Metrics for Main:bigenough3 from C

analyze2.0ms (0%)

Algorithm

1×

Search

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

Compiler

Compiled 9 to 7 computations (22.2% saved)

Precisions

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

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

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

const: 0.0ms (0% of total)

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

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

sample1.3s (13.4%)

Results

401.0ms	2396×	1	valid
365.0ms	1644×	2	valid
233.0ms	4216×	0	valid
0.0ms	9×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 584.0ms

ival-sqrt: 288.0ms (49.3% of total)

ival-add: 140.0ms (24% of total)

ival-sub: 73.0ms (12.5% of total)

backward-pass: 68.0ms (11.6% of total)

const: 14.0ms (2.4% of total)

Bogosity

preprocess40.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated
1×	saturated

Calls

Call 1

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

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

Call 2

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

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

explain90.0ms (1%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
128	-	-	`(-.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

22.0ms	110×	2	valid
19.0ms	146×	1	valid
17.0ms	256×	0	valid

Compiler

Compiled 48 to 20 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 31.0ms

ival-sqrt: 14.0ms (45.1% of total)

ival-add: 6.0ms (19.3% of total)

backward-pass: 6.0ms (19.3% of total)

ival-sub: 4.0ms (12.9% of total)

const: 1.0ms (3.2% of total)

eval0.0ms (0%)

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

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	52.3%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify15.0ms (0.2%)

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

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

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

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

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

localize41.0ms (0.4%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	52.3%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

12.0ms	55×	2	valid
11.0ms	73×	1	valid
8.0ms	128×	0	valid

Compiler

Compiled 20 to 7 computations (65% saved)

Precisions

Click to see histograms. Total time spent on operations: 18.0ms

ival-sqrt: 7.0ms (38.6% of total)

ival-add: 5.0ms (27.6% of total)

backward-pass: 4.0ms (22.1% of total)

ival-sub: 2.0ms (11% of total)

const: 0.0ms (0% of total)

series5.0ms (0%)

Counts

4 → 48

Calls

Call 1

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

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

Calls

12 calls:

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

rewrite252.0ms (2.7%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 233

Calls

Call 1

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

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

simplify228.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	434
1	325	384
2	1037	376
3	3221	373
4	7103	373
0	8112	373

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval35.0ms (0.4%)

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

prune43.0ms (0.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	272	9	281
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	272	10	282

Accuracy

99.9%

Counts

282 → 10

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.2%	(/.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)
	53.0%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
	51.1%	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) (sqrt.f64 x))
▶	51.1%	(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x))
✓	52.3%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	48.9%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
	49.9%	(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))))
	51.1%	(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64)))
▶	51.1%	(+.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)))
▶	53.3%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 220 to 168 computations (23.6% saved)

simplify168.0ms (1.8%)

Algorithm

1×	egg-herbie

Localize:

Found 17 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	(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))
✓	cost-diff	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
✓	cost-diff	(-.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))
✓	cost-diff	(+.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)))
✓	cost-diff	(sqrt.f64 x)
✓	cost-diff	(*.f64 x #s(literal 1/2 binary64))
✓	cost-diff	(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
✓	cost-diff	(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 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

1622×	`fma-lowering-fma.f32`
1622×	`fma-lowering-fma.f64`
1568×	`sum4-define`
1418×	`fma-define`
1366×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	152
1	61	140
2	151	140
3	323	140
4	903	140
5	3293	140
6	4398	140
7	7538	140
0	8097	140

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize130.0ms (1.4%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)))
✓	accuracy	99.8%	(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
✓	accuracy	99.6%	(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(-.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))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))
✓	accuracy	99.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/2 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x))
✓	accuracy	100.0%	(-.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

75.0ms

256×

valid

Compiler

Compiled 166 to 25 computations (84.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 32.0ms

ival-mult: 12.0ms (36.9% of total)

ival-add: 6.0ms (18.5% of total)

ival-sub: 5.0ms (15.4% of total)

ival-div: 4.0ms (12.3% of total)

ival-sqrt: 4.0ms (12.3% of total)

const: 1.0ms (3.1% of total)

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

series13.0ms (0.1%)

Counts

16 → 192

Calls

Call 1

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

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

Calls

48 calls:

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

rewrite378.0ms (4%)

Algorithm

1×	batch-egg-rewrite

Rules

3418×	`-lowering-.f32`
3418×	`-lowering-.f64`
2952×	`/-lowering-/.f32`
2952×	`/-lowering-/.f64`
2536×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	24	112
1	171	96
2	1628	96
0	8962	96

Stop Event

1×	iter limit
1×	node limit

Counts

16 → 480

Calls

Call 1

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

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

simplify220.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

3076×	`-lowering-.f32`
3076×	`-lowering-.f64`
1858×	`fnmadd-define`
1352×	`+-lowering-+.f64`
1352×	`+-lowering-+.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	132	1476
1	394	1295
2	1258	1274
3	3901	1253
0	8288	1253

Stop Event

1×	iter limit
1×	node limit

Counts

192 → 192

Calls

Call 1

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

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

eval166.0ms (1.8%)

Compiler: Compiled 20665 to 1944 computations (90.6% saved)

prune118.0ms (1.3%)

Pruning

18 alts after pruning (15 fresh and 3 done)

	Pruned	Kept	Total
New	812	12	824
Fresh	1	3	4
Picked	3	2	5
Done	0	1	1
Total	816	18	834

Accuracy

100.0%

Counts

834 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	50.1%	(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))) x) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (sqrt.f64 x)))
	50.2%	(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
	53.0%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
	53.2%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	51.1%	(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x))
	51.1%	(-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
✓	52.3%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	48.9%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
	49.9%	(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))))
	51.1%	(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64)))
▶	49.9%	(+.f64 #s(literal 1 binary64) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x)))
▶	48.4%	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
	48.4%	(+.f64 #s(literal 1 binary64) (.f64 #s(literal 1/16 binary64) (.f64 x (*.f64 x x))))
▶	53.4%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
	2.9%	(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
	53.0%	(*.f64 #s(literal 1/2 binary64) (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64)))
	49.5%	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))
▶	3.6%	(.f64 #s(literal 1/16 binary64) (.f64 x (*.f64 x x)))

Compiler

Compiled 416 to 271 computations (34.9% saved)

simplify343.0ms (3.6%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.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)))))))
✓	cost-diff	0	(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (+.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))))))))
✓	cost-diff	0	(-.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))) x)
✓	cost-diff	0	(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))) x) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (sqrt.f64 x)))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (*.f64 x #s(literal -1/8 binary64)))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
✓	cost-diff	0	(-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x)))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 x (.f64 x x))
✓	cost-diff	128	(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
✓	cost-diff	128	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 x (.f64 x x))
✓	cost-diff	0	(.f64 #s(literal 1/16 binary64) (.f64 x (*.f64 x x)))
✓	cost-diff	0	(pow.f64 x #s(literal -1/2 binary64))
✓	cost-diff	0	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))

Rules

3684×	`+-lowering-+.f64`
3684×	`+-lowering-+.f32`
2682×	`-lowering-.f32`
2682×	`-lowering-.f64`
2122×	`--lowering--.f32`

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	31	272
1	98	236
2	319	236
3	1283	236
4	5801	234
0	8708	234

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize210.0ms (2.2%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(-.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))) x)
✓	accuracy	99.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
✓	accuracy	99.9%	(.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (+.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))))))))
✓	accuracy	64.4%	(/.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))) x) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (sqrt.f64 x)))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x)))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))
✓	accuracy	100.0%	(-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x))
✓	accuracy	100.0%	(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	91.3%	(.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal 1/16 binary64) (.f64 x (*.f64 x x)))
✓	accuracy	99.9%	(.f64 x (.f64 x x))
✓	accuracy	100.0%	(pow.f64 x #s(literal -1/2 binary64))
✓	accuracy	100.0%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))

Results

156.0ms

256×

valid

Compiler

Compiled 290 to 32 computations (89% saved)

Precisions

Click to see histograms. Total time spent on operations: 81.0ms

ival-mult: 37.0ms (45.7% of total)

ival-add: 24.0ms (29.6% of total)

ival-pow: 9.0ms (11.1% of total)

ival-div: 5.0ms (6.2% of total)

ival-sub: 2.0ms (2.5% of total)

ival-sqrt: 2.0ms (2.5% of total)

const: 1.0ms (1.2% of total)

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

series15.0ms (0.2%)

Counts

18 → 216

Calls

Call 1

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

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

Calls

54 calls:

Time	Variable		Point	Expression
2.0ms	x	@	inf	(- (* (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16))))))) x)
2.0ms	x	@	inf	(* x x)
1.0ms	x	@	0	(/ (- (* (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16))))))) x) (+ (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (sqrt x)))
0.0ms	x	@	-inf	(/ (- (* (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16))))))) x) (+ (+ 1 (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))) (sqrt x)))
0.0ms	x	@	-inf	(+ 1 (- (* x (+ 1/2 (* x -1/8))) (sqrt x)))

rewrite488.0ms (5.2%)

Algorithm

1×	batch-egg-rewrite

Rules

3458×	`-lowering-.f32`
3458×	`-lowering-.f64`
2526×	`fma-lowering-fma.f32`
2526×	`fma-lowering-fma.f64`
2104×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	31	167
1	237	131
2	2355	129
0	9034	129

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 528

Calls

Call 1

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

Outputs
(*.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 (pow.f64 x #s(literal -1/4 binary64)) (.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 1/2 binary64)))
(.f64 (.f64 #s(literal 1/2 binary64) (pow.f64 x #s(literal -1/4 binary64))) (pow.f64 x #s(literal -1/4 binary64)))
(exp.f64 (*.f64 #s(literal -1/2 binary64) (log.f64 x)))
(exp.f64 (.f64 (log.f64 (.f64 x x)) #s(literal -1/4 binary64)))
(exp.f64 (*.f64 (log.f64 (pow.f64 x #s(literal -1/4 binary64))) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal 2 binary64)) #s(literal -1/4 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 x) #s(literal -1/4 binary64)) #s(literal 2 binary64)))
(exp.f64 (+.f64 (.f64 (log.f64 x) #s(literal -1/4 binary64)) (.f64 (log.f64 x) #s(literal -1/4 binary64))))
(pow.f64 x #s(literal -1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -1 binary64))
(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64))
(pow.f64 (exp.f64 #s(literal -1/2 binary64)) (log.f64 x))
(*.f64 (pow.f64 x #s(literal -1/4 binary64)) (pow.f64 x #s(literal -1/4 binary64)))
(.f64 x (.f64 x (*.f64 x #s(literal 1/16 binary64))))
(.f64 #s(literal 1/16 binary64) (.f64 x (*.f64 x x)))
(.f64 (.f64 x x) (*.f64 x #s(literal 1/16 binary64)))
(.f64 (.f64 x (*.f64 x x)) #s(literal 1/16 binary64))
(.f64 (.f64 x #s(literal 1/16 binary64)) (*.f64 x x))
(.f64 (.f64 x (*.f64 x #s(literal 1/16 binary64))) x)
(exp.f64 (*.f64 (log.f64 x) #s(literal 3 binary64)))
(exp.f64 (+.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 3 binary64)) (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal 3 binary64))))
(pow.f64 x #s(literal 3 binary64))
(pow.f64 (*.f64 x x) #s(literal 3/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 6 binary64))
(pow.f64 (pow.f64 x #s(literal 3/2 binary64)) #s(literal 2 binary64))
(.f64 x (.f64 x x))
(.f64 (.f64 x x) x)
(*.f64 (pow.f64 x #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal 2 binary64)))
(sqrt.f64 (.f64 (.f64 x x) (*.f64 x x)))
(pow.f64 x #s(literal 2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 4 binary64))
(pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 2 binary64))
(pow.f64 (.f64 (.f64 x x) (*.f64 x x)) #s(literal 1/2 binary64))
(*.f64 x x)
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x))
(.f64 (/.f64 #s(literal 1 binary64) x) (.f64 x (*.f64 x x)))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/16 binary64)))) (+.f64 (.f64 x (*.f64 x #s(literal -1/8 binary64))) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) #s(literal 1 binary64))
(+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x #s(literal 1/16 binary64))))) (.f64 x (*.f64 x #s(literal -1/8 binary64))))
(-.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (/.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))))
(fma.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) #s(literal 1 binary64))
(fma.f64 x (.f64 x (.f64 x #s(literal 1/16 binary64))) (+.f64 (.f64 x (.f64 x #s(literal -1/8 binary64))) #s(literal 1 binary64)))
(fma.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) #s(literal 1 binary64))
(fma.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x)) (+.f64 (.f64 x (.f64 x #s(literal -1/8 binary64))) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) (.f64 x #s(literal 1/16 binary64)) (+.f64 (.f64 x (.f64 x #s(literal -1/8 binary64))) #s(literal 1 binary64)))
(fma.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) #s(literal 1 binary64))
(fma.f64 (.f64 x x) (.f64 x (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) #s(literal 1 binary64))
(fma.f64 (.f64 x (.f64 x x)) #s(literal 1/16 binary64) (+.f64 (.f64 x (.f64 x #s(literal -1/8 binary64))) #s(literal 1 binary64)))
(fma.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) #s(literal 1 binary64))
(fma.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) #s(literal 1 binary64))
(fma.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) (.f64 x (.f64 x x)) #s(literal 1 binary64))
(fma.f64 (.f64 x #s(literal 1/16 binary64)) (.f64 x x) (+.f64 (.f64 x (.f64 x #s(literal -1/8 binary64))) #s(literal 1 binary64)))
(fma.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 x x) #s(literal 1 binary64))
(fma.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) x #s(literal 1 binary64))
(fma.f64 (.f64 x (.f64 x #s(literal 1/16 binary64))) x (+.f64 (.f64 x (.f64 x #s(literal -1/8 binary64))) #s(literal 1 binary64)))
(fma.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) #s(literal 1 binary64) #s(literal 1 binary64))
(fma.f64 (.f64 (.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) x #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal 1 binary64) x) (.f64 (*.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) #s(literal 1 binary64))
(fma.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) (.f64 x (*.f64 x x)) #s(literal 1 binary64))
(fma.f64 (.f64 (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) x) (.f64 x x) #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (-.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (-.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) #s(literal 1 binary64)))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))) (+.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))
(/.f64 (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))))) (neg.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (-.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) #s(literal 1 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))) (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))))
(/.f64 (-.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64)) (-.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) #s(literal 1 binary64)))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (-.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (-.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) #s(literal 1 binary64))))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))))
(+.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/16 binary64)))) (.f64 x (*.f64 x #s(literal -1/8 binary64))))
(+.f64 (.f64 x (.f64 x #s(literal -1/8 binary64))) (.f64 x (.f64 x (*.f64 x #s(literal 1/16 binary64)))))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 x (.f64 x (.f64 x #s(literal 1/16 binary64))))) (.f64 #s(literal 1 binary64) (.f64 x (*.f64 x #s(literal -1/8 binary64)))))
(+.f64 (.f64 (.f64 x (.f64 x (.f64 x #s(literal 1/16 binary64)))) #s(literal 1 binary64)) (.f64 (.f64 x (*.f64 x #s(literal -1/8 binary64))) #s(literal 1 binary64)))
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(/.f64 (.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))))) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))))) #s(literal 1 binary64)) (+.f64 #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)))))) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))))) #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))))
(pow.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) #s(literal 1 binary64))
(pow.f64 (/.f64 (+.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)))))) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (-.f64 #s(literal 1 binary64) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))))) #s(literal -1 binary64))
(.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))))
(.f64 (+.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))))))) #s(literal 1 binary64))
(.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))))) (/.f64 #s(literal 1 binary64) (+.f64 #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)))))) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))))
(.f64 (pow.f64 (+.f64 #s(literal 1 binary64) (.f64 (.f64 x (.f64 x x)) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (+.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)))))) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))))) #s(literal 1 binary64)))
(.f64 (pow.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))))) #s(literal 1 binary64)) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))) #s(literal 1 binary64)))
(+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))
(+.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/16 binary64))
(-.f64 (/.f64 #s(literal 1/256 binary64) (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))) (/.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 x x)) (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(fma.f64 #s(literal 1 binary64) (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/16 binary64))
(fma.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1 binary64) x) #s(literal 1/16 binary64))
(fma.f64 #s(literal 1/8 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)) #s(literal 1/16 binary64))
(fma.f64 (/.f64 #s(literal 1 binary64) x) #s(literal -1/8 binary64) #s(literal 1/16 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1/256 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/16 binary64)) (/.f64 x #s(literal -1/8 binary64)))) (+.f64 #s(literal 1/4096 binary64) (/.f64 #s(literal -1/512 binary64) (.f64 x (.f64 x x))))))
(/.f64 #s(literal 1 binary64) (/.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) (-.f64 #s(literal 1/256 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 x x)))))
(/.f64 (+.f64 #s(literal 1/4096 binary64) (/.f64 #s(literal -1/512 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1/256 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/16 binary64)) (/.f64 x #s(literal -1/8 binary64)))))
(/.f64 (+.f64 #s(literal 1/4096 binary64) (/.f64 #s(literal -1/512 binary64) (.f64 x (.f64 x x)))) (+.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 x x)) (-.f64 #s(literal 1/256 binary64) (/.f64 #s(literal -1/128 binary64) x))))
(/.f64 (-.f64 #s(literal 1/256 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 x x))) (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)))
(/.f64 (neg.f64 (+.f64 #s(literal 1/4096 binary64) (/.f64 #s(literal -1/512 binary64) (.f64 x (.f64 x x))))) (neg.f64 (+.f64 #s(literal 1/256 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/16 binary64)) (/.f64 x #s(literal -1/8 binary64))))))
(/.f64 (neg.f64 (-.f64 #s(literal 1/256 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 x x)))) (neg.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(/.f64 (-.f64 (/.f64 #s(literal 1/64 binary64) (*.f64 x x)) #s(literal 1/256 binary64)) (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/16 binary64)))
(pow.f64 (/.f64 (+.f64 #s(literal 1/256 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/16 binary64)) (/.f64 x #s(literal -1/8 binary64)))) (+.f64 #s(literal 1/4096 binary64) (/.f64 #s(literal -1/512 binary64) (.f64 x (.f64 x x))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x)) (-.f64 #s(literal 1/256 binary64) (/.f64 #s(literal 1/64 binary64) (*.f64 x x)))) #s(literal -1 binary64))
(.f64 (+.f64 #s(literal 1/4096 binary64) (/.f64 #s(literal -1/512 binary64) (.f64 x (*.f64 x x)))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/256 binary64) (/.f64 (-.f64 (/.f64 #s(literal -1/8 binary64) x) #s(literal 1/16 binary64)) (/.f64 x #s(literal -1/8 binary64))))))
(.f64 (-.f64 #s(literal 1/256 binary64) (/.f64 #s(literal 1/64 binary64) (.f64 x x))) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
(exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x)))
(fabs.f64 (sqrt.f64 x))
(sqrt.f64 x)
(pow.f64 x #s(literal 1/2 binary64))
(pow.f64 (*.f64 x x) #s(literal 1/4 binary64))
(pow.f64 (sqrt.f64 x) #s(literal 1 binary64))
(pow.f64 (pow.f64 x #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 x #s(literal 1/4 binary64)))
(*.f64 (sqrt.f64 (sqrt.f64 x)) (sqrt.f64 (sqrt.f64 x)))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))
(+.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x #s(literal 1/2 binary64)))
(+.f64 (.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(+.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(fma.f64 x #s(literal 1/2 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(fma.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1/2 binary64) x (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(fma.f64 (.f64 x x) (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))
(fma.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 x x) (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) x (*.f64 x #s(literal 1/2 binary64)))
(fma.f64 (.f64 x #s(literal 1/2 binary64)) #s(literal 1 binary64) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))) (+.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))))))
(/.f64 (-.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64))) (.f64 (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))
(/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) #s(literal 1/2 binary64)))))
(/.f64 (.f64 x (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (-.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))
(/.f64 (.f64 (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) #s(literal 1/2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (.f64 x x) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) x) (-.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) x)
(.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) #s(literal 1 binary64))
(.f64 (.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))
(.f64 (.f64 #s(literal 1 binary64) (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))) x)

simplify374.0ms (4%)

Algorithm

1×	egg-herbie

Rules

5048×	`-lowering-.f32`
5048×	`-lowering-.f64`
3766×	`+-lowering-+.f64`
3766×	`+-lowering-+.f32`
1654×	`fma-lowering-fma.f32`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	246	1798
1	757	1677
2	2454	1645
0	8339	1645

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

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))
(* 1/16 (pow x 3))
(* 1/16 (pow x 3))
(* 1/16 (pow x 3))
(* 1/16 (pow x 3))
(* 1/16 (pow x 3))
(* 1/16 (pow x 3))
(* 1/16 (pow x 3))
(* 1/16 (pow x 3))
(* 1/16 (pow x 3))
(* 1/16 (pow x 3))
(* 1/16 (pow x 3))
(* 1/16 (pow x 3))
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 3)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
(pow x 2)
1
(+ 1 (* -1/8 (pow x 2)))
(+ 1 (* (pow x 2) (- (* 1/16 x) 1/8)))
(+ 1 (* (pow x 2) (- (* 1/16 x) 1/8)))
(* 1/16 (pow x 3))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (/ 1 (pow x 3))) (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (/ 1 (pow x 3))) (* 1/8 (/ 1 x))))
(* 1/16 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 (pow x 2)) 1/8) x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (/ 1 (pow x 2)) 1/8) x)) 1/16)))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/16 x) 1/8))
(* (pow x 2) (- (* 1/16 x) 1/8))
(* (pow x 2) (- (* 1/16 x) 1/8))
(* 1/16 (pow x 3))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* 1/16 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(- (+ 1 (* x (+ 1/2 (* -1/8 x)))) (sqrt x))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(* (pow x 2) (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(* -1/8 (pow x 2))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2)))) 1/8))
(* -1 (sqrt x))
(- (* 1/2 x) (sqrt x))
(- (* x (+ 1/2 (* -1/8 x))) (sqrt x))
(- (* x (+ 1/2 (* -1/8 x))) (sqrt x))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(* (pow x 2) (- (* 1/2 (/ 1 x)) (+ 1/8 (sqrt (/ 1 (pow x 3))))))
(* -1/8 (pow x 2))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8))
(* (pow x 2) (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8))
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* -1/8 x)))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* -1/8 (pow x 2))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
(* (pow x 2) (- (* 1/2 (/ 1 x)) 1/8))
1/2
(+ 1/2 (* -1/8 x))
(+ 1/2 (* -1/8 x))
(+ 1/2 (* -1/8 x))
(* -1/8 x)
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* x (- (* 1/2 (/ 1 x)) 1/8))
(* -1/8 x)
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(* -1 (* x (- 1/8 (* 1/2 (/ 1 x)))))
(/ 1 (+ 1 (sqrt x)))
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(* 1/16 (pow x 3))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (+ (sqrt (/ 1 (pow x 5))) (* 1/8 (/ 1 x)))))
(* (pow x 3) (- (+ 1/16 (+ (* -1 (/ (+ 1 (+ (* -2 (+ 1/2 (sqrt (/ 1 x)))) (* -2 (- 1/2 (sqrt (/ 1 x)))))) (pow x 3))) (/ 1/2 (pow x 2)))) (+ (sqrt (/ 1 (pow x 5))) (* 1/8 (/ 1 x)))))
(* 1/16 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* (sqrt (/ 1 (pow x 3))) (pow (sqrt -1) 2)) (* 1/2 (/ 1 x))) 1/8) x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (+ (* -2 (/ (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))) x)) (+ (* 2 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) x)) (/ 1 x))) (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))) x)) 1/8) x)) 1/16)))
1
(+ 1 (* 5/64 (pow x 4)))
(+ 1 (* (pow x 4) (+ 5/64 (* -1/64 x))))
(+ 1 (* (pow x 4) (+ 5/64 (* x (- (* 1/256 x) 1/64)))))
(* 1/256 (pow x 6))
(* (pow x 6) (- 1/256 (* 1/64 (/ 1 x))))
(* (pow x 6) (- (+ 1/256 (/ 5/64 (pow x 2))) (* 1/64 (/ 1 x))))
(* (pow x 6) (- (+ 1/256 (+ (/ 5/64 (pow x 2)) (/ 1 (pow x 6)))) (* 1/64 (/ 1 x))))
(* 1/256 (pow x 6))
(* (pow x 6) (- 1/256 (* 1/64 (/ 1 x))))
(* (pow x 6) (+ 1/256 (* -1 (/ (- 1/64 (* 5/64 (/ 1 x))) x))))
(* (pow x 6) (+ 1/256 (* -1 (/ (+ 1/64 (* -1 (/ (+ 5/64 (/ 1 (pow x 4))) x))) x))))
1
(+ 1 x)
(+ 1 (* x (+ 1 (* 5/64 (pow x 3)))))
(+ 1 (* x (+ 1 (* (pow x 3) (+ 5/64 (* -1/64 x))))))
(* 1/256 (pow x 6))
(* (pow x 6) (- 1/256 (* 1/64 (/ 1 x))))
(* (pow x 6) (- (+ 1/256 (/ 5/64 (pow x 2))) (* 1/64 (/ 1 x))))
(* (pow x 6) (- (+ 1/256 (+ (/ 5/64 (pow x 2)) (/ 1 (pow x 5)))) (* 1/64 (/ 1 x))))
(* 1/256 (pow x 6))
(* (pow x 6) (- 1/256 (* 1/64 (/ 1 x))))
(* (pow x 6) (+ 1/256 (* -1 (/ (- 1/64 (* 5/64 (/ 1 x))) x))))
(* (pow x 6) (+ 1/256 (* -1 (/ (+ 1/64 (* -1 (/ (+ 5/64 (/ 1 (pow x 3))) x))) x))))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(* 1/16 (pow x 3))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (+ (/ 1/2 (pow x 2)) (/ 1 (pow x 3)))) (* 1/8 (/ 1 x))))
(* 1/16 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (+ (* 1/2 (/ 1 x)) (/ 1 (pow x 2))) 1/8) x)) 1/16)))
(/ -1/8 x)
(/ (- (* 1/16 x) 1/8) x)
(/ (- (* 1/16 x) 1/8) x)
(/ (- (* 1/16 x) 1/8) x)
1/16
(- 1/16 (* 1/8 (/ 1 x)))
(- 1/16 (* 1/8 (/ 1 x)))
(- 1/16 (* 1/8 (/ 1 x)))
1/16
(- 1/16 (* 1/8 (/ 1 x)))
(- 1/16 (* 1/8 (/ 1 x)))
(- 1/16 (* 1/8 (/ 1 x)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* 1/2 x)
(* x (+ 1/2 (* -1/8 x)))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))
(* 1/16 (pow x 3))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(* 1/16 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))

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

eval1.0s (10.8%)

Compiler: Compiled 54018 to 2569 computations (95.2% saved)

prune110.0ms (1.2%)

Pruning

18 alts after pruning (13 fresh and 5 done)

	Pruned	Kept	Total
New	966	8	974
Fresh	5	5	10
Picked	3	2	5
Done	0	3	3
Total	974	18	992

Accuracy

100.0%

Counts

992 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.2%	(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
	53.0%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
	51.7%	(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) (sqrt.f64 x)))
▶	57.4%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
▶	53.2%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	51.1%	(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x))
▶	51.1%	(-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
	49.9%	(-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
✓	52.3%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	48.9%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
	51.1%	(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64)))
✓	49.9%	(+.f64 #s(literal 1 binary64) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x)))
	47.4%	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
▶	53.0%	(*.f64 (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
✓	53.4%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
	49.5%	(.f64 (exp.f64 (.f64 #s(literal -1/2 binary64) (log.f64 x))) #s(literal 1/2 binary64))
	17.0%	(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) x))))
▶	50.2%	#s(literal 1 binary64)

Compiler

Compiled 323 to 240 computations (25.7% saved)

simplify352.0ms (3.7%)

Algorithm

1×	egg-herbie

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(pow.f64 x #s(literal -1/4 binary64))
✓	cost-diff	6464	(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64))
✓	cost-diff	6464	(*.f64 (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))
✓	cost-diff	0	(+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
✓	cost-diff	0	(-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (-.f64 (sqrt.f64 x) #s(literal 1 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 binary64) (sqrt.f64 x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))

Rules

4300×	`sum3-define`
1504×	`fma-lowering-fma.f32`
1504×	`fma-lowering-fma.f64`
1354×	`fma-define`
1136×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	102
1	53	90
2	144	90
3	298	90
4	850	90
5	2572	90
6	3849	90
7	6821	90
8	7364	90
9	7466	90
10	7480	90
11	7487	90
12	7679	90
13	7868	90
14	7927	90
15	7945	90
16	7961	90
17	7968	90
18	7971	90
19	7971	90
0	9791	90

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize159.0ms (1.7%)

Localize:

Found 12 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(pow.f64 x #s(literal -1/4 binary64))
✓	accuracy	99.2%	(pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))
✓	accuracy	99.9%	(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.5%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(+.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))

Results

65.0ms

256×

valid

Compiler

Compiled 106 to 22 computations (79.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 37.0ms

ival-pow: 13.0ms (35% of total)

ival-add: 8.0ms (21.5% of total)

ival-mult: 7.0ms (18.9% of total)

ival-div: 4.0ms (10.8% of total)

ival-sub: 2.0ms (5.4% of total)

ival-sqrt: 2.0ms (5.4% of total)

const: 1.0ms (2.7% of total)

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

series84.0ms (0.9%)

Counts

11 → 132

Calls

Call 1

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

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

Calls

33 calls:

Time	Variable		Point	Expression
59.0ms	x	@	0	(pow x -1/4)
12.0ms	x	@	-inf	(pow x -1/4)
8.0ms	x	@	inf	(pow x -1/4)
1.0ms	x	@	-inf	(/ 1/2 (sqrt x))
0.0ms	x	@	-inf	(/ 1 (+ 1 (sqrt x)))

rewrite343.0ms (3.6%)

Algorithm

1×	batch-egg-rewrite

Rules

3470×	`-lowering-.f32`
3470×	`-lowering-.f64`
3264×	`/-lowering-/.f32`
3264×	`/-lowering-/.f64`
2462×	`+-lowering-+.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	21	67
1	143	59
2	1142	59
0	8529	59

Stop Event

1×	iter limit
1×	node limit

Counts

11 → 446

Calls

Call 1

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

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

simplify232.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

2178×	`fma-lowering-fma.f32`
2178×	`fma-lowering-fma.f64`
2146×	`-lowering-.f32`
2146×	`-lowering-.f64`
1728×	`fmsub-define`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	147	958
1	452	858
2	1482	842
3	4940	840
0	8547	840

Stop Event

1×	iter limit
1×	node limit

Counts

132 → 132

Calls

Call 1

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

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

eval84.0ms (0.9%)

Compiler: Compiled 20093 to 1613 computations (92% saved)

prune83.0ms (0.9%)

Pruning

18 alts after pruning (8 fresh and 10 done)

	Pruned	Kept	Total
New	634	2	636
Fresh	2	6	8
Picked	0	5	5
Done	0	5	5
Total	636	18	654

Accuracy

100.0%

Counts

654 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	50.2%	(/.f64 (+.f64 (/.f64 #s(literal -1/8 binary64) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
	53.0%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
	51.7%	(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) (sqrt.f64 x)))
✓	57.4%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	53.2%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
	49.5%	(/.f64 #s(literal 1/2 binary64) (exp.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
✓	51.1%	(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x))
✓	51.1%	(-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
	49.9%	(-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
	51.1%	(-.f64 (*.f64 x #s(literal 1/2 binary64)) (-.f64 (sqrt.f64 x) #s(literal 1 binary64)))
✓	52.3%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	48.9%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	49.9%	(+.f64 #s(literal 1 binary64) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x)))
	47.4%	(+.f64 #s(literal 1 binary64) (.f64 (.f64 x x) #s(literal -1/8 binary64)))
✓	53.0%	(*.f64 (pow.f64 (pow.f64 x #s(literal -1/4 binary64)) #s(literal 2 binary64)) #s(literal 1/2 binary64))
✓	53.4%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
	17.0%	(.f64 x (.f64 (.f64 x x) (+.f64 #s(literal 1/16 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 #s(literal 1 binary64) (.f64 x x))) x))))
✓	50.2%	#s(literal 1 binary64)

Compiler

Compiled 525 to 226 computations (57% saved)

regimes20.0ms (0.2%)

Counts

32 → 2

Calls

Call 1

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

Outputs

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

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
100.0%	2	`x`
100.0%	2	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes19.0ms (0.2%)

Counts

31 → 2

Calls

Call 1

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

Calls

2 calls:

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

Results

Accuracy	Segments	Branch
99.8%	2	`x`
99.8%	2	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes10.0ms (0.1%)

Counts

27 → 2

Calls

Call 1

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

Outputs

(+.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)))

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

Calls

1 calls:

8.0ms

Results

Accuracy	Segments	Branch
99.3%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes6.0ms (0.1%)

Counts

18 → 2

Calls

Call 1

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

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
99.1%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes8.0ms (0.1%)

Counts

15 → 2

Calls

Call 1

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

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
98.8%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes6.0ms (0.1%)

Counts

14 → 2

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
98.8%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0.1%)

Counts

12 → 2

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
97.9%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Counts

9 → 2

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
97.6%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0.1%)

Accuracy

Total -31.4b remaining (-98.4%)

Threshold costs -31.4b (-98.4%)

Counts

8 → 1

Calls

Call 1

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

Outputs
#s(literal 1 binary64)

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
50.2%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	0.0	1.7369166016578674e-7

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.0321243684738874e-6	0.8650879925021593

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch15.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	0.021150434914224015	27192116955.241646

Results

8.0ms

160×

valid

Compiler

Compiled 262 to 209 computations (20.2% saved)

Precisions

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

ival-sqrt: 2.0ms (48.9% of total)

ival-sub: 1.0ms (24.5% of total)

ival-add: 1.0ms (24.5% of total)

const: 0.0ms (0% of total)

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

bsearch15.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	0.021150434914224015	27192116955.241646

Results

9.0ms

160×

valid

Compiler

Compiled 222 to 179 computations (19.4% saved)

Precisions

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

ival-sqrt: 2.0ms (48.3% of total)

ival-sub: 1.0ms (24.1% of total)

ival-add: 1.0ms (24.1% of total)

const: 0.0ms (0% of total)

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

bsearch14.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	0.021150434914224015	27192116955.241646

Results

8.0ms

160×

valid

Compiler

Compiled 182 to 149 computations (18.1% saved)

Precisions

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

ival-sqrt: 2.0ms (47.7% of total)

ival-sub: 1.0ms (23.8% of total)

ival-add: 1.0ms (23.8% of total)

const: 0.0ms (0% of total)

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

bsearch30.0ms (0.3%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
29.0ms	0.021150434914224015	27192116955.241646

Results

23.0ms

160×

valid

Compiler

Compiled 182 to 149 computations (18.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 20.0ms

ival-sub: 16.0ms (80.5% of total)

ival-sqrt: 2.0ms (10.1% of total)

ival-add: 1.0ms (5% of total)

const: 0.0ms (0% of total)

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

bsearch16.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
15.0ms	0.021150434914224015	27192116955.241646

Results

8.0ms

160×

valid

Compiler

Compiled 142 to 119 computations (16.2% saved)

Precisions

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

ival-sqrt: 2.0ms (46.3% of total)

ival-sub: 1.0ms (23.2% of total)

ival-add: 1.0ms (23.2% of total)

const: 0.0ms (0% of total)

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

bsearch14.0ms (0.2%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	0.021150434914224015	27192116955.241646

Results

8.0ms

160×

valid

Compiler

Compiled 132 to 109 computations (17.4% saved)

Precisions

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

ival-sqrt: 2.0ms (46.9% of total)

ival-sub: 1.0ms (23.5% of total)

ival-add: 1.0ms (23.5% of total)

const: 0.0ms (0% of total)

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

simplify12.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	54	157
1	81	157
2	92	157
3	96	157
4	98	157

Stop Event

1×

saturated

Calls

Call 1

Inputs
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 0 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 5902958103587057/1180591620717411303424 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(if (<=.f64 x #s(literal 5854679515581645/4503599627370496 binary64)) (+.f64 #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))) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 5494391545392005/4503599627370496 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x))) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 1 binary64)) (-.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 3242591731706757/9007199254740992 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 3242591731706757/9007199254740992 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(literal 1 binary64)

Outputs
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 0 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 0 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 5902958103587057/1180591620717411303424 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(if (<=.f64 x #s(literal 5854679515581645/4503599627370496 binary64)) (+.f64 #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))) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 5494391545392005/4503599627370496 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x))) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 1 binary64)) (-.f64 (+.f64 #s(literal 1 binary64) (.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 1 binary64)) (+.f64 (.f64 x #s(literal 1/2 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x))) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 3242591731706757/9007199254740992 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 3242591731706757/9007199254740992 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
#s(literal 1 binary64)

soundness2.0s (21.6%)

Rules

5048×	`-lowering-.f32`
5048×	`-lowering-.f64`
3766×	`+-lowering-+.f64`
3766×	`+-lowering-+.f32`
3418×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	132	1476
1	394	1295
2	1258	1274
3	3901	1253
0	8288	1253
0	24	112
1	171	96
2	1628	96
0	8962	96
0	113	434
1	325	384
2	1037	376
3	3221	373
4	7103	373
0	8112	373
0	246	1798
1	757	1677
2	2454	1645
0	8339	1645
0	6	16
1	39	16
2	300	16
3	3704	16
0	8338	16

Stop Event

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

Compiler

Compiled 384 to 234 computations (39.1% saved)

preprocess85.0ms (0.9%)

Compiler: Compiled 352 to 134 computations (61.9% saved)

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

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

analyze2.0ms (0%)

sample1.3s (13.4%)

preprocess40.0ms (0.4%)

explain90.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify15.0ms (0.2%)

localize41.0ms (0.4%)

series5.0ms (0%)

rewrite252.0ms (2.7%)

simplify228.0ms (2.4%)

eval35.0ms (0.4%)

prune43.0ms (0.5%)

simplify168.0ms (1.8%)

localize130.0ms (1.4%)

series13.0ms (0.1%)

rewrite378.0ms (4%)

simplify220.0ms (2.3%)

eval166.0ms (1.8%)

prune118.0ms (1.3%)

simplify343.0ms (3.6%)

localize210.0ms (2.2%)

series15.0ms (0.2%)

rewrite488.0ms (5.2%)

simplify374.0ms (4%)

eval1.0s (10.8%)

prune110.0ms (1.2%)

simplify352.0ms (3.7%)

localize159.0ms (1.7%)

series84.0ms (0.9%)

rewrite343.0ms (3.6%)

simplify232.0ms (2.5%)

eval84.0ms (0.9%)

prune83.0ms (0.9%)

regimes20.0ms (0.2%)

regimes19.0ms (0.2%)

regimes10.0ms (0.1%)

regimes6.0ms (0.1%)

regimes8.0ms (0.1%)

regimes6.0ms (0.1%)

regimes5.0ms (0.1%)

regimes4.0ms (0%)

regimes5.0ms (0.1%)

bsearch0.0ms (0%)

bsearch0.0ms (0%)

bsearch15.0ms (0.2%)

bsearch15.0ms (0.2%)

bsearch14.0ms (0.2%)

bsearch30.0ms (0.3%)

bsearch16.0ms (0.2%)

bsearch14.0ms (0.2%)

simplify12.0ms (0.1%)

soundness2.0s (21.6%)

preprocess85.0ms (0.9%)

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