ 3/2 (sqrt x)))))) (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))))) (+ 3/2 (sqrt x)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (.f64 x (+.f64 (.f64 x (+.f64 #s(literal 1/16 binary64) (.f64 (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)) (+.f64 (+.f64 #s(literal -3/8 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)) #s(literal 2 binary64))) #s(literal -3/8 binary64))))) (+.f64 #s(literal -3/8 binary64) (pow.f64 (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)) #s(literal 2 binary64))))) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(/ (+ (* -3/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -3/8 binary64))) (*.f64 x x))
(/ (- (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 3/8 (sqrt (/ 1 x)))) (pow x 2))
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 #s(literal -3/8 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))) (*.f64 x x))
(/ (- (+ (* -1 (/ (+ (* -9/32 (sqrt (pow x 5))) (* 1/8 (* (sqrt (pow x 3)) (- 1 (* 9/4 x))))) (pow x 4))) (* 1/2 (sqrt x))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3)))))) (pow x 2))
(/.f64 (+.f64 (-.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 (+.f64 (.f64 #s(literal -9/32 binary64) (sqrt.f64 (pow.f64 x #s(literal 5 binary64)))) (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal -9/4 binary64))) #s(literal 1/8 binary64)))) (.f64 (.f64 x x) (.f64 x x)))) (.f64 #s(literal -3/8 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))) (.f64 x x))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(/ (+ (* -3/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (pow x 2))
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 3/8 binary64))) (*.f64 x x))
(/ (- (+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (* 3/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) (pow x 2))
(/.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 #s(literal 3/8 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))) (*.f64 x x))
(/ (- (+ (* -1 (/ (- (+ (* -9/32 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (pow (sqrt -1) 2))))) (* -3/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 3))) (* 1/2 (sqrt x))) (* 3/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) (pow x 2))
(/.f64 (-.f64 (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 3/8 binary64))) (/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal -3/8 binary64)) (+.f64 (.f64 #s(literal -9/32 binary64) (/.f64 (sqrt.f64 (.f64 x (.f64 x x))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (.f64 (+.f64 #s(literal -1 binary64) (.f64 x #s(literal 9/4 binary64))) (.f64 (sqrt.f64 x) #s(literal 1/8 binary64))))) (.f64 x (.f64 x x)))) (.f64 x x))
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (sqrt (pow x 3))))
(+.f64 (sqrt.f64 x) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (*.f64 x x)))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))
(+.f64 (sqrt.f64 x) (.f64 (.f64 x x) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))
(+.f64 (sqrt.f64 x) (.f64 (.f64 x x) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 x (.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/16 binary64))))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(+.f64 #s(literal 1/2 binary64) x)
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(+.f64 (+.f64 #s(literal 1/2 binary64) x) (.f64 x (/.f64 #s(literal -1/8 binary64) (.f64 x x))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal -1/8 binary64) (.f64 x x)))))
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (- (pow (sqrt -1) 2) (* 1/2 (/ 1 x)))))
(-.f64 #s(literal 0 binary64) (+.f64 (-.f64 #s(literal 0 binary64) x) #s(literal -1/2 binary64)))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
(-.f64 #s(literal 0 binary64) (*.f64 x (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x))))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
(+.f64 x (.f64 x (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (/.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) x)))

eval100.0ms (1.1%)

Compiler: Compiled 20769 to 2173 computations (89.5% saved)

prune139.0ms (1.5%)

Pruning

15 alts after pruning (12 fresh and 3 done)

	Pruned	Kept	Total
New	787	9	796
Fresh	0	3	3
Picked	3	2	5
Done	0	1	1
Total	790	15	805

Accuracy

100.0%

Counts

805 → 15

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	74.9%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 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 x x))))
	53.3%	(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
	51.5%	(/.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)))
	55.5%	(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x)
	55.4%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
	47.8%	(-.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))
✓	46.5%	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 x))
✓	50.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	46.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
▶	48.4%	(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64)))
▶	55.6%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
	74.9%	(.f64 (/.f64 #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))))))
	53.2%	(.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))
▶	51.9%	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))
▶	1.8%	(.f64 #s(literal -1/8 binary64) (.f64 x x))

Compiler

Compiled 332 to 226 computations (31.9% saved)

simplify201.0ms (2.2%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(log.f64 x)
✓	cost-diff	0	(*.f64 (log.f64 x) #s(literal -1/2 binary64))
✓	cost-diff	6464	(exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))
✓	cost-diff	6464	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))
✓	cost-diff	0	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	cost-diff	0	(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	0	(pow.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 #s(literal -1/8 binary64) (.f64 x x))
✓	cost-diff	128	(-.f64 x x)
✓	cost-diff	256	(+.f64 #s(literal 1 binary64) (-.f64 x x))
✓	cost-diff	384	(/.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 x x)))
✓	cost-diff	384	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 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 x x))))

Rules

2768×	`sum3-define`
1752×	`fma-lowering-fma.f32`
1752×	`fma-lowering-fma.f64`
1732×	`fnmadd-define`
1510×	`fmm-def`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	152
1	72	142
2	134	138
3	244	138
4	473	138
5	995	138
6	2136	138
7	4438	138
8	7170	138
0	8028	138

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize150.0ms (1.7%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 (log.f64 x) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))
✓	accuracy	100.0%	(log.f64 x)
✓	accuracy	92.8%	(exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	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) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(pow.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal -1/8 binary64) (.f64 x x))
✓	accuracy	100.0%	(+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
✓	accuracy	100.0%	(*.f64 x (+.f64 #s(literal 1 binary64) x))
✓	accuracy	84.1%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 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 x x))))
✓	accuracy	76.7%	(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))

Results

107.0ms

256×

valid

Compiler

Compiled 170 to 33 computations (80.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 71.0ms

ival-pow: 27.0ms (38.2% of total)

ival-mult: 17.0ms (24.1% of total)

ival-add: 7.0ms (9.9% of total)

ival-exp: 4.0ms (5.7% of total)

ival-sub: 4.0ms (5.7% of total)

ival-sqrt: 4.0ms (5.7% of total)

ival-div: 3.0ms (4.2% of total)

ival-log: 3.0ms (4.2% of total)

const: 1.0ms (1.4% of total)

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

series63.0ms (0.7%)

Counts

19 → 228

Calls

Call 1

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

Outputs
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))>
#<alt (- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))>
#<alt (- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (* 3/8 (sqrt (/ 1 x)))) x)>
#<alt (/ (- (+ (* -1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3))))))) x)>
#<alt (* 1/2 (* (sqrt (/ 1 x)) (+ 2 (pow (sqrt -1) 2))))>
#<alt (* -1 (/ (+ (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2)))) (* -1/4 (sqrt (/ 1 x)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt -1) 4)))) (+ (* 3/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2)))))) x)) (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))>
#<alt 1>
#<alt (+ 1 (* x (+ 3/2 (sqrt x))))>
#<alt (+ 1 (* x (+ 3/2 (+ (sqrt x) (* 3/8 x)))))>
#<alt (+ 1 (* x (+ 3/2 (+ (sqrt x) (* x (+ 3/8 (* -1/16 x)))))))>
#<alt (* 2 (sqrt (pow x 3)))>
#<alt (* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))>
#<alt (* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt (/ 1 x))))))>
#<alt (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt (/ 1 x)))))))>
#<alt (* 2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))>
#<alt (* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt 0>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (pow x 2))>
#<alt (* -1/8 (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 (* 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 (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 (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 (* 1/2 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 (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 (* -1/2 (log x))>
#<alt (* -1/2 (log x))>
#<alt (* -1/2 (log x))>
#<alt (* -1/2 (log x))>
#<alt (* 1/2 (log (/ 1 x)))>
#<alt (* 1/2 (log (/ 1 x)))>
#<alt (* 1/2 (log (/ 1 x)))>
#<alt (* 1/2 (log (/ 1 x)))>
#<alt (* -1/2 (+ (log -1) (* -1 (log (/ -1 x)))))>
#<alt (* -1/2 (+ (log -1) (* -1 (log (/ -1 x)))))>
#<alt (* -1/2 (+ (log -1) (* -1 (log (/ -1 x)))))>
#<alt (* -1/2 (+ (log -1) (* -1 (log (/ -1 x)))))>
#<alt (log x)>
#<alt (log x)>
#<alt (log x)>
#<alt (log x)>
#<alt (* -1 (log (/ 1 x)))>
#<alt (* -1 (log (/ 1 x)))>
#<alt (* -1 (log (/ 1 x)))>
#<alt (* -1 (log (/ 1 x)))>
#<alt (+ (log -1) (* -1 (log (/ -1 x))))>
#<alt (+ (log -1) (* -1 (log (/ -1 x))))>
#<alt (+ (log -1) (* -1 (log (/ -1 x))))>
#<alt (+ (log -1) (* -1 (log (/ -1 x))))>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* 1/2 (sqrt (pow x 3))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))>
#<alt (* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))>
#<alt (* -1 (* x (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (- (pow (sqrt -1) 2) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))>
#<alt x>
#<alt (* x (+ 1 x))>
#<alt (* x (+ 1 x))>
#<alt (* x (+ 1 x))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* x (+ 3/2 (sqrt x))))>
#<alt (+ 1 (* x (+ 3/2 (+ (sqrt x) (* 3/8 x)))))>
#<alt (+ 1 (* x (+ 3/2 (+ (sqrt x) (* x (+ 3/8 (* -1/16 x)))))))>
#<alt (* 2 (sqrt (pow x 3)))>
#<alt (* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))>
#<alt (* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt (/ 1 x))))))>
#<alt (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt (/ 1 x)))))))>
#<alt (* 2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))>
#<alt (* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>

Calls

57 calls:

Time	Variable		Point	Expression
34.0ms	x	@	0	(* (log x) -1/2)
12.0ms	x	@	-inf	(* (log x) -1/2)
6.0ms	x	@	inf	(* (log x) -1/2)
2.0ms	x	@	inf	(* x 1/2)
0.0ms	x	@	0	(pow x -1/2)

rewrite363.0ms (4.1%)

Algorithm

1×	batch-egg-rewrite

Rules

3120×	`-lowering-.f32`
3120×	`-lowering-.f64`
2962×	`/-lowering-/.f32`
2962×	`/-lowering-/.f64`
2100×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	106
1	197	98
2	1512	93
0	8813	93

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 438

Calls

Call 1

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

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

simplify271.0ms (3%)

Algorithm

1×	egg-herbie

Rules

4414×	`-lowering-.f32`
4414×	`-lowering-.f64`
3030×	`+-lowering-+.f64`
3030×	`+-lowering-+.f32`
1260×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	270	1835
1	827	1562
2	2961	1533
0	8559	1533

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

Calls

Call 1

Inputs
(- 1 (sqrt x))
(- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (* 3/8 (sqrt (/ 1 x)))) x)
(/ (- (+ (* -1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3))))))) x)
(* 1/2 (* (sqrt (/ 1 x)) (+ 2 (pow (sqrt -1) 2))))
(* -1 (/ (+ (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2)))) (* -1/4 (sqrt (/ 1 x)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt -1) 4)))) (+ (* 3/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2)))))) x)) (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))
1
(+ 1 (* x (+ 3/2 (sqrt x))))
(+ 1 (* x (+ 3/2 (+ (sqrt x) (* 3/8 x)))))
(+ 1 (* x (+ 3/2 (+ (sqrt x) (* x (+ 3/8 (* -1/16 x)))))))
(* 2 (sqrt (pow x 3)))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt (/ 1 x))))))
(* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt (/ 1 x)))))))
(* 2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
1
1
1
1
1
1
1
1
1
1
1
1
0
0
0
0
0
0
0
0
0
0
0
0
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 (pow x 2))
(* -1/8 (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)
(* 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 (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 (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)))
(* 1/2 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 (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))
(* -1/2 (log x))
(* -1/2 (log x))
(* -1/2 (log x))
(* -1/2 (log x))
(* 1/2 (log (/ 1 x)))
(* 1/2 (log (/ 1 x)))
(* 1/2 (log (/ 1 x)))
(* 1/2 (log (/ 1 x)))
(* -1/2 (+ (log -1) (* -1 (log (/ -1 x)))))
(* -1/2 (+ (log -1) (* -1 (log (/ -1 x)))))
(* -1/2 (+ (log -1) (* -1 (log (/ -1 x)))))
(* -1/2 (+ (log -1) (* -1 (log (/ -1 x)))))
(log x)
(log x)
(log x)
(log x)
(* -1 (log (/ 1 x)))
(* -1 (log (/ 1 x)))
(* -1 (log (/ 1 x)))
(* -1 (log (/ 1 x)))
(+ (log -1) (* -1 (log (/ -1 x))))
(+ (log -1) (* -1 (log (/ -1 x))))
(+ (log -1) (* -1 (log (/ -1 x))))
(+ (log -1) (* -1 (log (/ -1 x))))
(sqrt x)
(+ (sqrt x) (* 1/2 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (- (pow (sqrt -1) 2) (* 1/2 (/ 1 x)))))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
x
(* x (+ 1 x))
(* x (+ 1 x))
(* x (+ 1 x))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
1
(+ 1 (* x (+ 3/2 (sqrt x))))
(+ 1 (* x (+ 3/2 (+ (sqrt x) (* 3/8 x)))))
(+ 1 (* x (+ 3/2 (+ (sqrt x) (* x (+ 3/8 (* -1/16 x)))))))
(* 2 (sqrt (pow x 3)))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt (/ 1 x))))))
(* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt (/ 1 x)))))))
(* 2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))

Outputs
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(+.f64 (.f64 x (+.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x))))) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(+.f64 (.f64 x (+.f64 (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -3/8 binary64)) (.f64 (+.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)))) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)))))) (+.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)))))) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(+.f64 (.f64 x (+.f64 #s(literal 2 binary64) (+.f64 (.f64 x (-.f64 (+.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -3/8 binary64)) (.f64 (+.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)))) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x))))) (.f64 x (+.f64 (.f64 (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)) (+.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -3/8 binary64)) (.f64 (+.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)))) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)))))) (+.f64 (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/16 binary64)) (.f64 (+.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)))) #s(literal 3/8 binary64))))))) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (-.f64 #s(literal -3/2 binary64) (sqrt.f64 x)))))) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(/ (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (* 3/8 (sqrt (/ 1 x)))) x)
(/.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (+.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 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -3/8 binary64))) x)
(/ (- (+ (* -1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3))))))) x)
(/.f64 (+.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (.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 -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -3/16 binary64)) (.f64 #s(literal -3/8 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))))) x)
(* 1/2 (* (sqrt (/ 1 x)) (+ 2 (pow (sqrt -1) 2))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(* -1 (/ (+ (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2)))) (* -1/4 (sqrt (/ 1 x)))) x))
(/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))
(/.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (/.f64 (+.f64 (/.f64 (+.f64 (.f64 #s(literal 3/8 binary64) (sqrt.f64 (.f64 x (.f64 x x)))) (.f64 (sqrt.f64 x) #s(literal 1/16 binary64))) x) (.f64 (sqrt.f64 x) #s(literal 1/4 binary64))) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt -1) 4)))) (+ (* 3/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2)))))) x)) (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))
(/.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/4 binary64)) (/.f64 (+.f64 (/.f64 (+.f64 (+.f64 (/.f64 (.f64 (sqrt.f64 x) #s(literal -1/32 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (.f64 #s(literal 3/8 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (.f64 #s(literal 3/16 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) x) (+.f64 (.f64 #s(literal 3/8 binary64) (sqrt.f64 (.f64 x (.f64 x x)))) (*.f64 (sqrt.f64 x) #s(literal 1/16 binary64)))) x)) x)) (-.f64 #s(literal 0 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* x (+ 3/2 (sqrt x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64))))
(+ 1 (* x (+ 3/2 (+ (sqrt x) (* 3/8 x)))))
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(* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
(+.f64 x (-.f64 #s(literal 0 binary64) (*.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) #s(literal 1 binary64)))))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
(.f64 x (+.f64 #s(literal 1 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (/.f64 #s(literal 1/16 binary64) (.f64 x (*.f64 x (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))))) x)))
x
(* x (+ 1 x))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(* x (+ 1 x))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(* x (+ 1 x))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(pow x 2)
(*.f64 x x)
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
(* (pow x 2) (+ 1 (/ 1 x)))
(*.f64 x (+.f64 #s(literal 1 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* x (+ 3/2 (sqrt x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64))))
(+ 1 (* x (+ 3/2 (+ (sqrt x) (* 3/8 x)))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (sqrt.f64 x) (+.f64 #s(literal 3/2 binary64) (.f64 x #s(literal 3/8 binary64))))))
(+ 1 (* x (+ 3/2 (+ (sqrt x) (* x (+ 3/8 (* -1/16 x)))))))
(+.f64 #s(literal 1 binary64) (.f64 x (+.f64 (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)) (.f64 x (+.f64 #s(literal 3/8 binary64) (*.f64 x #s(literal -1/16 binary64)))))))
(* 2 (sqrt (pow x 3)))
(.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 x (*.f64 x x))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(.f64 (.f64 x x) (+.f64 (.f64 #s(literal 3/2 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)))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt (/ 1 x))))))
(.f64 (.f64 x x) (+.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 3/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))
(* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt (/ 1 x)))))))
(.f64 (.f64 x x) (+.f64 (.f64 #s(literal 3/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (+.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -9/4 binary64))) #s(literal 1/2 binary64))))))
(* 2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) #s(literal -2 binary64))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 x (.f64 x (+.f64 (.f64 #s(literal 3/2 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)))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (.f64 #s(literal 3/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (-.f64 (.f64 #s(literal 3/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -3/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (+.f64 #s(literal -1/2 binary64) (.f64 #s(literal -1/2 binary64) (.f64 x #s(literal -9/4 binary64)))))) (.f64 x (.f64 x x))))))

eval99.0ms (1.1%)

Compiler: Compiled 19447 to 1616 computations (91.7% saved)

prune71.0ms (0.8%)

Pruning

14 alts after pruning (8 fresh and 6 done)

	Pruned	Kept	Total
New	664	2	666
Fresh	1	6	7
Picked	2	3	5
Done	0	3	3
Total	667	14	681

Accuracy

100.0%

Counts

681 → 14

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	74.9%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) 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))))
▶	53.3%	(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
▶	51.5%	(/.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)))
	55.5%	(/.f64 (*.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) x)
▶	55.4%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
	47.8%	(-.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))
✓	46.5%	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 x))
✓	50.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	48.4%	(-.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 #s(literal -1/2 binary64) x)))
✓	46.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	55.6%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
	53.2%	(.f64 (/.f64 #s(literal 1 binary64) x) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))))
✓	51.9%	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))
✓	1.8%	(.f64 #s(literal -1/8 binary64) (.f64 x x))

Compiler

Compiled 250 to 178 computations (28.8% saved)

simplify271.0ms (3%)

Algorithm

1×	egg-herbie

Localize:

Found 18 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	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
✓	cost-diff	0	(+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
✓	cost-diff	0	(*.f64 #s(literal -1/2 binary64) x)
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(+.f64 (sqrt.f64 x) (*.f64 #s(literal -1/2 binary64) x))
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 #s(literal -1/2 binary64) x)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	cost-diff	0	(*.f64 #s(literal 2 binary64) x)
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) x))
✓	cost-diff	0	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)) (sqrt.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))))
✓	cost-diff	0	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) 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))))

Rules

1766×	`-lowering-.f32`
1766×	`-lowering-.f64`
1466×	`--lowering--.f32`
1466×	`--lowering--.f64`
1334×	`+-lowering-+.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	176
1	66	169
2	123	161
3	261	160
4	520	160
5	1093	160
6	3184	160
7	6773	160
0	8062	160

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

localize287.0ms (3.2%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))
✓	accuracy	99.8%	(/.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	51.2%	(+.f64 x (-.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
✓	accuracy	99.7%	(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
✓	accuracy	99.7%	(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 #s(literal -1/2 binary64) x)))
✓	accuracy	100.0%	(*.f64 #s(literal -1/2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (sqrt.f64 x) (*.f64 #s(literal -1/2 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.7%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
✓	accuracy	100.0%	(*.f64 x (+.f64 #s(literal 1 binary64) x))
✓	accuracy	84.1%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) 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))))
✓	accuracy	76.7%	(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))

Results

147.0ms	123×	1	valid
57.0ms	133×	0	valid

Compiler

Compiled 185 to 33 computations (82.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 144.0ms

backward-pass: 35.0ms (24.4% of total)

ival-pow: 32.0ms (22.3% of total)

ival-div: 30.0ms (20.9% of total)

ival-add: 15.0ms (10.4% of total)

ival-sub: 13.0ms (9.1% of total)

ival-mult: 11.0ms (7.7% of total)

ival-sqrt: 6.0ms (4.2% of total)

const: 1.0ms (0.7% of total)

series12.0ms (0.1%)

Counts

20 → 240

Calls

Call 1

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

Outputs
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))>
#<alt (- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))>
#<alt (- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (* 3/8 (sqrt (/ 1 x)))) x)>
#<alt (/ (- (+ (* -1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3))))))) x)>
#<alt (* 1/2 (* (sqrt (/ 1 x)) (+ 2 (pow (sqrt -1) 2))))>
#<alt (* -1 (/ (+ (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2)))) (* -1/4 (sqrt (/ 1 x)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt -1) 4)))) (+ (* 3/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2)))))) x)) (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))>
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* 2 x)) (sqrt x))>
#<alt (- (+ 1 (* x (+ 2 (* -1/2 (sqrt x))))) (sqrt x))>
#<alt (- (+ 1 (* x (+ 2 (* x (- (* 1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))))) (sqrt x))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (+ 1 (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x)))))>
#<alt (* x (- (+ 1 (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x)))) (* 1/16 (/ 1 (pow x 3)))))>
#<alt (* x (+ 2 (pow (sqrt -1) 2)))>
#<alt (* x (+ 2 (+ (* 1/2 (/ 1 x)) (pow (sqrt -1) 2))))>
#<alt (* -1 (* x (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (+ 2 (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (- (* -1 (/ (+ 1/2 (* -1 (/ (+ (* 1/16 (/ 1 (* x (pow (sqrt -1) 4)))) (* 1/8 (/ 1 (pow (sqrt -1) 2)))) x))) x)) (+ 2 (pow (sqrt -1) 2)))))>
#<alt 1>
#<alt (+ 1 (* 2 x))>
#<alt (+ 1 (* 2 x))>
#<alt (+ 1 (* 2 x))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ 1 x)))>
#<alt (* x (+ 2 (/ 1 x)))>
#<alt (* x (+ 2 (/ 1 x)))>
#<alt (* 2 x)>
#<alt (* x (+ 2 (/ 1 x)))>
#<alt (* x (+ 2 (/ 1 x)))>
#<alt (* x (+ 2 (/ 1 x)))>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 2 x)>
#<alt (* 1/2 (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 (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 (sqrt x)>
#<alt (+ (sqrt x) (* -1/2 x))>
#<alt (+ (sqrt x) (* -1/2 x))>
#<alt (+ (sqrt x) (* -1/2 x))>
#<alt (* x (- (sqrt (/ 1 x)) 1/2))>
#<alt (* x (- (sqrt (/ 1 x)) 1/2))>
#<alt (* x (- (sqrt (/ 1 x)) 1/2))>
#<alt (* x (- (sqrt (/ 1 x)) 1/2))>
#<alt (* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/2 x)>
#<alt (* -1/8 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))>
#<alt (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))>
#<alt (+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)>
#<alt (* 1/2 (sqrt x))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))>
#<alt (* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 1 x)))>
#<alt (* -1/8 (sqrt (/ 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 (* 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))))))))>
#<alt (sqrt x)>
#<alt (+ (sqrt x) (* 1/2 (sqrt (pow x 3))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))>
#<alt (* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))>
#<alt (* -1 (* x (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (- (pow (sqrt -1) 2) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))>
#<alt x>
#<alt (* x (+ 1 x))>
#<alt (* x (+ 1 x))>
#<alt (* x (+ 1 x))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (pow x 2)>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt (* (pow x 2) (+ 1 (/ 1 x)))>
#<alt 1>
#<alt (+ 1 (* x (+ 3/2 (sqrt x))))>
#<alt (+ 1 (* x (+ 3/2 (+ (sqrt x) (* 3/8 x)))))>
#<alt (+ 1 (* x (+ 3/2 (+ (sqrt x) (* x (+ 3/8 (* -1/16 x)))))))>
#<alt (* 2 (sqrt (pow x 3)))>
#<alt (* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))>
#<alt (* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt (/ 1 x))))))>
#<alt (* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt (/ 1 x)))))))>
#<alt (* 2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))>
#<alt (* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* (pow x 2) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (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)))))))>

Calls

60 calls:

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

rewrite414.0ms (4.6%)

Algorithm

1×	batch-egg-rewrite

Rules

2518×	`fma-lowering-fma.f32`
2518×	`fma-lowering-fma.f64`
2314×	`-lowering-.f32`
2314×	`-lowering-.f64`
1816×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	32	141
1	235	124
2	2256	121
0	8469	121

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 518

Calls

Call 1

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

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

simplify355.0ms (4%)

Algorithm

1×	egg-herbie

Rules

4688×	`-lowering-.f32`
4688×	`-lowering-.f64`
2576×	`+-lowering-+.f64`
2576×	`+-lowering-+.f32`
1632×	`times-frac`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	462	2531
1	1527	2197
2	5638	2170
0	9204	2170

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
(- 1 (sqrt x))
(- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (* 3/8 (sqrt (/ 1 x)))) x)
(/ (- (+ (* -1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3))))))) x)
(* 1/2 (* (sqrt (/ 1 x)) (+ 2 (pow (sqrt -1) 2))))
(* -1 (/ (+ (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2)))) (* -1/4 (sqrt (/ 1 x)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt -1) 4)))) (+ (* 3/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2)))))) x)) (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))
(- 1 (sqrt x))
(- (+ 1 (* 2 x)) (sqrt x))
(- (+ 1 (* x (+ 2 (* -1/2 (sqrt x))))) (sqrt x))
(- (+ 1 (* x (+ 2 (* x (- (* 1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))))) (sqrt x))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (+ 1 (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x)))))
(* x (- (+ 1 (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x)))) (* 1/16 (/ 1 (pow x 3)))))
(* x (+ 2 (pow (sqrt -1) 2)))
(* x (+ 2 (+ (* 1/2 (/ 1 x)) (pow (sqrt -1) 2))))
(* -1 (* x (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (+ 2 (pow (sqrt -1) 2)))))
(* -1 (* x (- (* -1 (/ (+ 1/2 (* -1 (/ (+ (* 1/16 (/ 1 (* x (pow (sqrt -1) 4)))) (* 1/8 (/ 1 (pow (sqrt -1) 2)))) x))) x)) (+ 2 (pow (sqrt -1) 2)))))
1
(+ 1 (* 2 x))
(+ 1 (* 2 x))
(+ 1 (* 2 x))
(* 2 x)
(* x (+ 2 (/ 1 x)))
(* x (+ 2 (/ 1 x)))
(* x (+ 2 (/ 1 x)))
(* 2 x)
(* x (+ 2 (/ 1 x)))
(* x (+ 2 (/ 1 x)))
(* x (+ 2 (/ 1 x)))
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 2 x)
(* 1/2 (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 (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))))
(sqrt x)
(+ (sqrt x) (* -1/2 x))
(+ (sqrt x) (* -1/2 x))
(+ (sqrt x) (* -1/2 x))
(* x (- (sqrt (/ 1 x)) 1/2))
(* x (- (sqrt (/ 1 x)) 1/2))
(* x (- (sqrt (/ 1 x)) 1/2))
(* x (- (sqrt (/ 1 x)) 1/2))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/2 x)
(* -1/8 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(* 1/2 (sqrt (/ 1 x)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(+ (* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) (* -1/8 (sqrt (/ 1 (pow x 3)))))
(* -1/8 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) x)
(* 1/2 (sqrt x))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x)))))
(* -1/2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* 1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 1 x)))
(* -1/8 (sqrt (/ 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))))
(* 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))))))))
(sqrt x)
(+ (sqrt x) (* 1/2 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (- (pow (sqrt -1) 2) (* 1/2 (/ 1 x)))))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
x
(* x (+ 1 x))
(* x (+ 1 x))
(* x (+ 1 x))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(pow x 2)
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
(* (pow x 2) (+ 1 (/ 1 x)))
1
(+ 1 (* x (+ 3/2 (sqrt x))))
(+ 1 (* x (+ 3/2 (+ (sqrt x) (* 3/8 x)))))
(+ 1 (* x (+ 3/2 (+ (sqrt x) (* x (+ 3/8 (* -1/16 x)))))))
(* 2 (sqrt (pow x 3)))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt (/ 1 x))))))
(* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt (/ 1 x)))))))
(* 2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (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)))))))

Outputs
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(+.f64 #s(literal 1 binary64) (-.f64 (.f64 x (-.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64))))) (sqrt.f64 x)))
(- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(+.f64 (.f64 x (+.f64 (.f64 x (-.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3/8 binary64)) (.f64 (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)) (-.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)))))))) (-.f64 #s(literal 2 binary64) (*.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)))))) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(+.f64 #s(literal 1 binary64) (-.f64 (.f64 x (+.f64 #s(literal 2 binary64) (-.f64 (.f64 x (-.f64 (-.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 x (+.f64 (.f64 (-.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)))) #s(literal 3/8 binary64)) (+.f64 (.f64 (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)) (-.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (+.f64 (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3/8 binary64)) (.f64 (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)) (-.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)))))))) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal -1/16 binary64)))))) (+.f64 (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3/8 binary64)) (.f64 (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)) (-.f64 #s(literal 2 binary64) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)))))))) (.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (+.f64 (sqrt.f64 x) #s(literal 3/2 binary64)))))) (sqrt.f64 x)))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(/ (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (* 3/8 (sqrt (/ 1 x)))) x)
(/.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (.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 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -3/8 binary64)))) x)
(/ (- (+ (* -1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3))))))) x)
(/.f64 (+.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (+.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 (.f64 #s(literal -1/32 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal 3/16 binary64)) (.f64 #s(literal 3/8 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))))) x)
(* 1/2 (* (sqrt (/ 1 x)) (+ 2 (pow (sqrt -1) 2))))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(* -1 (/ (+ (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2)))) (* -1/4 (sqrt (/ 1 x)))) x))
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/4 binary64)) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))
(/.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (/.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/16 binary64)) (.f64 #s(literal -3/8 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) x)) x)) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt -1) 4)))) (+ (* 3/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2)))))) x)) (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))
(/.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)) (/.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/4 binary64)) (/.f64 (+.f64 (.f64 #s(literal -3/8 binary64) (sqrt.f64 (.f64 x (.f64 x x)))) (-.f64 (.f64 (sqrt.f64 x) #s(literal -1/16 binary64)) (/.f64 (+.f64 (-.f64 (/.f64 (.f64 (sqrt.f64 x) #s(literal -1/32 binary64)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) (.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal -3/16 binary64))) (.f64 #s(literal 3/8 binary64) (sqrt.f64 (.f64 x (*.f64 x x))))) x))) x)) x)) (-.f64 #s(literal 0 binary64) x))
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 2 x)) (sqrt x))
(+.f64 (*.f64 x #s(literal 2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 2 (* -1/2 (sqrt x))))) (sqrt x))
(+.f64 (.f64 x (+.f64 #s(literal 2 binary64) (.f64 (sqrt.f64 x) #s(literal -1/2 binary64)))) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* x (+ 2 (* x (- (* 1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x)))))))) (sqrt x))
(+.f64 #s(literal 1 binary64) (-.f64 (.f64 x (+.f64 #s(literal 2 binary64) (.f64 x (+.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/8 binary64)))))) (sqrt.f64 x)))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal 1/2 binary64))
(* x (+ 1 (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x)))))
(+.f64 (.f64 x (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/8 binary64) (.f64 x x)))) #s(literal 1/2 binary64))
(* x (- (+ 1 (+ (/ 1/8 (pow x 2)) (* 1/2 (/ 1 x)))) (* 1/16 (/ 1 (pow x 3)))))
(.f64 x (+.f64 (+.f64 (/.f64 #s(literal 1/2 binary64) x) (/.f64 #s(literal 1/8 binary64) (.f64 x x))) (+.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/16 binary64) (.f64 x (.f64 x x))))))
(* x (+ 2 (pow (sqrt -1) 2)))
x
(* x (+ 2 (+ (* 1/2 (/ 1 x)) (pow (sqrt -1) 2))))
(+.f64 x #s(literal 1/2 binary64))
(* -1 (* x (- (* -1 (/ (- 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (+ 2 (pow (sqrt -1) 2)))))
(*.f64 (+.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal 1/8 binary64) x)) x))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (- (* -1 (/ (+ 1/2 (* -1 (/ (+ (* 1/16 (/ 1 (* x (pow (sqrt -1) 4)))) (* 1/8 (/ 1 (pow (sqrt -1) 2)))) x))) x)) (+ 2 (pow (sqrt -1) 2)))))
(*.f64 (+.f64 #s(literal -1 binary64) (/.f64 (-.f64 #s(literal 1/2 binary64) (/.f64 (+.f64 (/.f64 (/.f64 #s(literal 1/16 binary64) x) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64))) #s(literal -1/8 binary64)) x)) (-.f64 #s(literal 0 binary64) x))) (-.f64 #s(literal 0 binary64) x))
1
#s(literal 1 binary64)
(+ 1 (* 2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 2 binary64)))
(+ 1 (* 2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 2 binary64)))
(+ 1 (* 2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 2 binary64)))
(* x (+ 2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 2 binary64)))
(* x (+ 2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* x (+ 2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 2 binary64)))
(* x (+ 2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 2 binary64)))
(* x (+ 2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 2 binary64)))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 2 x)
(*.f64 x #s(literal 2 binary64))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(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 (*.f64 x #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* 1/2 x)) (sqrt x))
(+.f64 (*.f64 x #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(- (+ 1 (* 1/2 x)) (sqrt x))
(+.f64 (*.f64 x #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (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 (*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(+.f64 (*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(+.f64 (*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(* 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 (*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(+.f64 (*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(+.f64 (*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) #s(literal 1 binary64))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* -1/2 x))
(+.f64 (sqrt.f64 x) (*.f64 x #s(literal -1/2 binary64)))
(+ (sqrt x) (* -1/2 x))
(+.f64 (sqrt.f64 x) (*.f64 x #s(literal -1/2 binary64)))
(+ (sqrt x) (* -1/2 x))
(+.f64 (sqrt.f64 x) (*.f64 x #s(literal -1/2 binary64)))
(* x (- (sqrt (/ 1 x)) 1/2))
(*.f64 x (+.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (- (sqrt (/ 1 x)) 1/2))
(*.f64 x (+.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (- (sqrt (/ 1 x)) 1/2))
(*.f64 x (+.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (- (sqrt (/ 1 x)) 1/2))
(*.f64 x (+.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 binary64) x))
(* -1 (* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(*.f64 (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 binary64) x))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/2 x)
(*.f64 x #s(literal -1/2 binary64))
(* -1/8 (sqrt (/ 1 (pow x 3))))
(.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -1/8 binary64))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (*.f64 x x))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (*.f64 x x))
(/ (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (pow x 3)))) (pow x 2))
(/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (.f64 x x))))) (*.f64 x x))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/8 binary64)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/8 binary64)))
(+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt (/ 1 x))))
(+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) #s(literal -1/8 binary64)))
(* -1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
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(.f64 #s(literal 2 binary64) (sqrt.f64 (.f64 x (*.f64 x x))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(.f64 (.f64 x x) (+.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 3/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt (/ 1 x))))))
(.f64 (.f64 x x) (+.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 #s(literal 3/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))
(* (pow x 2) (+ (* 1/2 (* (sqrt (/ 1 (pow x 7))) (- 1 (* 9/4 x)))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (sqrt (/ 1 x)))))))
(.f64 (.f64 x x) (+.f64 (.f64 #s(literal 3/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))))) (+.f64 (.f64 #s(literal 2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 7 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal -9/4 binary64))) #s(literal 1/2 binary64))))))
(* 2 (* (sqrt (pow x 3)) (pow (sqrt -1) 2)))
(.f64 (sqrt.f64 (.f64 x (*.f64 x x))) #s(literal -2 binary64))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(.f64 x (.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (.f64 #s(literal 3/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))))
(* (pow x 2) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (+ (* 3/2 (sqrt (/ 1 (pow x 5)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (.f64 x x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (.f64 #s(literal 3/2 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64))))))))
(* (pow x 2) (+ (* -1 (/ (+ (* -3/2 (sqrt x)) (* -1/2 (* (sqrt (/ 1 x)) (- 1 (* -9/4 (/ x (pow (sqrt -1) 2))))))) (pow x 3))) (+ (* 3/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (.f64 x x) (-.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -2 binary64)) (.f64 #s(literal 3/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal -3/2 binary64)) (.f64 (.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 1 binary64) (/.f64 (.f64 x #s(literal -9/4 binary64)) #s(literal -1 binary64))))) (.f64 x (.f64 x x)))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
(+ 1 (* x (+ 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) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 binary64)) (+.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)))) (+ (* 1/16 (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 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal -1/8 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 #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))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64)) (-.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (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 #s(literal 0 binary64) (.f64 x (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 5 binary64)))) #s(literal 1/8 binary64)) (+.f64 (.f64 #s(literal 1/16 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 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))

eval115.0ms (1.3%)

Compiler: Compiled 20140 to 2212 computations (89% saved)

prune194.0ms (2.2%)

Pruning

16 alts after pruning (7 fresh and 9 done)

	Pruned	Kept	Total
New	848	6	854
Fresh	2	1	3
Picked	2	3	5
Done	0	6	6
Total	852	16	868

Accuracy

100.0%

Counts

868 → 16

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	53.3%	(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
	48.9%	(/.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 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))) (+.f64 (.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) x)))))
	51.5%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (/.f64 #s(literal 1 binary64) (sqrt.f64 (/.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))) (sqrt.f64 x)))
	48.2%	(/.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)))
	55.5%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) 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)))
	55.7%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	55.4%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
	47.8%	(-.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))
✓	46.5%	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))) (sqrt.f64 x))
✓	50.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	48.4%	(-.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (*.f64 #s(literal -1/2 binary64) x)))
✓	46.5%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	55.6%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
✓	51.9%	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))
✓	1.8%	(.f64 #s(literal -1/8 binary64) (.f64 x x))

Compiler

Compiled 547 to 237 computations (56.7% saved)

regimes17.0ms (0.2%)

Counts

26 → 1

Calls

Call 1

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

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

Calls

2 calls:

8.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
8.0ms	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)

regimes11.0ms (0.1%)

Counts

15 → 2

Calls

Call 1

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

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:

6.0ms	x
4.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
99.5%	2	`x`
99.5%	2	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes5.0ms (0.1%)

Counts

14 → 2

Calls

Call 1

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

Outputs

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
98.5%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0.1%)

Counts

11 → 2

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
98.4%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Counts

10 → 2

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
98.4%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0.1%)

Counts

9 → 2

Calls

Call 1

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

5.0ms

Results

Accuracy	Segments	Branch
98.4%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Counts

8 → 2

Calls

Call 1

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

3.0ms

Results

Accuracy	Segments	Branch
98.2%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

3 → 2

Calls

Call 1

Inputs
(.f64 #s(literal -1/8 binary64) (.f64 x 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:

2.0ms

Results

Accuracy	Segments	Branch
98.0%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

2 → 1

Calls

Call 1

Inputs
(.f64 #s(literal -1/8 binary64) (.f64 x x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
46.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

Inputs
(.f64 #s(literal -1/8 binary64) (.f64 x x))

Outputs
(.f64 #s(literal -1/8 binary64) (.f64 x x))

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
1.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	2.4629793188069016e-5	0.010985140435010976

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch13.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	0.012484588304161466	30.69229050516152

Results

6.0ms

128×

valid

Compiler

Compiled 212 to 169 computations (20.3% saved)

Precisions

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

ival-sqrt: 2.0ms (56.5% of total)

ival-sub: 1.0ms (28.2% of total)

ival-add: 1.0ms (28.2% of total)

const: 0.0ms (0% of total)

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

bsearch12.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.012484588304161466	30.69229050516152

Results

6.0ms

128×

valid

Compiler

Compiled 180 to 145 computations (19.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-sqrt: 2.0ms (59.4% of total)

ival-sub: 1.0ms (29.7% of total)

ival-add: 1.0ms (29.7% of total)

const: 0.0ms (0% of total)

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

bsearch14.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	0.012484588304161466	30.69229050516152

Results

8.0ms

128×

valid

Compiler

Compiled 148 to 121 computations (18.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-sqrt: 2.0ms (60.8% of total)

ival-sub: 1.0ms (30.4% of total)

ival-add: 1.0ms (30.4% of total)

const: 0.0ms (0% of total)

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

bsearch11.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.012484588304161466	30.69229050516152

Results

6.0ms

128×

valid

Compiler

Compiled 148 to 121 computations (18.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-sqrt: 2.0ms (60.1% of total)

ival-sub: 1.0ms (30.1% of total)

ival-add: 1.0ms (30.1% of total)

const: 0.0ms (0% of total)

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

bsearch22.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
20.0ms	0.012484588304161466	30.69229050516152

Results

16.0ms

128×

valid

Compiler

Compiled 116 to 97 computations (16.4% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-sqrt: 12.0ms (90.2% of total)

ival-sub: 1.0ms (7.5% of total)

ival-add: 1.0ms (7.5% of total)

const: 0.0ms (0% of total)

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

bsearch11.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
10.0ms	0.012484588304161466	30.69229050516152

Results

6.0ms

128×

valid

Compiler

Compiled 108 to 89 computations (17.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 3.0ms

ival-sqrt: 2.0ms (60.5% of total)

ival-sub: 1.0ms (30.2% of total)

ival-add: 1.0ms (30.2% of total)

const: 0.0ms (0% of total)

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

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

38×	`+-commutative_binary64`
28×	`*-commutative_binary64`
20×	`sub-neg_binary64`
10×	`neg-sub0_binary64`
10×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	146
1	80	146
2	93	146
3	107	146
4	115	146
5	120	146
6	122	146

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 5902958103587057/147573952589676412928 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 5854679515581645/4503599627370496 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 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 5404319552844595/4503599627370496 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 (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 (sqrt.f64 x) (.f64 #s(literal -1/2 binary64) 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)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(.f64 #s(literal -1/8 binary64) (.f64 x x))

Outputs
(/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #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)))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 5902958103587057/147573952589676412928 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 5902958103587057/147573952589676412928 binary64)) (*.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(if (<=.f64 x #s(literal 5854679515581645/4503599627370496 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 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 5854679515581645/4503599627370496 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 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))))
(if (<=.f64 x #s(literal 5404319552844595/4503599627370496 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 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 5404319552844595/4503599627370496 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 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/2 binary64))))
(if (<=.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (.f64 #s(literal -1/2 binary64) x))) (.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 (sqrt.f64 x) (.f64 x #s(literal -1/2 binary64)))) (.f64 #s(literal 1/2 binary64) (pow.f64 x #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 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x #s(literal 1/2 binary64))) (.f64 #s(literal 1/2 binary64) (pow.f64 x #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) (pow.f64 x #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)))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(.f64 #s(literal -1/8 binary64) (.f64 x x))

soundness2.3s (25.9%)

Rules

4688×	`-lowering-.f32`
4688×	`-lowering-.f64`
4006×	`-lowering-.f32`
4006×	`-lowering-.f64`
3588×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	311	2017
1	982	1657
2	3815	1617
0	8291	1617
0	113	434
1	325	384
2	1037	376
3	3221	373
4	7103	373
0	8112	373
0	32	106
1	197	98
2	1512	93
0	8813	93
0	462	2531
1	1527	2197
2	5638	2170
0	9204	2170
0	31	131
1	232	117
2	2319	115
0	9732	115
0	6	16
1	39	16
2	300	16
3	3704	16
0	8338	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

Compiler

Compiled 354 to 216 computations (39% saved)

preprocess58.0ms (0.6%)

Compiler: Compiled 330 to 130 computations (60.6% 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%)

sample1.3s (14.2%)

preprocess38.0ms (0.4%)

explain91.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify15.0ms (0.2%)

localize44.0ms (0.5%)

series6.0ms (0.1%)

rewrite266.0ms (3%)

simplify256.0ms (2.9%)

eval34.0ms (0.4%)

prune37.0ms (0.4%)

simplify219.0ms (2.4%)

localize223.0ms (2.5%)

series17.0ms (0.2%)

rewrite578.0ms (6.5%)

simplify229.0ms (2.6%)

eval100.0ms (1.1%)

prune139.0ms (1.5%)

simplify201.0ms (2.2%)

localize150.0ms (1.7%)

series63.0ms (0.7%)

rewrite363.0ms (4.1%)

simplify271.0ms (3%)

eval99.0ms (1.1%)

prune71.0ms (0.8%)

simplify271.0ms (3%)

localize287.0ms (3.2%)

series12.0ms (0.1%)

rewrite414.0ms (4.6%)

simplify355.0ms (4%)

eval115.0ms (1.3%)

prune194.0ms (2.2%)

regimes17.0ms (0.2%)

regimes11.0ms (0.1%)

regimes5.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0%)

regimes5.0ms (0.1%)

regimes4.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

regimes2.0ms (0%)

bsearch0.0ms (0%)

bsearch13.0ms (0.1%)

bsearch12.0ms (0.1%)

bsearch14.0ms (0.2%)

bsearch11.0ms (0.1%)

bsearch22.0ms (0.2%)

bsearch11.0ms (0.1%)

simplify12.0ms (0.1%)

soundness2.3s (25.9%)

preprocess58.0ms (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