Metrics for 2sqrt (example 3.1)

analyze2.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 15 to 10 computations (33.3% saved)

Precisions

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

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

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

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

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

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

const: 0.0ms (0% of total)

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

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

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

sample2.0s (22.4%)

Results

889.0ms	4727×	1	valid
782.0ms	3366×	2	valid
17.0ms	163×	0	valid

Precisions

Click to see histograms. Total time spent on operations: 1.2s

ival-sqrt: 364.0ms (30.5% of total)

ival-add: 210.0ms (17.6% of total)

backward-pass: 149.0ms (12.5% of total)

...c/correct-round.rkt:119:19: 147.0ms (12.3% of total)

ival-sub: 137.0ms (11.5% of total)

ival->: 103.0ms (8.6% of total)

ival-<: 40.0ms (3.4% of total)

ival-and: 25.0ms (2.1% of total)

const: 16.0ms (1.3% of total)

Bogosity

preprocess39.0ms (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)))

explain120.0ms (1.3%)

FPErrors

Click to see full error table

Ground Truth	Overpredictions	Example	Example	Subexpression
255	1	(157.83282348267716)	-	`(-.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

45.0ms	224×	2	valid
40.0ms	270×	1	valid
1.0ms	18×	0	valid

Compiler

Compiled 48 to 20 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 51.0ms

ival-sqrt: 22.0ms (43.4% of total)

backward-pass: 12.0ms (23.7% of total)

ival-add: 9.0ms (17.8% of total)

ival-sub: 6.0ms (11.8% of total)

const: 1.0ms (2% 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
▶	7.0%	(-.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)

localize58.0ms (0.6%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	7.0%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

22.0ms	112×	2	valid
17.0ms	135×	1	valid
1.0ms	9×	0	valid

Compiler

Compiled 20 to 7 computations (65% saved)

Precisions

Click to see histograms. Total time spent on operations: 22.0ms

ival-sqrt: 9.0ms (41.1% of total)

backward-pass: 5.0ms (22.9% of total)

ival-add: 4.0ms (18.3% of total)

ival-sub: 3.0ms (13.7% of total)

const: 1.0ms (4.6% of total)

series4.0ms (0%)

Counts

4 → 48

Calls

Call 1

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

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

Calls

12 calls:

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

rewrite257.0ms (2.8%)

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

simplify196.0ms (2.2%)

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)

eval37.0ms (0.4%)

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

prune47.0ms (0.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	274	7	281
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	274	8	282

Accuracy

99.9%

Counts

282 → 8

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.0%	(/.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)
▶	98.4%	(/.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)
	8.8%	(/.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)))
▶	7.0%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))
✓	7.0%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	1.6%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
	6.5%	(.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))))))
▶	97.6%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 224 to 152 computations (32.1% saved)

simplify152.0ms (1.7%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

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

Rules

2504×	`fmm-def`
1902×	`fma-lowering-fma.f32`
1902×	`fma-lowering-fma.f64`
1772×	`fmsub-define`
1680×	`fnmadd-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	183
1	55	183
2	90	183
3	126	183
4	174	183
5	252	183
6	392	183
7	526	183
8	624	183
9	829	183
10	1088	183
11	1210	183
12	1438	183
13	2007	183
14	4043	183
15	7471	183
0	8344	183

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize284.0ms (3.1%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	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	99.6%	(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))
✓	accuracy	99.5%	(/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
✓	accuracy	7.0%	(-.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) 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))
✓	accuracy	100.0%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.6%	(/.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)
✓	accuracy	99.0%	(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
✓	accuracy	73.0%	(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))

Results

118.0ms	104×	2	valid
105.0ms	143×	1	valid
3.0ms	9×	0	valid

Compiler

Compiled 234 to 28 computations (88% saved)

Precisions

Click to see histograms. Total time spent on operations: 138.0ms

ival-pow: 31.0ms (22.5% of total)

backward-pass: 29.0ms (21% of total)

ival-mult: 23.0ms (16.7% of total)

ival-div: 22.0ms (15.9% of total)

ival-sqrt: 14.0ms (10.1% of total)

ival-add: 11.0ms (8% of total)

ival-sub: 6.0ms (4.3% of total)

const: 2.0ms (1.4% of total)

series13.0ms (0.1%)

Counts

16 → 192

Calls

Call 1

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

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

Calls

48 calls:

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

rewrite339.0ms (3.7%)

Algorithm

1×	batch-egg-rewrite

Rules

2990×	`-lowering-.f32`
2990×	`-lowering-.f64`
2634×	`/-lowering-/.f32`
2634×	`/-lowering-/.f64`
2438×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	27	110
1	169	97
2	1398	96
0	8405	96

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 626

Calls

Call 1

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

Outputs
(exp.f64 (.f64 (log.f64 (/.f64 x (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))) #s(literal -1 binary64)))
(-.f64 (/.f64 #s(literal 0 binary64) (-.f64 #s(literal 0 binary64) x)) (/.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (-.f64 #s(literal 0 binary64) x)))
(-.f64 (/.f64 (/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (-.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))))) x) (/.f64 (/.f64 (pow.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 2 binary64)) (-.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))))) x))
(-.f64 (/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x (-.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))))) (/.f64 (pow.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 2 binary64)) (.f64 x (-.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))))))
(neg.f64 (/.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) (-.f64 #s(literal 0 binary64) x)))
(neg.f64 (/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) x))
(/.f64 #s(literal 1 binary64) (/.f64 x (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (/.f64 x (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) #s(literal 1 binary64)))
(/.f64 #s(literal 1 binary64) (neg.f64 (neg.f64 (/.f64 x (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))))
(/.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) x)
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 x (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))))
(/.f64 #s(literal -1 binary64) (neg.f64 (/.f64 (/.f64 x (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) #s(literal 1 binary64))))
(/.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 3 binary64))) (.f64 x (+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))))
(/.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 2 binary64))) (.f64 x (-.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))))))
(/.f64 (.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 3 binary64))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) x))
(/.f64 (.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 3 binary64))) #s(literal -1 binary64)) (.f64 (+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 2 binary64))) #s(literal 1 binary64)) (.f64 (-.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) x))
(/.f64 (.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 2 binary64))) #s(literal -1 binary64)) (.f64 (-.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 #s(literal 0 binary64) x)))
(/.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))) (neg.f64 (-.f64 #s(literal 0 binary64) x)))
(/.f64 (neg.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 3 binary64)))) (neg.f64 (.f64 x (+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 2 binary64)))) (neg.f64 (.f64 x (-.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))))))
(/.f64 (.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) #s(literal 1 binary64)) x)
(/.f64 (.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))) #s(literal -1 binary64)) (-.f64 #s(literal 0 binary64) x))
(/.f64 (.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 3 binary64))) (/.f64 #s(literal 1 binary64) x)) (+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal 1/16 binary64) (pow.f64 x #s(literal 3/2 binary64)))) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))))
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(/.f64 (neg.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))) (neg.f64 (+.f64 (.f64 x #s(literal 1/4 binary64)) (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))))))
(/.f64 (neg.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x #s(literal 1/4 binary64)))) (neg.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))))
(/.f64 (-.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64))) (-.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))))
(/.f64 (-.f64 (.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (+.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 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (.f64 x #s(literal 1/4 binary64)))) (.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))))
(/.f64 (neg.f64 (neg.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64))))) (neg.f64 (neg.f64 (-.f64 (+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x #s(literal 1/4 binary64))) (.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))))))
(/.f64 (neg.f64 (neg.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x #s(literal 1/4 binary64))))) (neg.f64 (neg.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))))
(/.f64 (neg.f64 (-.f64 (.f64 x #s(literal 1/4 binary64)) (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)))) (neg.f64 (-.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)))))
(/.f64 (-.f64 (pow.f64 (/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) #s(literal 3 binary64))) (+.f64 (.f64 (/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (+.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 binary64) x) #s(literal 1/64 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) (+.f64 (.f64 (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))) (.f64 (/.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))) (/.f64 (.f64 x #s(literal 1/4 binary64)) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 #s(literal -1/2 binary64) (sqrt.f64 x))))))))
(pow.f64 (/.f64 (-.f64 (+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x #s(literal 1/4 binary64))) (.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 #s(literal -1/8 binary64) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))))) (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.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 binary64) x) #s(literal 1/64 binary64)) (*.f64 x #s(literal 1/4 binary64)))) #s(literal -1 binary64))
(.f64 (+.f64 (/.f64 #s(literal -1/512 binary64) (pow.f64 x #s(literal 3/2 binary64))) (pow.f64 (.f64 x #s(literal 1/4 binary64)) #s(literal 3/2 binary64))) (/.f64 #s(literal 1 binary64) (-.f64 (+.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x #s(literal 1/4 binary64))) (.f64 (pow.f64 x #s(literal -1/2 binary64)) (.f64 #s(literal -1/8 binary64) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))))))
(.f64 (-.f64 (.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/64 binary64)) (.f64 x #s(literal 1/4 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (.f64 #s(literal -1/2 binary64) (sqrt.f64 x)))))
(exp.f64 (.f64 (.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal -1/2 binary64))) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 3 binary64) (log.f64 x)) #s(literal -1/2 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal 3/2 binary64))) #s(literal -1 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal 3 binary64)))
(exp.f64 (.f64 (.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 3 binary64)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 3 binary64))))
(fabs.f64 (pow.f64 x #s(literal -3/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))
(/.f64 #s(literal 1 binary64) (pow.f64 x #s(literal 3/2 binary64)))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (neg.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 (pow.f64 x #s(literal -1/2 binary64)) x)
(/.f64 #s(literal -1 binary64) (*.f64 #s(literal -1 binary64) (pow.f64 x #s(literal 3/2 binary64))))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (*.f64 x (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64))))
(/.f64 (neg.f64 (pow.f64 x #s(literal -1/2 binary64))) (-.f64 #s(literal 0 binary64) x))
(/.f64 (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64)) #s(literal 3 binary64)))
(/.f64 (sqrt.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x))) (sqrt.f64 (neg.f64 (*.f64 x x))))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (*.f64 x (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64)))))
(pow.f64 x #s(literal -3/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64))
(pow.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 3 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -3 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal -3/4 binary64)) #s(literal 2 binary64))
(pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal 1/4 binary64))
(*.f64 #s(literal 1 binary64) (pow.f64 x #s(literal -3/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 x #s(literal -1/2 binary64)))
(*.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 #s(literal 1 binary64) x))
(.f64 (pow.f64 x #s(literal -1/2 binary64)) (pow.f64 (/.f64 (.f64 x x) #s(literal 1 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) (/.f64 (pow.f64 x #s(literal -1/2 binary64)) (sqrt.f64 x)))
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal -3/2 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 x (*.f64 x x))) #s(literal 1/2 binary64)))
(.f64 (sqrt.f64 #s(literal -1 binary64)) (sqrt.f64 (/.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x)))))
(*.f64 (pow.f64 x #s(literal -3/4 binary64)) (pow.f64 x #s(literal -3/4 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 3 binary64)) (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 3 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/2 binary64)) (pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal -1 binary64)) (pow.f64 (pow.f64 x #s(literal 3/4 binary64)) #s(literal -1 binary64)))
(*.f64 (sqrt.f64 (pow.f64 x #s(literal -3/2 binary64))) (sqrt.f64 (pow.f64 x #s(literal -3/2 binary64))))
(*.f64 (/.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64)) (/.f64 (pow.f64 x #s(literal -1/4 binary64)) x))
(*.f64 (/.f64 (pow.f64 x #s(literal -1/4 binary64)) x) (/.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1 binary64)))
(*.f64 (/.f64 (pow.f64 x #s(literal -1/4 binary64)) (sqrt.f64 x)) (/.f64 (pow.f64 x #s(literal -1/4 binary64)) (sqrt.f64 x)))
(exp.f64 (*.f64 #s(literal -3 binary64) (log.f64 x)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -3 binary64)))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64)) (.f64 (.f64 #s(literal -3 binary64) (log.f64 x)) #s(literal 1/2 binary64))))
(exp.f64 (-.f64 (log.f64 (/.f64 #s(literal 1 binary64) x)) (*.f64 (log.f64 x) #s(literal 2 binary64))))
(sqrt.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(neg.f64 (/.f64 #s(literal -1 binary64) (.f64 x (.f64 x x))))
(/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))))
(/.f64 (/.f64 #s(literal 1 binary64) x) (*.f64 x x))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))
(/.f64 #s(literal -1 binary64) (neg.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x))))))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x)) (neg.f64 (*.f64 x x)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) x)
(/.f64 (neg.f64 (neg.f64 (/.f64 #s(literal 1 binary64) x))) (neg.f64 (neg.f64 (*.f64 x x))))
(/.f64 (neg.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x))) (-.f64 #s(literal 0 binary64) x))
(pow.f64 x #s(literal -3 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -6 binary64))
(pow.f64 (*.f64 x x) #s(literal -3/2 binary64))
(pow.f64 (.f64 x (.f64 x x)) #s(literal -1 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal -3/2 binary64)) #s(literal 2 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal -2 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (.f64 x (.f64 x x)))) #s(literal -1 binary64))
(pow.f64 (.f64 (.f64 x x) (.f64 (.f64 x x) (*.f64 x x))) #s(literal -1/2 binary64))
(pow.f64 (.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal 1/2 binary64))
(.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))
(.f64 (/.f64 #s(literal 1 binary64) x) (/.f64 #s(literal 1 binary64) (.f64 x x)))
(.f64 (/.f64 #s(literal 1 binary64) x) (pow.f64 (/.f64 (.f64 x x) #s(literal 1 binary64)) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))) #s(literal 1 binary64))
(*.f64 (pow.f64 x #s(literal -3/2 binary64)) (pow.f64 x #s(literal -3/2 binary64)))
(.f64 #s(literal -1 binary64) (/.f64 #s(literal -1 binary64) (.f64 x (*.f64 x x))))
(*.f64 (/.f64 #s(literal -1 binary64) x) (/.f64 (/.f64 #s(literal -1 binary64) x) x))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) x))

simplify214.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

3292×	`+-lowering-+.f64`
3292×	`+-lowering-+.f32`
3242×	`-lowering-.f32`
3242×	`-lowering-.f64`
1062×	`--lowering--.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	2163
1	814	1825
2	3118	1810
0	8247	1810

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

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

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

eval147.0ms (1.6%)

Compiler: Compiled 24358 to 2769 computations (88.6% saved)

prune100.0ms (1.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	1052	7	1059
Fresh	1	1	2
Picked	5	0	5
Done	0	1	1
Total	1058	9	1067

Accuracy

100.0%

Counts

1067 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	33.6%	(/.f64 (/.f64 (+.f64 (.f64 (sqrt.f64 (.f64 x (.f64 x x))) (.f64 x #s(literal 1/2 binary64))) (.f64 (sqrt.f64 x) (+.f64 #s(literal 1/16 binary64) (.f64 x #s(literal -1/8 binary64))))) (*.f64 x x)) x)
▶	8.8%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
▶	98.4%	(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
▶	97.5%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
▶	97.5%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	7.0%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	97.9%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
▶	6.5%	(.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))))))
	90.6%	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))

Compiler

Compiled 224 to 144 computations (35.7% saved)

simplify156.0ms (1.7%)

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

Rules

2516×	`-lowering-.f32`
2516×	`-lowering-.f64`
1772×	`+-lowering-+.f64`
1772×	`+-lowering-+.f32`
1510×	`fnmadd-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	202
1	69	165
2	164	161
3	398	161
4	1026	161
5	4454	161
0	8216	161

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

localize265.0ms (2.9%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.9%	(/.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	65.8%	(.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	51.8%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))
✓	accuracy	8.0%	(+.f64 x (-.f64 #s(literal 1 binary64) x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
✓	accuracy	99.6%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
✓	accuracy	8.0%	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
✓	accuracy	100.0%	(*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
✓	accuracy	99.6%	(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
✓	accuracy	99.6%	(/.f64 #s(literal -1/8 binary64) (sqrt.f64 x))

Results

193.0ms	239×	1	valid
6.0ms	17×	0	valid

Compiler

Compiled 199 to 30 computations (84.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 138.0ms

ival-pow: 40.0ms (29% of total)

ival-div: 29.0ms (21% of total)

ival-add: 26.0ms (18.8% of total)

backward-pass: 15.0ms (10.9% of total)

ival-sqrt: 10.0ms (7.2% of total)

ival-mult: 10.0ms (7.2% of total)

ival-sub: 7.0ms (5.1% of total)

const: 1.0ms (0.7% of total)

series16.0ms (0.2%)

Counts

16 → 192

Calls

Call 1

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

48 calls:

Time	Variable		Point	Expression
4.0ms	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	(/ (+ (/ -1/8 (sqrt x)) (* (sqrt x) 1/2)) x)
1.0ms	x	@	-inf	(/ (+ x (- 1 x)) (+ (pow (+ x 1) 3/2) (pow x 3/2)))
1.0ms	x	@	-inf	(/ (- (+ 1 x) x) (+ (sqrt x) (pow (+ 1 x) 1/2)))
1.0ms	x	@	0	(* (/ (+ x (- 1 x)) (+ (pow (+ x 1) 3/2) (pow x 3/2))) (- (+ x (+ x 1)) (sqrt (* x (+ x 1)))))

rewrite381.0ms (4.2%)

Algorithm

1×	batch-egg-rewrite

Rules

4508×	`-lowering-.f32`
4508×	`-lowering-.f64`
2786×	`/-lowering-/.f32`
2786×	`/-lowering-/.f64`
2692×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	29	108
1	241	82
2	2357	81
0	10388	81

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 495

Calls

Call 1

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

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

simplify268.0ms (3%)

Algorithm

1×	egg-herbie

Rules

3962×	`-lowering-.f32`
3962×	`-lowering-.f64`
2026×	`+-lowering-+.f64`
2026×	`+-lowering-+.f32`
1822×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	399	2036
1	1293	1781
2	4965	1751
0	8815	1751

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

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

eval419.0ms (4.6%)

Compiler: Compiled 21437 to 2007 computations (90.6% saved)

prune118.0ms (1.3%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	895	5	900
Fresh	2	1	3
Picked	3	2	5
Done	0	1	1
Total	900	9	909

Accuracy

100.0%

Counts

909 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	8.8%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))
▶	64.6%	(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (.f64 (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x))))
✓	97.5%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
▶	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))))
✓	97.5%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
▶	90.6%	(/.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
✓	7.0%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	97.9%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
	47.9%	(.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))))))

Compiler

Compiled 208 to 131 computations (37% saved)

simplify187.0ms (2.1%)

Algorithm

1×	egg-herbie

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	64	(+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	64	(.f64 (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)))
✓	cost-diff	128	(.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))
✓	cost-diff	832	(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (.f64 (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x))))
✓	cost-diff	64	(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
✓	cost-diff	64	(+.f64 (sqrt.f64 x) (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
✓	cost-diff	256	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
✓	cost-diff	320	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))
✓	cost-diff	0	(log.f64 x)
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) (log.f64 x))
✓	cost-diff	6528	(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
✓	cost-diff	6528	(/.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
✓	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	(sqrt.f64 x)
✓	cost-diff	64	(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	64	(+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	64	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))))

Rules

2402×	`-lowering-.f32`
2402×	`-lowering-.f64`
1824×	`fma-define`
1818×	`+-lowering-+.f64`
1818×	`+-lowering-+.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	180
1	75	171
2	175	164
3	445	164
4	909	164
5	1912	164
6	7647	164
0	8460	164

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize292.0ms (3.2%)

Localize:

Found 18 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	99.8%	(.f64 (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)))
✓	accuracy	64.7%	(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (.f64 (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x))))
✓	accuracy	100.0%	(+.f64 (sqrt.f64 x) (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))
✓	accuracy	99.6%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))
✓	accuracy	51.7%	(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x))
✓	accuracy	8.0%	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (log.f64 x))
✓	accuracy	100.0%	(log.f64 x)
✓	accuracy	99.6%	(/.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
✓	accuracy	92.6%	(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
✓	accuracy	100.0%	(pow.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))))

Results

232.0ms	239×	1	valid
6.0ms	17×	0	valid

Compiler

Compiled 215 to 31 computations (85.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 141.0ms

ival-pow: 39.0ms (27.6% of total)

ival-mult: 23.0ms (16.3% of total)

ival-div: 18.0ms (12.7% of total)

backward-pass: 16.0ms (11.3% of total)

ival-add: 14.0ms (9.9% of total)

ival-sub: 14.0ms (9.9% of total)

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

ival-exp: 5.0ms (3.5% of total)

ival-sqrt: 5.0ms (3.5% of total)

const: 1.0ms (0.7% of total)

series66.0ms (0.7%)

Counts

19 → 228

Calls

Call 1

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

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

Calls

57 calls:

Time	Variable		Point	Expression
34.0ms	x	@	0	(* 1/2 (log x))
12.0ms	x	@	-inf	(* 1/2 (log x))
6.0ms	x	@	inf	(* 1/2 (log x))
5.0ms	x	@	0	(/ (- 1 (* x x)) (- 1 x))
0.0ms	x	@	0	(pow x -1/2)

rewrite413.0ms (4.6%)

Algorithm

1×	batch-egg-rewrite

Rules

5714×	`-lowering-.f32`
5714×	`-lowering-.f64`
3058×	`/-lowering-/.f32`
3058×	`/-lowering-/.f64`
2654×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	109
1	218	101
2	1842	97
0	9842	97

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 926

Calls

Call 1

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

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

simplify263.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

4124×	`-lowering-.f32`
4124×	`-lowering-.f64`
4026×	`+-lowering-+.f64`
4026×	`+-lowering-+.f32`
1312×	`associate-r`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	2394
1	822	2128
2	2944	2084
0	8296	2084

Stop Event

1×	iter limit
1×	node limit

Counts

228 → 228

Calls

Call 1

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

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

eval194.0ms (2.1%)

Compiler: Compiled 43719 to 3496 computations (92% saved)

prune160.0ms (1.8%)

Pruning

9 alts after pruning (4 fresh and 5 done)

	Pruned	Kept	Total
New	1482	4	1486
Fresh	1	0	1
Picked	3	2	5
Done	0	3	3
Total	1486	9	1495

Accuracy

100.0%

Counts

1495 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	99.5%	(/.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 2 binary64))) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x)))) (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 2 binary64))))
	64.6%	(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 2 binary64))) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 2 binary64))) (sqrt.f64 x))))
✓	97.5%	(/.f64 (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) x)
	99.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
	50.0%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (-.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))
✓	97.5%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	90.6%	(/.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
✓	7.0%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	97.9%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))

Compiler

Compiled 444 to 170 computations (61.7% saved)

regimes14.0ms (0.1%)

Counts

24 → 1

Calls

Call 1

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

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

Calls

2 calls:

7.0ms	x
5.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
99.6%	1	`x`
99.6%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes9.0ms (0.1%)

Counts

8 → 1

Calls

Call 1

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

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

Calls

2 calls:

6.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
3.0ms	x

Results

Accuracy	Segments	Branch
97.9%	1	`x`
97.9%	1	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes2.0ms (0%)

Counts

2 → 1

Calls

Call 1

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

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

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
97.5%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
1.6%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	21	22
2	25	22
3	27	22
4	28	22

Stop Event

1×

saturated

Calls

Call 1

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

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

soundness1.7s (19%)

Rules

5714×	`-lowering-.f32`
5714×	`-lowering-.f64`
4508×	`-lowering-.f32`
4508×	`-lowering-.f64`
3058×	`/-lowering-/.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	113	434
1	325	384
2	1037	376
3	3221	373
4	7103	373
0	8112	373
0	30	109
1	218	101
2	1842	97
0	9842	97
0	29	108
1	241	82
2	2357	81
0	10388	81
0	27	110
1	169	97
2	1398	96
0	8405	96
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

Compiler

Compiled 102 to 71 computations (30.4% saved)

preprocess41.0ms (0.5%)

Compiler: Compiled 82 to 52 computations (36.6% 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%)

sample2.0s (22.4%)

preprocess39.0ms (0.4%)

explain120.0ms (1.3%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify15.0ms (0.2%)

localize58.0ms (0.6%)

series4.0ms (0%)

rewrite257.0ms (2.8%)

simplify196.0ms (2.2%)

eval37.0ms (0.4%)

prune47.0ms (0.5%)

simplify152.0ms (1.7%)

localize284.0ms (3.1%)

series13.0ms (0.1%)

rewrite339.0ms (3.7%)

simplify214.0ms (2.4%)

eval147.0ms (1.6%)

prune100.0ms (1.1%)

simplify156.0ms (1.7%)

localize265.0ms (2.9%)

series16.0ms (0.2%)

rewrite381.0ms (4.2%)

simplify268.0ms (3%)

eval419.0ms (4.6%)

prune118.0ms (1.3%)

simplify187.0ms (2.1%)

localize292.0ms (3.2%)

series66.0ms (0.7%)

rewrite413.0ms (4.6%)

simplify263.0ms (2.9%)

eval194.0ms (2.1%)

prune160.0ms (1.8%)

regimes14.0ms (0.1%)

regimes9.0ms (0.1%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify7.0ms (0.1%)

soundness1.7s (19%)

preprocess41.0ms (0.5%)

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