Metrics for 2sqrt (example 3.1)

analyze4.0ms (0.1%)

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)

sample2.3s (33.1%)

Results

979.0ms	4733×	1	valid
855.0ms	3347×	2	valid
19.0ms	176×	0	valid

Precisions

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

ival-sqrt: 354.0ms (27.6% of total)

...c/correct-round.rkt:119:19: 258.0ms (20.1% of total)

backward-pass: 192.0ms (15% of total)

ival-add: 157.0ms (12.2% of total)

ival->: 120.0ms (9.4% of total)

ival-sub: 110.0ms (8.6% of total)

ival-and: 38.0ms (3% of total)

ival-<: 35.0ms (2.7% of total)

const: 18.0ms (1.4% of total)

Bogosity

preprocess40.0ms (0.6%)

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)))

explain172.0ms (2.5%)

FPErrors

Click to see full error table

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

Results

66.0ms	222×	2	valid
65.0ms	288×	1	valid
0.0ms	2×	0	valid

Compiler

Compiled 48 to 20 computations (58.3% saved)

Precisions

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

ival-sqrt: 23.0ms (40.5% of total)

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

ival-sub: 9.0ms (15.9% of total)

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

const: 1.0ms (1.8% of total)

eval0.0ms (0%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	5.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify14.0ms (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)

localize76.0ms (1.1%)

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	5.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

35.0ms	111×	2	valid
29.0ms	144×	1	valid
0.0ms	1×	0	valid

Compiler

Compiled 20 to 7 computations (65% saved)

Precisions

Click to see histograms. Total time spent on operations: 30.0ms

backward-pass: 12.0ms (40.1% of total)

ival-sqrt: 10.0ms (33.4% of total)

ival-add: 4.0ms (13.4% of total)

ival-sub: 3.0ms (10% of total)

const: 1.0ms (3.3% of total)

series4.0ms (0.1%)

Counts

4 → 48

Calls

Call 1

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

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

Calls

12 calls:

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

rewrite405.0ms (5.9%)

Algorithm

1×	batch-egg-rewrite

Rules

2262×	`sum3-define`
1950×	`fnmadd-define`
1764×	`sum5-define`
1584×	`fmm-def`
1548×	`fnmsub-define`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	14	16
2	24	16
3	38	16
4	59	16
5	96	16
6	165	16
7	298	16
8	1656	16
9	2756	16
10	6603	16
0	8415	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 270

Calls

Call 1

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

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

simplify201.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	434
1	325	384
2	1039	376
3	3228	373
4	7108	373
0	8118	373

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval56.0ms (0.8%)

Compiler: Compiled 5368 to 611 computations (88.6% saved)

prune51.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	315	3	318
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	315	4	319

Accuracy

99.9%

Counts

319 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
✓	5.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	1.6%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
▶	99.0%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 34 to 27 computations (20.6% saved)

simplify10.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 9 expressions of interest:

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

Rules

62×	`sum3-define`
40×	`+-lowering-+.f64`
40×	`+-lowering-+.f32`
32×	`fma-define`
28×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	61
1	23	61
2	30	61
3	36	61
4	44	61
5	57	61
6	74	61
7	91	61
8	111	61
9	130	61
10	149	61
0	149	61

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

localize102.0ms (1.5%)

Localize:

Found 9 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%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(/.f64 #s(literal 1 binary64) x)
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))

Results

58.0ms

256×

valid

Compiler

Compiled 73 to 14 computations (80.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 17.0ms

ival-mult: 5.0ms (30% of total)

ival-div: 4.0ms (24% of total)

ival-sqrt: 4.0ms (24% of total)

ival-sub: 1.0ms (6% of total)

ival-add: 1.0ms (6% of total)

const: 1.0ms (6% of total)

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

series5.0ms (0.1%)

Counts

8 → 96

Calls

Call 1

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

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

Calls

24 calls:

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

rewrite230.0ms (3.3%)

Algorithm

1×	batch-egg-rewrite

Rules

2698×	`-lowering-.f32`
2698×	`-lowering-.f64`
2178×	`/-lowering-/.f32`
2178×	`/-lowering-/.f64`
1292×	`+-lowering-+.f64`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	13	41
1	40	36
2	133	36
3	450	36
4	1588	35
0	8843	35

Stop Event

1×	iter limit
1×	node limit

Counts

8 → 694

Calls

Call 1

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

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

simplify194.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

2470×	`-lowering-.f32`
2470×	`-lowering-.f64`
1720×	`fnmadd-define`
1376×	`fma-lowering-fma.f32`
1376×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	50	661
1	126	539
2	358	533
3	953	527
4	2597	527
5	5497	527
6	6827	527
7	7818	527
0	8077	527

Stop Event

1×	iter limit
1×	node limit

Counts

96 → 96

Calls

Call 1

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

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

eval99.0ms (1.4%)

Compiler: Compiled 15600 to 2396 computations (84.6% saved)

prune104.0ms (1.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	987	5	992
Fresh	0	0	0
Picked	3	0	3
Done	0	1	1
Total	990	6	996

Accuracy

100.0%

Counts

996 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.3%	(/.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) x)
▶	98.8%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
▶	99.3%	(-.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))
✓	5.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	99.2%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
▶	91.6%	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))

Compiler

Compiled 92 to 72 computations (21.7% saved)

simplify149.0ms (2.2%)

Algorithm

1×	egg-herbie

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	cost-diff	0	(-.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))
✓	cost-diff	0	(log.f64 x)
✓	cost-diff	0	(*.f64 (log.f64 x) #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))
✓	cost-diff	6464	(exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))
✓	cost-diff	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	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

1430×	`fnmadd-define`
1056×	`fmsub-define`
1050×	`fma-define`
1010×	`fnmsub-define`
878×	`sum3-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	21	97
1	36	97
2	65	95
3	111	95
4	183	95
5	318	95
6	632	95
7	1054	95
8	1891	95
9	3521	95
10	4593	95
11	4907	95
12	5341	95
13	5520	95
14	5572	95
15	5580	95
16	5582	95
17	5584	95
0	5584	95

Stop Event

1×	iter limit
1×	saturated

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

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

localize128.0ms (1.9%)

Localize:

Found 16 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(-.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))
✓	accuracy	99.6%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	accuracy	99.3%	(/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64)))
✓	accuracy	100.0%	(*.f64 (log.f64 x) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))
✓	accuracy	100.0%	(log.f64 x)
✓	accuracy	92.3%	(exp.f64 (*.f64 (log.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%	(pow.f64 x #s(literal -1/2 binary64))
✓	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

100.0ms

256×

valid

Compiler

Compiled 103 to 22 computations (78.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 42.0ms

ival-pow: 12.0ms (28.5% of total)

ival-div: 11.0ms (26.2% of total)

ival-mult: 7.0ms (16.6% of total)

ival-exp: 3.0ms (7.1% of total)

ival-sub: 3.0ms (7.1% of total)

ival-log: 3.0ms (7.1% of total)

ival-sqrt: 2.0ms (4.8% of total)

const: 1.0ms (2.4% of total)

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

series62.0ms (0.9%)

Counts

13 → 156

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

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

Calls

39 calls:

Time	Variable		Point	Expression
26.0ms	x	@	0	(* (log x) -1/2)
20.0ms	x	@	-inf	(* (log x) -1/2)
6.0ms	x	@	inf	(* (log x) -1/2)
2.0ms	x	@	inf	(/ (- (/ -1/8 (sqrt x)) (* (sqrt x) -1/2)) x)
2.0ms	x	@	-inf	(/ (- (/ -1/8 (sqrt x)) (* (sqrt x) -1/2)) x)

rewrite359.0ms (5.2%)

Algorithm

1×	batch-egg-rewrite

Rules

2616×	`-lowering-.f32`
2616×	`-lowering-.f64`
2316×	`/-lowering-/.f32`
2316×	`/-lowering-/.f64`
1584×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	21	66
1	70	61
2	330	61
3	2147	59
0	8886	59

Stop Event

1×	iter limit
1×	node limit

Counts

13 → 1917

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

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

simplify176.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

3436×	`-lowering-.f32`
3436×	`-lowering-.f64`
1684×	`times-frac`
1440×	`fnmadd-define`
1248×	`fma-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	58	1015
1	135	937
2	342	929
3	852	929
4	2940	929
5	7645	929
0	8182	929

Stop Event

1×	iter limit
1×	node limit

Counts

156 → 156

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

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

eval391.0ms (5.7%)

Compiler: Compiled 45518 to 2935 computations (93.6% saved)

prune172.0ms (2.5%)

Pruning

7 alts after pruning (1 fresh and 6 done)

	Pruned	Kept	Total
New	2238	1	2239
Fresh	0	0	0
Picked	0	5	5
Done	0	1	1
Total	2238	7	2245

Accuracy

100.0%

Counts

2245 → 7

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.3%	(/.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) x)
✓	98.8%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	99.3%	(-.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))
✓	5.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	45.7%	(.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))
✓	99.2%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
✓	91.6%	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))

Compiler

Compiled 60 to 46 computations (23.3% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Program
✓	cost-diff	(*.f64 x x)
✓	cost-diff	(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
✓	cost-diff	(pow.f64 x #s(literal 3/2 binary64))
✓	cost-diff	(.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))

Rules

26×	`-lowering-.f32`
26×	`-lowering-.f64`
18×	`/-lowering-/.f32`
18×	`/-lowering-/.f64`
8×	`associate-*l/`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	20
1	13	20
2	23	20
3	29	20
4	31	20
0	31	20

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize44.0ms (0.6%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 x #s(literal 3/2 binary64))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.3%	(/.f64 #s(literal 1/2 binary64) (*.f64 x x))
✓	accuracy	48.3%	(.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))

Results

35.0ms

256×

valid

Compiler

Compiled 25 to 8 computations (68% saved)

Precisions

Click to see histograms. Total time spent on operations: 16.0ms

ival-mult: 7.0ms (43.6% of total)

ival-pow: 7.0ms (43.6% of total)

ival-div: 2.0ms (12.4% of total)

const: 1.0ms (6.2% of total)

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

series3.0ms (0%)

Counts

4 → 48

Calls

Call 1

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

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

Calls

12 calls:

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

rewrite220.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

1884×	`fma-lowering-fma.f32`
1884×	`fma-lowering-fma.f64`
1498×	`+-lowering-+.f64`
1498×	`+-lowering-+.f32`
1418×	`-lowering-.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	27	17
2	108	14
3	449	14
4	1780	13
5	4431	13
0	8177	13

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 220

Calls

Call 1

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

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

simplify16.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

100×	`fma-define`
78×	`sum3-define`
70×	`-lowering-.f32`
70×	`-lowering-.f64`
60×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	244
1	30	188
2	52	184
3	71	184
4	87	184
5	90	184
6	96	184
7	128	184
8	142	184
9	168	184
10	272	184
11	275	184
0	275	184

Stop Event

1×	iter limit
1×	saturated

Counts

48 → 48

Calls

Call 1

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

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

eval30.0ms (0.4%)

Compiler: Compiled 3115 to 553 computations (82.2% saved)

prune30.0ms (0.4%)

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	266	2	268
Fresh	0	0	0
Picked	0	1	1
Done	0	6	6
Total	266	9	275

Accuracy

100.0%

Counts

275 → 9

Alt Table

Click to see full alt table

Status	Accuracy	Program
	45.7%	(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64))))
✓	99.3%	(/.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal -1/2 binary64))) x)
✓	98.8%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	99.3%	(-.f64 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))
✓	5.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
	45.7%	(.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))) x))
✓	45.7%	(.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))
✓	99.2%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
✓	91.6%	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))

Compiler

Compiled 195 to 113 computations (42.1% saved)

regimes11.0ms (0.2%)

Counts

12 → 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 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64))))
(.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))) 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 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))
(/.f64 (-.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 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)

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

Calls

2 calls:

7.0ms	x
3.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes7.0ms (0.1%)

Counts

10 → 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 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 #s(literal 1/2 binary64) (.f64 x x)))
(/.f64 (/.f64 #s(literal 1 binary64) (*.f64 x x)) (/.f64 #s(literal 2 binary64) (pow.f64 x #s(literal 3/2 binary64))))
(.f64 (pow.f64 x #s(literal 3/2 binary64)) (/.f64 (-.f64 #s(literal 0 binary64) (.f64 (-.f64 #s(literal 0 binary64) x) (/.f64 #s(literal 1/2 binary64) (*.f64 x x)))) 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 (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/8 binary64) (pow.f64 x #s(literal 3/2 binary64))))

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

Calls

2 calls:

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

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes6.0ms (0.1%)

Counts

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

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

Calls

2 calls:

3.0ms	x
2.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
99.2%	1	`x`
99.2%	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
98.8%	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)

simplify19.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

18×	`+-commutative_binary64`
18×	`sub-neg_binary64`
16×	`*-commutative_binary64`
12×	`neg-sub0_binary64`
12×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	34
1	32	34
2	51	34
3	63	34
4	72	34
5	75	34

Stop Event

1×

saturated

Calls

Call 1

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

soundness972.0ms (14.1%)

Rules

2970×	`-lowering-.f32`
2970×	`-lowering-.f64`
2698×	`-lowering-.f32`
2698×	`-lowering-.f64`
2178×	`/-lowering-/.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	113	434
1	325	384
2	1039	376
3	3228	373
4	7108	373
0	8118	373
0	13	41
1	40	36
2	133	36
3	450	36
4	1588	35
0	8843	35

Stop Event

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

Compiler

Compiled 106 to 75 computations (29.2% saved)

preprocess49.0ms (0.7%)

Compiler: Compiled 106 to 64 computations (39.6% 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	13	61
1	23	61
2	30	61
3	36	61
4	44	61
5	57	61
6	74	61
7	91	61
8	111	61
9	130	61
10	149	61
0	149	61

Iter	Nodes	Cost
0	18	244
1	30	188
2	52	184
3	71	184
4	87	184
5	90	184
6	96	184
7	128	184
8	142	184
9	168	184
10	272	184
11	275	184
0	275	184

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	13	61
1	23	61
2	30	61
3	36	61
4	44	61
5	57	61
6	74	61
7	91	61
8	111	61
9	130	61
10	149	61
0	149	61

Iter	Nodes	Cost
0	18	244
1	30	188
2	52	184
3	71	184
4	87	184
5	90	184
6	96	184
7	128	184
8	142	184
9	168	184
10	272	184
11	275	184
0	275	184

analyze4.0ms (0.1%)

sample2.3s (33.1%)

preprocess40.0ms (0.6%)

explain172.0ms (2.5%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify14.0ms (0.2%)

localize76.0ms (1.1%)

series4.0ms (0.1%)

rewrite405.0ms (5.9%)

simplify201.0ms (2.9%)

eval56.0ms (0.8%)

prune51.0ms (0.7%)

simplify10.0ms (0.1%)

localize102.0ms (1.5%)

series5.0ms (0.1%)

rewrite230.0ms (3.3%)

simplify194.0ms (2.8%)

eval99.0ms (1.4%)

prune104.0ms (1.5%)

simplify149.0ms (2.2%)

localize128.0ms (1.9%)

series62.0ms (0.9%)

rewrite359.0ms (5.2%)

simplify176.0ms (2.5%)

eval391.0ms (5.7%)

prune172.0ms (2.5%)

simplify5.0ms (0.1%)

localize44.0ms (0.6%)

series3.0ms (0%)

rewrite220.0ms (3.2%)

simplify16.0ms (0.2%)

eval30.0ms (0.4%)

prune30.0ms (0.4%)

regimes11.0ms (0.2%)

regimes7.0ms (0.1%)

regimes6.0ms (0.1%)

regimes2.0ms (0%)

regimes1.0ms (0%)

simplify19.0ms (0.3%)

soundness972.0ms (14.1%)

preprocess49.0ms (0.7%)

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

Iter	Nodes	Cost
0	13	61
1	23	61
2	30	61
3	36	61
4	44	61
5	57	61
6	74	61
7	91	61
8	111	61
9	130	61
10	149	61
0	149	61

Iter	Nodes	Cost
0	18	244
1	30	188
2	52	184
3	71	184
4	87	184
5	90	184
6	96	184
7	128	184
8	142	184
9	168	184
10	272	184
11	275	184
0	275	184