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 (11.4%)

Results

529.0ms	1725×	2	valid
307.0ms	2386×	1	valid
244.0ms	4145×	0	valid
1.0ms	16×	0	invalid

Precisions

Click to see histograms. Total time spent on operations: 548.0ms

ival-sqrt: 238.0ms (43.5% of total)

ival-add: 105.0ms (19.2% of total)

backward-pass: 102.0ms (18.6% of total)

ival-sub: 87.0ms (15.9% of total)

const: 15.0ms (2.7% of total)

Bogosity

preprocess42.0ms (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)))

explain115.0ms (1%)

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
134	-	-	`(-.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

33.0ms	108×	2	valid
31.0ms	154×	1	valid
22.0ms	250×	0	valid

Compiler

Compiled 48 to 20 computations (58.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 38.0ms

ival-sqrt: 17.0ms (44.7% of total)

backward-pass: 8.0ms (21% of total)

ival-add: 6.0ms (15.8% of total)

ival-sub: 6.0ms (15.8% of total)

const: 1.0ms (2.6% 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
▶	51.0%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Compiler

Compiled 8 to 6 computations (25% saved)

simplify25.0ms (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)

localize52.0ms (0.5%)

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 x #s(literal 1 binary64))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(sqrt.f64 (+.f64 x #s(literal 1 binary64)))
✓	accuracy	51.0%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

16.0ms	54×	2	valid
15.0ms	77×	1	valid
12.0ms	125×	0	valid

Compiler

Compiled 20 to 7 computations (65% saved)

Precisions

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

ival-sqrt: 8.0ms (39.2% of total)

ival-add: 5.0ms (24.5% of total)

backward-pass: 5.0ms (24.5% of total)

ival-sub: 2.0ms (9.8% of total)

const: 1.0ms (4.9% 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)

rewrite343.0ms (3%)

Algorithm

1×	batch-egg-rewrite

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	39	16
2	303	16
3	3722	16
0	8049	16

Stop Event

1×	iter limit
1×	node limit

Counts

4 → 220

Calls

Call 1

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

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

simplify333.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 3 (0.0ms)

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

Stop Event

1×	iter limit
1×	node limit

Counts

48 → 48

Calls

Call 1

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

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

eval34.0ms (0.3%)

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

prune64.0ms (0.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	256	12	268
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	256	13	269

Accuracy

100.0%

Counts

269 → 13

Alt Table

Click to see full alt table

Status	Accuracy	Program
	49.9%	(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)))))
	52.3%	(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
	52.7%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
▶	50.6%	(-.f64 (pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 x))
▶	49.0%	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) (sqrt.f64 x))
▶	49.3%	(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x))
	50.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (pow.f64 (*.f64 x x) #s(literal 1/4 binary64)))
✓	51.0%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
▶	46.9%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
	49.3%	(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64)))
	47.7%	(+.f64 #s(literal 1 binary64) (-.f64 (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))) (sqrt.f64 x)))
	51.6%	(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))))
▶	54.9%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))

Compiler

Compiled 368 to 242 computations (34.2% saved)

simplify237.0ms (2.1%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 x #s(literal 1 binary64))
✓	cost-diff	(*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))
✓	cost-diff	(pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/4 binary64))
✓	cost-diff	(-.f64 (pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 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 #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	(-.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	(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

1804×	`fma-lowering-fma.f32`
1804×	`fma-lowering-fma.f64`
1490×	`fma-define`
1378×	`fmsub-define`
1364×	`sum4-define`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	25	140
1	65	126
2	174	126
3	447	126
4	1164	126
5	3554	126
6	4888	126
7	7117	126
8	7609	126
9	7925	126
0	8008	126

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))))))
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)
(- (pow (* (+ x 1) (+ x 1)) 1/4) (sqrt x))
(pow (* (+ x 1) (+ x 1)) 1/4)
(* (+ x 1) (+ x 1))
(+ x 1)
x
1
1/4
(sqrt x)

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

localize358.0ms (3.1%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64)))
✓	accuracy	74.5%	(pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/4 binary64))
✓	accuracy	51.0%	(-.f64 (pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 x))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))
✓	accuracy	100.0%	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) (sqrt.f64 x))
✓	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

164.0ms	125×	0	valid
81.0ms	77×	1	valid
71.0ms	54×	2	valid

Compiler

Compiled 154 to 26 computations (83.1% saved)

Precisions

Click to see histograms. Total time spent on operations: 86.0ms

ival-pow: 18.0ms (21% of total)

backward-pass: 15.0ms (17.5% of total)

ival-add: 15.0ms (17.5% of total)

ival-mult: 15.0ms (17.5% of total)

ival-sub: 9.0ms (10.5% of total)

ival-sqrt: 7.0ms (8.2% of total)

ival-div: 5.0ms (5.8% of total)

const: 1.0ms (1.2% of total)

series64.0ms (0.6%)

Counts

17 → 204

Calls

Call 1

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

Calls

51 calls:

Time	Variable		Point	Expression
55.0ms	x	@	0	(- (pow (* (+ x 1) (+ x 1)) 1/4) (sqrt x))
1.0ms	x	@	-inf	(* 1/2 (sqrt (/ 1 x)))
0.0ms	x	@	inf	(- (+ 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)))))) (sqrt x))
0.0ms	x	@	-inf	(- (pow (* (+ x 1) (+ x 1)) 1/4) (sqrt x))

rewrite1.6s (13.9%)

Algorithm

1×	batch-egg-rewrite

Rules

3564×	`-lowering-.f32`
3564×	`-lowering-.f64`
3176×	`/-lowering-/.f32`
3176×	`/-lowering-/.f64`
2618×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	25	110
1	187	93
2	1758	91
0	9591	91

Stop Event

1×	iter limit
1×	node limit

Counts

17 → 650

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))
(+ 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))))
(- (pow (* (+ x 1) (+ x 1)) 1/4) (sqrt x))
(pow (* (+ x 1) (+ x 1)) 1/4)
(* (+ x 1) (+ x 1))
(+ x 1)
(* 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))
(exp.f64 (*.f64 (-.f64 #s(literal 0 binary64) (log.f64 x)) #s(literal 1/2 binary64)))
(exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))
(exp.f64 (.f64 (.f64 #s(literal 1/2 binary64) (log.f64 x)) #s(literal -1 binary64)))
(exp.f64 (neg.f64 (*.f64 #s(literal 1/2 binary64) (log.f64 x))))
(fabs.f64 (pow.f64 x #s(literal -1/2 binary64)))
(sqrt.f64 (/.f64 #s(literal 1 binary64) x))
(/.f64 #s(literal 1 binary64) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (neg.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 x))))
(/.f64 #s(literal 1 binary64) (sqrt.f64 (neg.f64 (-.f64 #s(literal 0 binary64) x))))
(/.f64 #s(literal -1 binary64) (-.f64 #s(literal 0 binary64) (sqrt.f64 x)))
(/.f64 (sqrt.f64 #s(literal -1 binary64)) (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64)))
(/.f64 (neg.f64 (sqrt.f64 #s(literal -1 binary64))) (neg.f64 (pow.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1/2 binary64))))
(pow.f64 x #s(literal -1/2 binary64))
(pow.f64 (/.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
(pow.f64 (sqrt.f64 x) #s(literal -1 binary64))
(pow.f64 (*.f64 x x) #s(literal -1/4 binary64))
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(/.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 (.f64 x (.f64 x x)) #s(literal -1/512 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/4096 binary64))))) (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 x (.f64 x x)) (.f64 (.f64 x (.f64 x x)) #s(literal 1/4096 binary64))) (.f64 (.f64 x (.f64 x x)) #s(literal -1/512 binary64))) (+.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)

simplify254.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

3792×	`-lowering-.f32`
3792×	`-lowering-.f64`
2438×	`+-lowering-+.f64`
2438×	`+-lowering-+.f32`
1712×	`fma-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	199	1547
1	615	1347
2	2025	1285
3	7160	1285
0	8034	1285

Stop Event

1×	iter limit
1×	node limit

Counts

204 → 204

Calls

Call 1

Inputs
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (sqrt (/ 1 x)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(* 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(sqrt (/ 1 x))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(* (sqrt (/ 1 x)) (pow (sqrt -1) 2))
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(/ 1 x)
(- 1 (sqrt x))
(- 1 (sqrt x))
(- 1 (sqrt x))
(- 1 (sqrt x))
(* -1 (sqrt x))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(* (sqrt x) (pow (sqrt -1) 2))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(- 1 (sqrt x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(- (+ 1 (* 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
(+ 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)))
(* 1/2 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 (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 (* 2 x))
(+ 1 (* x (+ 2 x)))
(+ 1 (* x (+ 2 x)))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ 1 (pow x 2)))))
(pow x 2)
(* (pow x 2) (+ 1 (* 2 (/ 1 x))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ 1 (pow x 2)))))
(* (pow x 2) (+ 1 (+ (* 2 (/ 1 x)) (/ 1 (pow x 2)))))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* -1/8 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 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) x)))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) x)))
(* x (- (/ 1 x) (sqrt (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) x)))
(* (sqrt x) (pow (sqrt -1) 2))
(-.f64 #s(literal 0 binary64) (sqrt.f64 x))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) x)))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) x)))
(* x (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (-.f64 #s(literal 0 binary64) x)))
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(sqrt x)
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(sqrt.f64 x)
(- 1 (sqrt x))
(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
(- (+ 1 (* 1/2 x)) (sqrt x))
(+.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)))
(- (+ 1 (* 1/2 x)) (sqrt x))
(+.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)))
(- (+ 1 (* 1/2 x)) (sqrt x))
(+.f64 #s(literal 1 binary64) (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)))
(* x (- 1/2 (sqrt (/ 1 x))))
(*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (- (+ 1/2 (/ 1 x)) (sqrt (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ 1/2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))
(*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
(* x (+ 1/2 (+ (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(+.f64 #s(literal 1 binary64) (*.f64 x (-.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))
1
#s(literal 1 binary64)
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(+ 1 (* 1/2 x))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* 1/2 x)
(*.f64 #s(literal 1/2 binary64) x)
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
(* x (+ 1/2 (/ 1 x)))
(+.f64 #s(literal 1 binary64) (*.f64 #s(literal 1/2 binary64) x))
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1
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(* -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))
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1
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1
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x
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x
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(* 1/16 (pow x 2))
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(* (pow x 2) (- 1/16 (* 1/8 (/ 1 x))))
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eval146.0ms (1.3%)

Compiler: Compiled 26958 to 2873 computations (89.3% saved)

prune175.0ms (1.5%)

Pruning

18 alts after pruning (13 fresh and 5 done)

	Pruned	Kept	Total
New	990	10	1000
Fresh	4	3	7
Picked	1	4	5
Done	0	1	1
Total	995	18	1013

Accuracy

100.0%

Counts

1013 → 18

Alt Table

Click to see full alt table

Status	Accuracy	Program
	49.9%	(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)))))
▶	52.7%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
	48.0%	(/.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 #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))))
	52.3%	(/.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)
	54.8%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	50.6%	(-.f64 (pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 x))
✓	49.0%	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) (sqrt.f64 x))
	50.2%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (pow.f64 (*.f64 x x) #s(literal 1/4 binary64)))
✓	51.0%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	46.9%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
▶	49.3%	(+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) #s(literal 1 binary64))
	47.7%	(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))))
▶	55.0%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
	51.6%	(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))))
	3.1%	(.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))
▶	3.7%	(.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x)))
✓	54.9%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
▶	51.2%	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))

Compiler

Compiled 476 to 285 computations (40.1% saved)

simplify172.0ms (1.5%)

Algorithm

1×	egg-herbie

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
✓	cost-diff	256	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
✓	cost-diff	0	(log.f64 x)
✓	cost-diff	0	(*.f64 (log.f64 x) #s(literal -1/2 binary64))
✓	cost-diff	0	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))
✓	cost-diff	6464	(exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(*.f64 #s(literal 1/2 binary64) x)
✓	cost-diff	0	(-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
✓	cost-diff	0	(+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) #s(literal 1 binary64))
✓	cost-diff	0	(*.f64 x x)
✓	cost-diff	0	(.f64 #s(literal 1/16 binary64) (.f64 x x))
✓	cost-diff	0	(.f64 x (.f64 #s(literal 1/16 binary64) (*.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

1578×	`--lowering--.f32`
1578×	`--lowering--.f64`
1344×	`-lowering-.f32`
1344×	`-lowering-.f64`
1328×	`sum5-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	95
1	54	91
2	102	89
3	142	89
4	227	89
5	399	89
6	726	89
7	1279	89
8	2101	89
9	3356	89
10	6387	89
0	8210	89

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
(* x (* 1/16 (* x x)))
x
(* 1/16 (* x x))
1/16
(* x x)
(+ (- (* 1/2 x) (sqrt x)) 1)
(- (* 1/2 x) (sqrt x))
(* 1/2 x)
1/2
x
(sqrt x)
1
(* 1/2 (exp (* (log x) -1/2)))
1/2
(exp (* (log x) -1/2))
(* (log x) -1/2)
(log x)
x
-1/2
(/ (- (+ 1 x) x) (+ (sqrt x) (pow (+ 1 x) 1/2)))
(- (+ 1 x) x)
(+ 1 x)
1
x
(+ (sqrt x) (pow (+ 1 x) 1/2))
(sqrt x)
(pow (+ 1 x) 1/2)
1/2

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

localize216.0ms (1.9%)

Localize:

Found 17 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
✓	accuracy	99.7%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
✓	accuracy	52.4%	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
✓	accuracy	100.0%	(*.f64 (log.f64 x) #s(literal -1/2 binary64))
✓	accuracy	100.0%	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))
✓	accuracy	100.0%	(log.f64 x)
✓	accuracy	92.8%	(exp.f64 (*.f64 (log.f64 x) #s(literal -1/2 binary64)))
✓	accuracy	100.0%	(+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) #s(literal 1 binary64))
✓	accuracy	100.0%	(*.f64 #s(literal 1/2 binary64) x)
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x))
✓	accuracy	100.0%	(*.f64 x x)
✓	accuracy	100.0%	(.f64 #s(literal 1/16 binary64) (.f64 x x))
✓	accuracy	99.9%	(.f64 x (.f64 #s(literal 1/16 binary64) (*.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

103.0ms	122×	1	valid
55.0ms	134×	0	valid

Compiler

Compiled 113 to 24 computations (78.8% saved)

Precisions

Click to see histograms. Total time spent on operations: 74.0ms

ival-mult: 19.0ms (25.8% of total)

ival-pow: 18.0ms (24.5% of total)

backward-pass: 9.0ms (12.2% of total)

ival-add: 8.0ms (10.9% of total)

ival-log: 5.0ms (6.8% of total)

ival-exp: 4.0ms (5.4% of total)

ival-sub: 4.0ms (5.4% of total)

ival-div: 3.0ms (4.1% of total)

ival-sqrt: 3.0ms (4.1% of total)

const: 1.0ms (1.4% of total)

series41.0ms (0.4%)

Counts

18 → 216

Calls

Call 1

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

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

Calls

54 calls:

Time	Variable		Point	Expression
17.0ms	x	@	-inf	(* (log x) -1/2)
8.0ms	x	@	inf	(* (log x) -1/2)
6.0ms	x	@	0	(* (log x) -1/2)
1.0ms	x	@	-inf	(/ (- (+ 1 x) x) (+ (sqrt x) (pow (+ 1 x) 1/2)))
1.0ms	x	@	0	(/ (- (+ 1 x) x) (+ (sqrt x) (pow (+ 1 x) 1/2)))

rewrite320.0ms (2.8%)

Algorithm

1×	batch-egg-rewrite

Rules

3440×	`/-lowering-/.f32`
3440×	`/-lowering-/.f64`
3352×	`-lowering-.f32`
3352×	`-lowering-.f64`
2000×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	23	83
1	129	73
2	1072	72
0	8402	72

Stop Event

1×	iter limit
1×	node limit

Counts

18 → 434

Calls

Call 1

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

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

simplify294.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

3856×	`-lowering-.f32`
3856×	`-lowering-.f64`
2314×	`+-lowering-+.f64`
2314×	`+-lowering-+.f32`
1204×	`--lowering--.f32`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	215	1526
1	667	1316
2	2271	1309
3	6855	1306
0	8363	1306

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

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

eval187.0ms (1.6%)

Compiler: Compiled 15797 to 1785 computations (88.7% saved)

prune334.0ms (2.9%)

Pruning

17 alts after pruning (9 fresh and 8 done)

	Pruned	Kept	Total
New	747	3	750
Fresh	2	6	8
Picked	1	4	5
Done	1	4	5
Total	751	17	768

Accuracy

100.0%

Counts

768 → 17

Alt Table

Click to see full alt table

Status	Accuracy	Program
	49.9%	(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)))))
▶	49.4%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) 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))))))))
	52.3%	(/.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)
▶	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))))
▶	56.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	54.8%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	49.0%	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) (sqrt.f64 x))
✓	51.0%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	46.9%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	49.3%	(+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) #s(literal 1 binary64))
	47.7%	(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))))
✓	55.0%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
▶	51.6%	(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))))
▶	3.1%	(.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))
✓	3.7%	(.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x)))
✓	54.9%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	51.2%	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))

Compiler

Compiled 368 to 243 computations (34% saved)

simplify205.0ms (1.8%)

Algorithm

1×	egg-herbie

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(-.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))
✓	cost-diff	128	(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))))
✓	cost-diff	256	(+.f64 x (-.f64 #s(literal 1 binary64) x))
✓	cost-diff	0	(+.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)))))))
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) x)
✓	cost-diff	0	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) 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))))))))
✓	cost-diff	256	(-.f64 (+.f64 #s(literal 1 binary64) x) x)
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(+.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
✓	cost-diff	0	(*.f64 x #s(literal 1/16 binary64))
✓	cost-diff	0	(+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))
✓	cost-diff	0	(.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))
✓	cost-diff	0	(.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))
✓	cost-diff	0	(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
✓	cost-diff	0	(sqrt.f64 x)
✓	cost-diff	0	(+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))
✓	cost-diff	0	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))))

Rules

2064×	`fma-lowering-fma.f32`
2064×	`fma-lowering-fma.f64`
1844×	`+-lowering-+.f64`
1844×	`+-lowering-+.f32`
1776×	`fma-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	251
1	93	218
2	268	214
3	747	214
4	1982	214
5	6609	214
0	8161	214

Stop Event

1×	iter limit
1×	node limit

Calls

Call 1

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

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

localize367.0ms (3.2%)

Localize:

Found 19 expressions of interest:

New	Metric	Score	Program
✓	accuracy	98.7%	(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))
✓	accuracy	83.2%	(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))))
✓	accuracy	75.3%	(sqrt.f64 (*.f64 x (+.f64 x #s(literal 1 binary64))))
✓	accuracy	52.4%	(+.f64 x (-.f64 #s(literal 1 binary64) 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	99.4%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) 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))))))))
✓	accuracy	52.4%	(-.f64 (+.f64 #s(literal 1 binary64) x) 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)))
✓	accuracy	100.0%	(+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))
✓	accuracy	100.0%	(*.f64 x #s(literal 1/16 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 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))
✓	accuracy	100.0%	(sqrt.f64 x)
✓	accuracy	100.0%	(pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))
✓	accuracy	100.0%	(+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)))
✓	accuracy	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))))

Results

161.0ms	122×	1	valid
124.0ms	134×	0	valid

Compiler

Compiled 268 to 35 computations (86.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 136.0ms

ival-pow: 31.0ms (22.7% of total)

ival-div: 27.0ms (19.8% of total)

ival-mult: 27.0ms (19.8% of total)

ival-add: 20.0ms (14.7% of total)

backward-pass: 14.0ms (10.3% of total)

ival-sqrt: 10.0ms (7.3% of total)

ival-sub: 6.0ms (4.4% of total)

const: 1.0ms (0.7% of total)

series18.0ms (0.2%)

Counts

20 → 240

Calls

Call 1

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

Outputs
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)>
#<alt (/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)>
#<alt (* -1/2 (sqrt (/ 1 x)))>
#<alt (* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))>
#<alt (* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))>
#<alt (* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (+ (sqrt x) (* 1/2 x)))>
#<alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))>
#<alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))>
#<alt (* 2 (sqrt x))>
#<alt (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))>
#<alt (* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))>
#<alt (* -2 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))>
#<alt (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>
#<alt (+ 1 (* 1/2 x))>
#<alt (+ 1 (* x (+ 1/2 (* -1/8 x))))>
#<alt (+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))>
#<alt (* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))>
#<alt (* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))>
#<alt (* -1/8 (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 (* -1/8 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 -1/8>
#<alt (- (* 1/16 x) 1/8)>
#<alt (- (* 1/16 x) 1/8)>
#<alt (- (* 1/16 x) 1/8)>
#<alt (* 1/16 x)>
#<alt (* x (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* x (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* x (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* 1/16 x)>
#<alt (* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (* 1/16 x)>
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (sqrt (/ 1 x))>
#<alt (/ (- (sqrt x) 1) x)>
#<alt (/ (- (+ (sqrt x) (sqrt (/ 1 x))) 1) x)>
#<alt (/ (- (sqrt x) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (/ 1 x)))) x)>
#<alt (* -1 (sqrt (/ 1 x)))>
#<alt (* -1 (/ (- (sqrt x) (/ 1 (pow (sqrt -1) 2))) x))>
#<alt (* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x))>
#<alt (* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (/ (- (/ x (pow (sqrt -1) 4)) (* -1 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (sqrt x))>
#<alt (sqrt x)>
#<alt (* x (+ (sqrt (/ 1 x)) (/ 1 x)))>
#<alt (* x (+ (sqrt (/ 1 x)) (/ 1 x)))>
#<alt (* x (+ (sqrt (/ 1 x)) (/ 1 x)))>
#<alt (* -1 (* (sqrt x) (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt (* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt (/ 1 (+ 1 (sqrt x)))>
#<alt (+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))>
#<alt (/ 16 (pow x 3))>
#<alt (/ (+ 16 (* 32 (/ 1 x))) (pow x 3))>
#<alt (/ (- (+ 16 (+ (* 32 (/ 1 x)) (/ 64 (pow x 2)))) (* 256 (/ (+ 1/2 (sqrt (/ 1 x))) (pow x 2)))) (pow x 3))>
#<alt (/ (- (+ 16 (+ (* -1 (/ (+ 256 (+ (* -2 (- 64 (* 256 (+ 1/2 (sqrt (/ 1 x)))))) (* 512 (+ 1/2 (sqrt (/ 1 x)))))) (pow x 3))) (+ (* 32 (/ 1 x)) (/ 64 (pow x 2))))) (* 256 (/ (+ 1/2 (sqrt (/ 1 x))) (pow x 2)))) (pow x 3))>
#<alt (/ 16 (pow x 3))>
#<alt (/ (+ 16 (* 32 (/ 1 x))) (pow x 3))>
#<alt (* -1 (/ (- (* -1 (/ (+ 32 (+ (* 256 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) x)) (* 64 (/ 1 x)))) x)) 16) (pow x 3)))>
#<alt (* -1 (/ (- (* -1 (/ (+ 32 (* -1 (/ (- (+ (* -512 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) x)) (+ (* -2 (/ (+ 64 (* 256 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2))) x)) (* 256 (/ 1 x)))) (+ 64 (* 256 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))) x))) x)) 16) (pow x 3)))>
#<alt 1>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt (+ 1 x)>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt x>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (* x (+ 1 (/ 1 x)))>
#<alt (+ 1 (sqrt x))>
#<alt (+ 1 (+ (sqrt x) (* 1/2 x)))>
#<alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))>
#<alt (+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))>
#<alt (* 1/16 (pow x 3))>
#<alt (* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/16 (+ (sqrt (/ 1 (pow x 5))) (/ 1/2 (pow x 2)))) (* 1/8 (/ 1 x))))>
#<alt (* (pow x 3) (- (+ 1/16 (+ (sqrt (/ 1 (pow x 5))) (+ (/ 1/2 (pow x 2)) (/ 1 (pow x 3))))) (* 1/8 (/ 1 x))))>
#<alt (* 1/16 (pow x 3))>
#<alt (* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) x)) 1/8) x)) 1/16)))>
#<alt (* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (+ 1/2 (/ 1 x))) x)) 1/8) x)) 1/16)))>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt 1>
#<alt (- 1 (sqrt x))>
#<alt (- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))>
#<alt (- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))>
#<alt (- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))>
#<alt (* 1/2 (sqrt (/ 1 x)))>
#<alt (/ (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)>
#<alt (/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (* 3/8 (sqrt (/ 1 x)))) x)>
#<alt (/ (- (+ (* -1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3))))))) x)>
#<alt (* 1/2 (* (sqrt (/ 1 x)) (+ 2 (pow (sqrt -1) 2))))>
#<alt (* -1 (/ (+ (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2)))) (* -1/4 (sqrt (/ 1 x)))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))>
#<alt (* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt -1) 4)))) (+ (* 3/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2)))))) x)) (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))>
#<alt 1>
#<alt (+ 1 (* -1 (* x (+ 3/2 (sqrt x)))))>
#<alt (+ 1 (* x (- (* -1 (* x (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))))) (+ 3/2 (sqrt x)))))>
#<alt (+ 1 (* x (- (* x (- (* x (- 1/16 (+ (* -1 (* (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))) (+ 3/2 (sqrt x)))) (* -3/8 (+ 3/2 (sqrt x)))))) (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))))) (+ 3/2 (sqrt x)))))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -3/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))>
#<alt (/ (- (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 3/8 (sqrt (/ 1 x)))) (pow x 2))>
#<alt (/ (- (+ (* -1 (/ (+ (* -9/32 (sqrt (pow x 5))) (* 1/8 (* (sqrt (pow x 3)) (- 1 (* 9/4 x))))) (pow x 4))) (* 1/2 (sqrt x))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3)))))) (pow x 2))>
#<alt (* 1/2 (sqrt (/ 1 (pow x 3))))>
#<alt (/ (+ (* -3/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (pow x 2))>
#<alt (/ (- (+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (* 3/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) (pow x 2))>
#<alt (/ (- (+ (* -1 (/ (- (+ (* -9/32 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (pow (sqrt -1) 2))))) (* -3/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 3))) (* 1/2 (sqrt x))) (* 3/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) (pow x 2))>
#<alt 1>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (+ 1 (* -1 x))>
#<alt (* -1 x)>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* x (- (/ 1 x) 1))>
#<alt (* -1 x)>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* -1 (* x (- 1 (/ 1 x))))>
#<alt (* 1/2 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 (sqrt x)>
#<alt (+ (sqrt x) (* 1/2 (sqrt (pow x 3))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))>
#<alt (+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))>
#<alt x>
#<alt (* x (+ 1 (* 1/2 (/ 1 x))))>
#<alt (* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))>
#<alt (* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))>
#<alt (* -1 (* x (pow (sqrt -1) 2)))>
#<alt (* -1 (* x (- (pow (sqrt -1) 2) (* 1/2 (/ 1 x)))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))>
#<alt (* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))>

Calls

60 calls:

Time	Variable		Point	Expression
5.0ms	x	@	-inf	(* (/ (+ x (- 1 x)) (+ (pow (+ x 1) 3/2) (pow x 3/2))) (- (+ x (+ x 1)) (sqrt (* x (+ x 1)))))
1.0ms	x	@	inf	(* (/ (+ x (- 1 x)) (+ (pow (+ x 1) 3/2) (pow x 3/2))) (- (+ x (+ x 1)) (sqrt (* x (+ x 1)))))
1.0ms	x	@	-inf	(/ (+ x (- 1 x)) (+ (pow (+ x 1) 3/2) (pow x 3/2)))
1.0ms	x	@	0	(* (/ (+ x (- 1 x)) (+ (pow (+ x 1) 3/2) (pow x 3/2))) (- (+ x (+ x 1)) (sqrt (* x (+ x 1)))))
1.0ms	x	@	-inf	(/ (- (+ 1 x) x) (+ (+ 1 (sqrt x)) (* x (+ 1/2 (* x (+ -1/8 (* x 1/16)))))))

rewrite355.0ms (3.1%)

Algorithm

1×	batch-egg-rewrite

Rules

2450×	`fma-lowering-fma.f32`
2450×	`fma-lowering-fma.f64`
2384×	`-lowering-.f32`
2384×	`-lowering-.f64`
1656×	`+-lowering-+.f64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	34	146
1	285	117
2	2903	116
0	8385	116

Stop Event

1×	iter limit
1×	node limit

Counts

20 → 488

Calls

Call 1

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

Outputs
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) x) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (+.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))))
(+.f64 (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x))) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))))
(+.f64 (.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) (.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))))
(+.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))))
(exp.f64 (*.f64 (log.f64 (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))) #s(literal -1 binary64)))
(fma.f64 x (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (.f64 (+.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) x (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (+.f64 #s(literal 1 binary64) (-.f64 x (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))))
(fma.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)) (.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))))
(fma.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (.f64 (-.f64 #s(literal 0 binary64) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))))
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(/.f64 (.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x))) (.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (-.f64 x (-.f64 #s(literal 1 binary64) x))))
(/.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x))))
(/.f64 (.f64 (.f64 (+.f64 (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) x))) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 x x) (*.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) x))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))))
(/.f64 (.f64 (.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)))) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) x)))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))))
(/.f64 (.f64 (.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (*.f64 (-.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) #s(literal 1 binary64)) (.f64 (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) x)) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))))
(/.f64 (.f64 (.f64 (+.f64 (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) x))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) (+.f64 (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) x))))
(/.f64 (.f64 (.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)))) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)))))
(/.f64 (.f64 (.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x))) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) (-.f64 x (-.f64 #s(literal 1 binary64) x)))
(/.f64 (.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)))
(pow.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1 binary64)) #s(literal -1 binary64))
(pow.f64 (neg.f64 (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))) #s(literal -1 binary64))
(pow.f64 (/.f64 (/.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) #s(literal 1 binary64)) #s(literal 1 binary64)) #s(literal -1 binary64))
(*.f64 #s(literal 1 binary64) (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))))
(*.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal 1 binary64))
(*.f64 #s(literal -1 binary64) (/.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (.f64 #s(literal 2 binary64) x) (-.f64 #s(literal 1 binary64) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))))) (neg.f64 (-.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64)))) (-.f64 (.f64 (+.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x))) (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 3/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 9/2 binary64)) (pow.f64 x #s(literal 9/2 binary64)))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (.f64 (+.f64 (.f64 x x) (.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1 binary64))) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x))) (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 3/2 binary64)))) #s(literal -1 binary64)))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) x)))) #s(literal 1 binary64))) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))))
(.f64 (/.f64 #s(literal 1 binary64) (.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (.f64 x (+.f64 #s(literal 1 binary64) (*.f64 #s(literal 2 binary64) x)))) #s(literal 1 binary64))) (pow.f64 (/.f64 #s(literal 1 binary64) (-.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) #s(literal -1 binary64)))
(.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (.f64 (+.f64 (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) x))) #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 x x) (.f64 (-.f64 #s(literal 1 binary64) x) (-.f64 (-.f64 #s(literal 1 binary64) x) x)))))
(.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (.f64 (+.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)))) #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (+.f64 #s(literal 1 binary64) x)) (.f64 x (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x))))))
(.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x)))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (-.f64 x (-.f64 #s(literal 1 binary64) x))))
(.f64 (pow.f64 (/.f64 (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64))) (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)) #s(literal 1 binary64))) #s(literal -1 binary64)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x))))
(+.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x))
(+.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64)))
(+.f64 #s(literal 1 binary64) (*.f64 (neg.f64 (sqrt.f64 x)) (sqrt.f64 x)))
(+.f64 (-.f64 #s(literal 0 binary64) x) #s(literal 1 binary64))
(-.f64 #s(literal 1 binary64) x)
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x)))) (/.f64 (.f64 x (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x)))))
(-.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)) (/.f64 (*.f64 x x) (+.f64 #s(literal 1 binary64) x)))
(fma.f64 #s(literal -1 binary64) x #s(literal 1 binary64))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))))
(/.f64 #s(literal 1 binary64) (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))))
(/.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x)) (+.f64 #s(literal 1 binary64) x))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (*.f64 x x))) (neg.f64 (+.f64 #s(literal 1 binary64) x)))
(/.f64 (neg.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (neg.f64 (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 #s(literal 1 binary64) x)))))
(/.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal -1 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x)) (*.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))))
(/.f64 (-.f64 #s(literal 1 binary64) (*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal 0 binary64) x))) (-.f64 #s(literal 1 binary64) (-.f64 #s(literal 0 binary64) x)))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x)))) #s(literal -1 binary64))
(pow.f64 (/.f64 (+.f64 #s(literal 1 binary64) x) (-.f64 #s(literal 1 binary64) (*.f64 x x))) #s(literal -1 binary64))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1 binary64) x)))))
(.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (-.f64 #s(literal 1 binary64) (*.f64 x x))) (-.f64 #s(literal 1 binary64) x))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (+.f64 #s(literal 1 binary64) (*.f64 x (+.f64 x #s(literal -1 binary64)))))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))) (+.f64 (-.f64 #s(literal 1 binary64) x) (*.f64 x x)))
(.f64 (/.f64 (-.f64 #s(literal 1 binary64) (.f64 x x)) (+.f64 (*.f64 x x) #s(literal -1 binary64))) (+.f64 x #s(literal -1 binary64)))
(+.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 x x)) (.f64 x #s(literal 1/2 binary64)))
(+.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 x x)))
(fma.f64 x #s(literal 1/2 binary64) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (*.f64 x x)))
(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 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (*.f64 x x)))
(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 x) (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (*.f64 x #s(literal 1/2 binary64)))
(/.f64 (+.f64 (.f64 (.f64 x (.f64 x x)) #s(literal 1/8 binary64)) (.f64 (.f64 x (.f64 x x)) (.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 x x)))))) (+.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64))) (-.f64 (.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 x x)) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 x x))) (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (*.f64 x x))))))
(/.f64 (-.f64 (.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 x #s(literal 1/2 binary64))) (.f64 (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 x x)) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 x x)))) (-.f64 (.f64 x #s(literal 1/2 binary64)) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 x x))))
(/.f64 (.f64 x (+.f64 #s(literal 1/8 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 x 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 x (-.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 x 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 1/8 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 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 x x))))) x) (+.f64 #s(literal 1/4 binary64) (.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) (-.f64 (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64)))) #s(literal 1/2 binary64)))))
(/.f64 (.f64 (-.f64 #s(literal 1/4 binary64) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))) (.f64 x x)))) x) (-.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))
(.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))
(.f64 (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))) x)
(exp.f64 (.f64 (log.f64 (.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)))
(hypot.f64 x (sqrt.f64 x))
(hypot.f64 (sqrt.f64 x) x)
(sqrt.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)))
(pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64))
(pow.f64 (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)) #s(literal 1 binary64))
(pow.f64 (.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) (*.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1/4 binary64))
(pow.f64 (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) #s(literal 2 binary64))
(*.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)))
(*.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64)) (sqrt.f64 x))
(.f64 (pow.f64 x #s(literal 1/4 binary64)) (pow.f64 (pow.f64 (.f64 (+.f64 #s(literal 1 binary64) x) (*.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)))
(.f64 (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)) (pow.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/4 binary64)))
(.f64 (.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64))) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))
(.f64 (pow.f64 (pow.f64 (.f64 (*.f64 x (+.f64 #s(literal 1 binary64) x)) x) #s(literal 1/2 binary64)) #s(literal 1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/4 binary64)))

simplify271.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

3556×	`-lowering-.f32`
3556×	`-lowering-.f64`
3014×	`+-lowering-+.f64`
3014×	`+-lowering-+.f32`
1972×	`sum4-define`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	553	2814
1	1832	2391
2	6931	2388
0	8175	2388

Stop Event

1×	iter limit
1×	node limit

Counts

240 → 240

Calls

Call 1

Inputs
(/ 1 (+ 1 (sqrt x)))
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)
(* -1/2 (sqrt (/ 1 x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))
(* -1 (/ (- (+ (* -1 (/ (+ (* 1/128 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6)))) (* 1/32 (* (sqrt (pow x 7)) (/ 1 (pow (sqrt -1) 6))))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))))) x))
(+ 1 (sqrt x))
(+ 1 (+ (sqrt x) (* 1/2 x)))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))
(* 2 (sqrt x))
(* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x))))))
(* x (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (sqrt (/ 1 x)))))))
(* -2 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* 2 (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))))
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(sqrt x)
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
1
(+ 1 (* 1/2 x))
(+ 1 (* x (+ 1/2 (* -1/8 x))))
(+ 1 (* x (+ 1/2 (* x (- (* 1/16 x) 1/8)))))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (* 1/2 (sqrt (/ 1 (pow x 3))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (* 1/2 (sqrt (/ 1 (pow x 3)))))))
(* x (+ (sqrt (/ 1 x)) (+ (* -1/8 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 7)))) (* 1/2 (sqrt (/ 1 (pow x 3))))))))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2))))))
(* -1 (* x (+ (* -1/8 (* (sqrt (/ 1 (pow x 5))) (/ 1 (pow (sqrt -1) 2)))) (+ (* 1/16 (* (sqrt (/ 1 (pow x 7))) (/ 1 (pow (sqrt -1) 4)))) (+ (* 1/2 (sqrt (/ 1 (pow x 3)))) (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)))))))
(* -1/8 (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)))
(* -1/8 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))))
-1/8
(- (* 1/16 x) 1/8)
(- (* 1/16 x) 1/8)
(- (* 1/16 x) 1/8)
(* 1/16 x)
(* x (- 1/16 (* 1/8 (/ 1 x))))
(* x (- 1/16 (* 1/8 (/ 1 x))))
(* x (- 1/16 (* 1/8 (/ 1 x))))
(* 1/16 x)
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* x (- (* 1/8 (/ 1 x)) 1/16)))
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(* 1/16 x)
(/ 1 (+ 1 (sqrt x)))
(/ 1 (+ 1 (sqrt x)))
(/ 1 (+ 1 (sqrt x)))
(/ 1 (+ 1 (sqrt x)))
(sqrt (/ 1 x))
(/ (- (sqrt x) 1) x)
(/ (- (+ (sqrt x) (sqrt (/ 1 x))) 1) x)
(/ (- (sqrt x) (+ 1 (+ (* -1 (sqrt (/ 1 x))) (/ 1 x)))) x)
(* -1 (sqrt (/ 1 x)))
(* -1 (/ (- (sqrt x) (/ 1 (pow (sqrt -1) 2))) x))
(* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x))
(* -1 (/ (+ (sqrt x) (* -1 (/ (- (* -1 (/ (- (/ x (pow (sqrt -1) 4)) (* -1 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) x)) (* -1 (/ x (pow (sqrt -1) 2)))) x))) x))
(+ 1 (sqrt x))
(+ 1 (sqrt x))
(+ 1 (sqrt x))
(+ 1 (sqrt x))
(sqrt x)
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(* x (+ (sqrt (/ 1 x)) (/ 1 x)))
(* -1 (* (sqrt x) (pow (sqrt -1) 2)))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
(* -1 (* x (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (/ 1 x))))
1
1
1
1
1
1
1
1
1
1
1
1
(/ 1 (+ 1 (sqrt x)))
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(/ 16 (pow x 3))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 3))
(/ (- (+ 16 (+ (* 32 (/ 1 x)) (/ 64 (pow x 2)))) (* 256 (/ (+ 1/2 (sqrt (/ 1 x))) (pow x 2)))) (pow x 3))
(/ (- (+ 16 (+ (* -1 (/ (+ 256 (+ (* -2 (- 64 (* 256 (+ 1/2 (sqrt (/ 1 x)))))) (* 512 (+ 1/2 (sqrt (/ 1 x)))))) (pow x 3))) (+ (* 32 (/ 1 x)) (/ 64 (pow x 2))))) (* 256 (/ (+ 1/2 (sqrt (/ 1 x))) (pow x 2)))) (pow x 3))
(/ 16 (pow x 3))
(/ (+ 16 (* 32 (/ 1 x))) (pow x 3))
(* -1 (/ (- (* -1 (/ (+ 32 (+ (* 256 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) x)) (* 64 (/ 1 x)))) x)) 16) (pow x 3)))
(* -1 (/ (- (* -1 (/ (+ 32 (* -1 (/ (- (+ (* -512 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) x)) (+ (* -2 (/ (+ 64 (* 256 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2))) x)) (* 256 (/ 1 x)))) (+ 64 (* 256 (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2)))) x))) x)) 16) (pow x 3)))
1
(+ 1 x)
(+ 1 x)
(+ 1 x)
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
x
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(* x (+ 1 (/ 1 x)))
(+ 1 (sqrt x))
(+ 1 (+ (sqrt x) (* 1/2 x)))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* -1/8 x)))))
(+ 1 (+ (sqrt x) (* x (+ 1/2 (* x (- (* 1/16 x) 1/8))))))
(* 1/16 (pow x 3))
(* (pow x 3) (- 1/16 (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (+ (sqrt (/ 1 (pow x 5))) (/ 1/2 (pow x 2)))) (* 1/8 (/ 1 x))))
(* (pow x 3) (- (+ 1/16 (+ (sqrt (/ 1 (pow x 5))) (+ (/ 1/2 (pow x 2)) (/ 1 (pow x 3))))) (* 1/8 (/ 1 x))))
(* 1/16 (pow x 3))
(* -1 (* (pow x 3) (- (* 1/8 (/ 1 x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) 1/2) x)) 1/8) x)) 1/16)))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* -1 (/ (- (* (sqrt (/ 1 x)) (pow (sqrt -1) 2)) (+ 1/2 (/ 1 x))) x)) 1/8) x)) 1/16)))
1
1
1
1
1
1
1
1
1
1
1
1
(- 1 (sqrt x))
(- (+ 1 (* x (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (- (+ 2 (* x (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(- (+ 1 (* x (- (+ 2 (* x (- (+ (* -1 (* x (+ (* -1/16 (- 1 (sqrt x))) (+ (* 3/8 (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))) (* (+ 3/2 (sqrt x)) (- (* -1/2 (sqrt (/ 1 x))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))))))))) (* -1/2 (sqrt (/ 1 x)))) (+ (* 3/8 (- 1 (sqrt x))) (* (+ 3/2 (sqrt x)) (- 2 (* (+ 3/2 (sqrt x)) (- 1 (sqrt x))))))))) (* (+ 3/2 (sqrt x)) (- 1 (sqrt x)))))) (sqrt x))
(* 1/2 (sqrt (/ 1 x)))
(/ (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x)))) (* 3/8 (sqrt (/ 1 x)))) x)
(/ (- (+ (* -1/32 (sqrt (/ 1 (pow x 5)))) (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (+ (* 1/4 (sqrt (/ 1 x))) (* 1/2 (sqrt x))))) (+ (* 3/16 (sqrt (/ 1 (pow x 3)))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3))))))) x)
(* 1/2 (* (sqrt (/ 1 x)) (+ 2 (pow (sqrt -1) 2))))
(* -1 (/ (+ (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2)))) (* -1/4 (sqrt (/ 1 x)))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2)))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))
(* -1 (/ (+ (* -1 (/ (+ (* -1 (/ (- (+ (* -1 (/ (- (* -1/32 (* (sqrt x) (/ 1 (pow (sqrt -1) 4)))) (+ (* 3/16 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2)))) (* 3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2)))))) x)) (* 1/16 (* (sqrt x) (/ 1 (pow (sqrt -1) 2))))) (* -3/8 (* (sqrt (pow x 3)) (/ (+ 2 (pow (sqrt -1) 2)) (pow (sqrt -1) 2))))) x)) (* 1/4 (sqrt x))) x)) (* -1/2 (* (sqrt x) (+ 2 (pow (sqrt -1) 2))))) x))
1
(+ 1 (* -1 (* x (+ 3/2 (sqrt x)))))
(+ 1 (* x (- (* -1 (* x (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))))) (+ 3/2 (sqrt x)))))
(+ 1 (* x (- (* x (- (* x (- 1/16 (+ (* -1 (* (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))) (+ 3/2 (sqrt x)))) (* -3/8 (+ 3/2 (sqrt x)))))) (+ 3/8 (* -1 (pow (+ 3/2 (sqrt x)) 2))))) (+ 3/2 (sqrt x)))))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -3/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) (pow x 2))
(/ (- (+ (* -3/8 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 3/8 (sqrt (/ 1 x)))) (pow x 2))
(/ (- (+ (* -1 (/ (+ (* -9/32 (sqrt (pow x 5))) (* 1/8 (* (sqrt (pow x 3)) (- 1 (* 9/4 x))))) (pow x 4))) (* 1/2 (sqrt x))) (+ (* 3/8 (sqrt (/ 1 x))) (* 3/8 (sqrt (/ 1 (pow x 3)))))) (pow x 2))
(* 1/2 (sqrt (/ 1 (pow x 3))))
(/ (+ (* -3/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (pow x 2))
(/ (- (+ (* -3/8 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) (* 3/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) (pow x 2))
(/ (- (+ (* -1 (/ (- (+ (* -9/32 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (pow (sqrt -1) 2))))) (* -3/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 3))) (* 1/2 (sqrt x))) (* 3/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) (pow x 2))
1
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(+ 1 (* -1 x))
(* -1 x)
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* x (- (/ 1 x) 1))
(* -1 x)
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* -1 (* x (- 1 (/ 1 x))))
(* 1/2 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)))
(sqrt x)
(+ (sqrt x) (* 1/2 (sqrt (pow x 3))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(* -1 (* x (pow (sqrt -1) 2)))
(* -1 (* x (- (pow (sqrt -1) 2) (* 1/2 (/ 1 x)))))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))

Outputs
(/ 1 (+ 1 (sqrt x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+ (* -1/2 (/ x (pow (+ 1 (sqrt x)) 2))) (/ 1 (+ 1 (sqrt x))))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (/.f64 (*.f64 x #s(literal -1/2 binary64)) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))))
(+ (* x (- (* x (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (.f64 x (+.f64 (.f64 x (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))))))
(+ (* x (- (* x (+ (* -1 (* x (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 2))) (+ (* 1/16 (/ 1 (pow (+ 1 (sqrt x)) 3))) (* 1/2 (/ (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))) (+ 1 (sqrt x)))))))) (+ (* 1/8 (/ 1 (pow (+ 1 (sqrt x)) 2))) (* 1/4 (/ 1 (pow (+ 1 (sqrt x)) 3)))))) (* 1/2 (/ 1 (pow (+ 1 (sqrt x)) 2))))) (/ 1 (+ 1 (sqrt x))))
(+.f64 (/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (.f64 x (+.f64 (.f64 x (-.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)))) (.f64 x (+.f64 (/.f64 (.f64 (+.f64 (/.f64 #s(literal 1/8 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1/4 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)))) #s(literal 1/2 binary64)) (+.f64 #s(literal 1 binary64) (sqrt.f64 x))) (+.f64 (/.f64 #s(literal 1/16 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))) (/.f64 #s(literal 1/16 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 3 binary64)))))))) (/.f64 #s(literal -1/2 binary64) (pow.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) #s(literal 2 binary64))))))
(* 1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/ (+ (* -1/8 (sqrt (/ 1 x))) (* 1/2 (sqrt x))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(/ (- (+ (* 1/16 (sqrt (/ 1 (pow x 3)))) (* 1/2 (sqrt x))) (* 1/8 (sqrt (/ 1 x)))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (*.f64 x x))))))) x)
(/ (- (+ (* -1 (/ (+ (* 1/128 (sqrt (pow x 7))) (* 1/32 (sqrt (pow x 7)))) (pow x 6))) (* 1/2 (sqrt x))) (+ (* -1/16 (sqrt (/ 1 (pow x 3)))) (* 1/8 (sqrt (/ 1 x))))) x)
(/.f64 (+.f64 (+.f64 (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (.f64 (sqrt.f64 (pow.f64 x #s(literal 7 binary64))) (/.f64 #s(literal 5/128 binary64) (pow.f64 x #s(literal 6 binary64))))) (.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x)))))) (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64))) x)
(* -1/2 (sqrt (/ 1 x)))
(*.f64 #s(literal -1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(* -1 (/ (+ (* -1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2)))) (* 1/2 (sqrt x))) x))
(/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (.f64 #s(literal 1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))) (-.f64 #s(literal 0 binary64) x))
(* -1 (/ (- (+ (* 1/16 (* (sqrt (/ 1 (pow x 3))) (/ 1 (pow (sqrt -1) 4)))) (* 1/2 (sqrt x))) (* 1/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) x))
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(/.f64 (+.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (.f64 #s(literal 3/8 binary64) (+.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))))) (*.f64 x x))
(/ (- (+ (* -1 (/ (- (+ (* -9/32 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 4)))) (* 1/8 (* (sqrt x) (/ (- 1 (* -9/4 (/ x (pow (sqrt -1) 2)))) (pow (sqrt -1) 2))))) (* -3/8 (* (sqrt (pow x 3)) (/ 1 (pow (sqrt -1) 2))))) (pow x 3))) (* 1/2 (sqrt x))) (* 3/8 (* (sqrt (/ 1 x)) (/ 1 (pow (sqrt -1) 2))))) (pow x 2))
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal 3/8 binary64)) (-.f64 (.f64 (sqrt.f64 x) #s(literal 1/2 binary64)) (/.f64 (+.f64 (.f64 #s(literal -9/32 binary64) (/.f64 (sqrt.f64 (.f64 x (.f64 x x))) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) (+.f64 (.f64 (-.f64 #s(literal -1 binary64) (.f64 x #s(literal -9/4 binary64))) (.f64 (sqrt.f64 x) #s(literal 1/8 binary64))) (.f64 (sqrt.f64 (.f64 x (.f64 x x))) #s(literal -3/8 binary64)))) (.f64 x (.f64 x x))))) (.f64 x x))
1
#s(literal 1 binary64)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(+ 1 (* -1 x))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* x (- (/ 1 x) 1))
(-.f64 #s(literal 1 binary64) x)
(* -1 x)
(-.f64 #s(literal 0 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* -1 (* x (- 1 (/ 1 x))))
(-.f64 #s(literal 1 binary64) x)
(* 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 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 (/ 1/2 (pow x 2))) (* 1/8 (/ 1 x))))
(.f64 (.f64 x (*.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 (.f64 x (*.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 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)) (neg.f64 (+.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 (+.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1/8 binary64)) x)) (neg.f64 (.f64 x (*.f64 x x))))
(* -1 (* (pow x 3) (- (* -1 (/ (- (* 1/2 (/ 1 x)) 1/8) x)) 1/16)))
(.f64 (+.f64 #s(literal -1/16 binary64) (/.f64 (+.f64 (/.f64 #s(literal -1/2 binary64) x) #s(literal 1/8 binary64)) x)) (neg.f64 (.f64 x (*.f64 x x))))
(sqrt x)
(sqrt.f64 x)
(+ (sqrt x) (* 1/2 (sqrt (pow x 3))))
(+.f64 (sqrt.f64 x) (.f64 #s(literal 1/2 binary64) (sqrt.f64 (.f64 x (*.f64 x x)))))
(+ (sqrt x) (* (pow x 2) (+ (* -1/8 (sqrt x)) (* 1/2 (sqrt (/ 1 x))))))
(+.f64 (sqrt.f64 x) (.f64 (.f64 x x) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal -1/8 binary64)))))
(+ (sqrt x) (* (pow x 2) (+ (* 1/2 (sqrt (/ 1 x))) (* (pow x 2) (+ (* -1/8 (sqrt (/ 1 (pow x 3)))) (* 1/16 (sqrt (/ 1 x))))))))
(+.f64 (sqrt.f64 x) (.f64 (.f64 x x) (+.f64 (.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 x (.f64 x (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) (.f64 x (.f64 x x))))) (*.f64 #s(literal 1/16 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))))))))
x
(* x (+ 1 (* 1/2 (/ 1 x))))
(+.f64 x #s(literal 1/2 binary64))
(* x (- (+ 1 (* 1/2 (/ 1 x))) (/ 1/8 (pow x 2))))
(+.f64 (+.f64 x #s(literal 1/2 binary64)) (.f64 x (/.f64 #s(literal -1/8 binary64) (.f64 x x))))
(* x (- (+ 1 (+ (* 1/2 (/ 1 x)) (* 1/16 (/ 1 (pow x 3))))) (/ 1/8 (pow x 2))))
(.f64 x (+.f64 (+.f64 #s(literal 1 binary64) (/.f64 #s(literal 1/2 binary64) x)) (+.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x (.f64 x x))) (/.f64 #s(literal -1/8 binary64) (.f64 x x)))))
(* -1 (* x (pow (sqrt -1) 2)))
x
(* -1 (* x (- (pow (sqrt -1) 2) (* 1/2 (/ 1 x)))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (+.f64 #s(literal -1 binary64) (/.f64 #s(literal -1/2 binary64) x)))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (* 1/8 (/ 1 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
(*.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) x)))
(* -1 (* x (+ (* -1 (/ (+ 1/2 (+ (/ 1/16 (* (pow x 2) (pow (sqrt -1) 4))) (/ 1/8 (* x (pow (sqrt -1) 2))))) x)) (pow (sqrt -1) 2))))
(.f64 (-.f64 #s(literal 0 binary64) x) (-.f64 #s(literal -1 binary64) (/.f64 (+.f64 (+.f64 #s(literal 1/2 binary64) (/.f64 #s(literal -1/8 binary64) x)) (/.f64 (/.f64 #s(literal 1/16 binary64) (.f64 x x)) (pow.f64 (sqrt.f64 #s(literal -1 binary64)) #s(literal 4 binary64)))) x)))

eval114.0ms (1%)

Compiler: Compiled 24286 to 2151 computations (91.1% saved)

prune113.0ms (1%)

Pruning

24 alts after pruning (15 fresh and 9 done)

	Pruned	Kept	Total
New	869	13	882
Fresh	2	2	4
Picked	4	1	5
Done	0	8	8
Total	875	24	899

Accuracy

100.0%

Counts

899 → 24

Alt Table

Click to see full alt table

Status	Accuracy	Program
	18.5%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 (+.f64 #s(literal -1/16 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 binary64) x))) x))) (neg.f64 (.f64 x (*.f64 x x)))))
	2.7%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 (.f64 x (*.f64 x x)) (+.f64 #s(literal 1/16 binary64) (/.f64 #s(literal -1/8 binary64) x))))
	4.1%	(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x))))
	52.3%	(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
	4.3%	(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (.f64 x (.f64 x x)))
	68.6%	(/.f64 (.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x))) (.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))))
	4.4%	(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
	49.6%	(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))))
	48.9%	(/.f64 #s(literal 1 binary64) (+.f64 (+.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64))))))
	50.6%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64)))))
	99.7%	(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
✓	56.0%	(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
	54.8%	(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
✓	49.0%	(-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64))))))) (sqrt.f64 x))
✓	51.0%	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
✓	46.9%	(-.f64 #s(literal 1 binary64) (sqrt.f64 x))
✓	49.3%	(+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) #s(literal 1 binary64))
	47.7%	(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))))
✓	55.0%	(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
	7.5%	(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 (+.f64 x #s(literal 1/2 binary64)) (.f64 x (/.f64 #s(literal -1/8 binary64) (*.f64 x x))))))
	1.8%	(.f64 x (.f64 x #s(literal -1/8 binary64)))
✓	3.7%	(.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x)))
✓	54.9%	(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
✓	51.2%	(.f64 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))

Compiler

Compiled 905 to 382 computations (57.8% saved)

regimes26.0ms (0.2%)

Counts

39 → 1

Calls

Call 1

Inputs
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x)))
(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
(.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (.f64 x (.f64 x x)))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x))))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) 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) (sqrt.f64 x))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) #s(literal 1 binary64))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 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 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (+.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 #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) (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))))))))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) 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))))))))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 (+.f64 #s(literal -1/16 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 binary64) x))) x))) (neg.f64 (.f64 x (*.f64 x 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 #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 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (pow.f64 (*.f64 x x) #s(literal 1/4 binary64)))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64))))
(-.f64 (pow.f64 (*.f64 (+.f64 x #s(literal 1 binary64)) (+.f64 x #s(literal 1 binary64))) #s(literal 1/4 binary64)) (sqrt.f64 x))
(/.f64 (+.f64 (.f64 #s(literal -1/8 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (.f64 #s(literal 1/2 binary64) (sqrt.f64 x))) x)
(/.f64 (+.f64 (.f64 (sqrt.f64 (/.f64 #s(literal 1 binary64) x)) #s(literal -1/8 binary64)) (.f64 (sqrt.f64 x) #s(literal 1/2 binary64))) x)
(/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 1/2 binary64)) (sqrt.f64 x)))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (+.f64 (sqrt.f64 x) (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 1/2 binary64))))
(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (+.f64 (+.f64 x #s(literal 1/2 binary64)) (.f64 x (/.f64 #s(literal -1/8 binary64) (*.f64 x x))))))
(.f64 (/.f64 (+.f64 x (-.f64 #s(literal 1 binary64) x)) (+.f64 (pow.f64 (+.f64 x #s(literal 1 binary64)) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))) (-.f64 (+.f64 x (+.f64 x #s(literal 1 binary64))) (sqrt.f64 (.f64 x (+.f64 x #s(literal 1 binary64))))))
(/.f64 (.f64 (-.f64 (.f64 (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x)) (+.f64 #s(literal 1 binary64) (.f64 #s(literal 2 binary64) x))) (.f64 x (+.f64 #s(literal 1 binary64) x))) #s(literal 1 binary64)) (.f64 (+.f64 (.f64 #s(literal 2 binary64) x) (+.f64 #s(literal 1 binary64) (pow.f64 (.f64 x (+.f64 #s(literal 1 binary64) x)) #s(literal 1/2 binary64)))) (+.f64 (pow.f64 (+.f64 #s(literal 1 binary64) x) #s(literal 3/2 binary64)) (pow.f64 x #s(literal 3/2 binary64)))))
(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)))))

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

Calls

2 calls:

12.0ms	x
10.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

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

Compiler

Compiled 10 to 7 computations (30% saved)

regimes17.0ms (0.1%)

Counts

26 → 2

Calls

Call 1

Inputs
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x)))
(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
(.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (.f64 x (.f64 x x)))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x))))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) 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) (sqrt.f64 x))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) #s(literal 1 binary64))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 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 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (+.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 #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) (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))))))))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) 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))))))))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 (+.f64 #s(literal -1/16 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 binary64) x))) x))) (neg.f64 (.f64 x (*.f64 x 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 #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 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))
(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

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

Calls

2 calls:

8.0ms	x
6.0ms	(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))

Results

Accuracy	Segments	Branch
99.6%	2	`x`
99.6%	2	`(-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x))`

Compiler

Compiled 10 to 7 computations (30% saved)

regimes9.0ms (0.1%)

Counts

25 → 2

Calls

Call 1

Inputs
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x)))
(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
(.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (.f64 x (.f64 x x)))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x))))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) 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) (sqrt.f64 x))
(/.f64 #s(literal 1/2 binary64) (sqrt.f64 x))
(*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64))
(*.f64 #s(literal 1/2 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x)))
(/.f64 #s(literal 1 binary64) (+.f64 #s(literal 1 binary64) (sqrt.f64 x)))
(+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 x #s(literal 1/2 binary64)))
(+.f64 (-.f64 (*.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) #s(literal 1 binary64))
(-.f64 (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 binary64))) (sqrt.f64 x))
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (+.f64 #s(literal 1 binary64) (*.f64 x #s(literal 1/2 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 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x #s(literal -1/8 binary64)))))
(/.f64 #s(literal 1 binary64) (+.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 #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) (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))))))))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) 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))))))))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 (+.f64 #s(literal -1/16 binary64) (-.f64 #s(literal 0 binary64) (/.f64 (+.f64 #s(literal -1/8 binary64) (/.f64 (+.f64 (-.f64 #s(literal 0 binary64) (sqrt.f64 (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal -1/2 binary64) (/.f64 #s(literal 1 binary64) x))) (-.f64 #s(literal 0 binary64) x))) x))) (neg.f64 (.f64 x (*.f64 x 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 #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 #s(literal 1/2 binary64) (exp.f64 (.f64 (log.f64 x) #s(literal -1/2 binary64))))

Outputs

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

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

Calls

1 calls:

7.0ms

Results

Accuracy	Segments	Branch
98.8%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes28.0ms (0.2%)

Counts

19 → 2

Calls

Call 1

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

26.0ms

Results

Accuracy	Segments	Branch
98.8%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes7.0ms (0.1%)

Counts

16 → 2

Calls

Call 1

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

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
98.5%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0%)

Counts

13 → 2

Calls

Call 1

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

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

Calls

1 calls:

4.0ms

Results

Accuracy	Segments	Branch
98.5%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0%)

Counts

12 → 2

Calls

Call 1

Inputs
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x)))
(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
(.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (.f64 x (.f64 x x)))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x))))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) 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) (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
97.8%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Counts

9 → 2

Calls

Call 1

Inputs
(.f64 x (.f64 x #s(literal -1/8 binary64)))
(.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x)))
(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
(.f64 x (.f64 x (+.f64 #s(literal -1/8 binary64) (*.f64 x #s(literal 1/16 binary64)))))
(/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (.f64 x (.f64 x x)))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) x) x) (.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x))))
(/.f64 (-.f64 (+.f64 #s(literal 1 binary64) 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) (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
97.5%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes5.0ms (0%)

Counts

8 → 2

Calls

Call 1

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

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

Calls

1 calls:

5.0ms

Results

Accuracy	Segments	Branch
48.6%	2	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes4.0ms (0%)

Counts

7 → 1

Calls

Call 1

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

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

Calls

1 calls:

3.0ms

Results

Accuracy	Segments	Branch
4.4%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes2.0ms (0%)

Counts

2 → 1

Calls

Call 1

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

Outputs
(.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x)))

Calls

1 calls:

2.0ms

Results

Accuracy	Segments	Branch
3.7%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

regimes1.0ms (0%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0b (0%)

Counts

1 → 1

Calls

Call 1

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

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

Calls

1 calls:

1.0ms

Results

Accuracy	Segments	Branch
1.8%	1	`x`

Compiler

Compiled 2 to 1 computations (50% saved)

bsearch0.0ms (0%)

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	3.2247044146060944e-7	0.00042630874122551177

Compiler

Compiled 12 to 9 computations (25% saved)

bsearch13.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	0.0019170400098111214	4.606365766930146

Results

8.0ms

128×

valid

Compiler

Compiled 212 to 169 computations (20.3% saved)

Precisions

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

ival-sqrt: 2.0ms (49.8% of total)

ival-sub: 1.0ms (24.9% of total)

ival-add: 1.0ms (24.9% of total)

const: 0.0ms (0% of total)

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

bsearch13.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	0.0019170400098111214	4.606365766930146

Results

7.0ms

128×

valid

Compiler

Compiled 180 to 145 computations (19.4% saved)

Precisions

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

ival-sqrt: 2.0ms (59.1% of total)

ival-sub: 1.0ms (29.6% of total)

ival-add: 1.0ms (29.6% of total)

const: 0.0ms (0% of total)

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

bsearch15.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
14.0ms	0.0019170400098111214	4.606365766930146

Results

9.0ms

128×

valid

Compiler

Compiled 148 to 121 computations (18.2% saved)

Precisions

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

ival-sqrt: 2.0ms (58.7% of total)

ival-sub: 1.0ms (29.4% of total)

ival-add: 1.0ms (29.4% of total)

const: 0.0ms (0% of total)

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

bsearch13.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	0.0019170400098111214	4.606365766930146

Results

8.0ms

128×

valid

Compiler

Compiled 148 to 121 computations (18.2% saved)

Precisions

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

ival-add: 2.0ms (46.8% of total)

ival-sqrt: 2.0ms (46.8% of total)

ival-sub: 1.0ms (23.4% of total)

const: 0.0ms (0% of total)

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

bsearch14.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
12.0ms	0.0019170400098111214	4.606365766930146

Results

8.0ms

128×

valid

Compiler

Compiled 116 to 97 computations (16.4% saved)

Precisions

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

ival-sqrt: 2.0ms (56.8% of total)

ival-sub: 1.0ms (28.4% of total)

ival-add: 1.0ms (28.4% of total)

const: 0.0ms (0% of total)

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

bsearch12.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
11.0ms	0.0019170400098111214	4.606365766930146

Results

7.0ms

128×

valid

Compiler

Compiled 108 to 89 computations (17.6% saved)

Precisions

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

ival-sqrt: 2.0ms (58.1% of total)

ival-sub: 1.0ms (29% of total)

ival-add: 1.0ms (29% of total)

const: 0.0ms (0% of total)

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

bsearch14.0ms (0.1%)

Algorithm

1×	binary-search

Stop Event

1×	narrow-enough

Steps

Time	Left	Right
13.0ms	0.0019170400098111214	4.606365766930146

Results

9.0ms

128×

valid

Compiler

Compiled 164 to 121 computations (26.2% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-sqrt: 3.0ms (61.5% of total)

ival-sub: 1.0ms (20.5% of total)

ival-add: 1.0ms (20.5% of total)

const: 0.0ms (0% of total)

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

simplify38.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

32×	`+-commutative_binary64`
24×	`*-commutative_binary64`
12×	`sub-neg_binary64`
2×	`1-exp_binary64`
2×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	63	174
1	95	174
2	103	174
3	105	174
4	106	174

Stop Event

1×

saturated

Calls

Call 1

Inputs
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 4722366482869645/9444732965739290427392 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(if (<=.f64 x #s(literal 5854679515581645/4503599627370496 binary64)) (-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (sqrt.f64 x)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 5404319552844595/4503599627370496 binary64)) (+.f64 #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 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) #s(literal 1 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 3242591731706757/9007199254740992 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 3242591731706757/9007199254740992 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(if (<=.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (.f64 x (.f64 x x))))
(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
(.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x)))
(.f64 x (.f64 x #s(literal -1/8 binary64)))

Outputs
(/.f64 #s(literal 1 binary64) (+.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 #s(literal 1 binary64) x))))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)) #s(literal 4722366482869645/9444732965739290427392 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (-.f64 (sqrt.f64 (+.f64 x #s(literal 1 binary64))) (sqrt.f64 x)))
(if (<=.f64 (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)) #s(literal 4722366482869645/9444732965739290427392 binary64)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)) (-.f64 (sqrt.f64 (+.f64 #s(literal 1 binary64) x)) (sqrt.f64 x)))
(if (<=.f64 x #s(literal 5854679515581645/4503599627370496 binary64)) (-.f64 (+.f64 #s(literal 1 binary64) (.f64 x (+.f64 #s(literal 1/2 binary64) (.f64 x (+.f64 #s(literal -1/8 binary64) (.f64 x #s(literal 1/16 binary64))))))) (sqrt.f64 x)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 5404319552844595/4503599627370496 binary64)) (+.f64 #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 (.f64 #s(literal 1/2 binary64) x) (sqrt.f64 x)) #s(literal 1 binary64)) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 1 binary64)) (+.f64 #s(literal 1 binary64) (-.f64 (.f64 x #s(literal 1/2 binary64)) (sqrt.f64 x))) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 1 binary64)) (+.f64 (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (.f64 x #s(literal 1/2 binary64))) (.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 3242591731706757/9007199254740992 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (*.f64 (pow.f64 x #s(literal -1/2 binary64)) #s(literal 1/2 binary64)))
(if (<=.f64 x #s(literal 3242591731706757/9007199254740992 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 #s(literal 1/2 binary64) (sqrt.f64 x)))
(if (<=.f64 x #s(literal 1 binary64)) (-.f64 #s(literal 1 binary64) (sqrt.f64 x)) (/.f64 (+.f64 #s(literal 16 binary64) (/.f64 #s(literal 32 binary64) x)) (.f64 x (.f64 x x))))
(/.f64 #s(literal 16 binary64) (.f64 x (.f64 x x)))
(.f64 x (.f64 #s(literal 1/16 binary64) (*.f64 x x)))
(.f64 x (.f64 x #s(literal -1/8 binary64)))

soundness3.0s (25.8%)

Rules

3856×	`-lowering-.f32`
3856×	`-lowering-.f64`
3792×	`-lowering-.f32`
3792×	`-lowering-.f64`
3564×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	199	1547
1	615	1347
2	2025	1285
3	7160	1285
0	8034	1285
0	113	434
1	325	384
2	1039	376
3	3226	373
4	7122	373
0	8132	373
0	25	110
1	187	93
2	1758	91
0	9591	91
0	215	1526
1	667	1316
2	2271	1309
3	6855	1306
0	8363	1306
0	6	16
1	39	16
2	303	16
3	3722	16
0	8049	16
0	553	2814
1	1832	2391
2	6931	2388
0	8175	2388
0	34	146
1	285	117
2	2903	116
0	8385	116
0	23	83
1	129	73
2	1072	72
0	8402	72

Stop Event

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

Compiler

Compiled 515 to 315 computations (38.8% saved)

preprocess115.0ms (1%)

Compiler: Compiled 386 to 146 computations (62.2% 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 (11.4%)

preprocess42.0ms (0.4%)

explain115.0ms (1%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify25.0ms (0.2%)

localize52.0ms (0.5%)

series5.0ms (0%)

rewrite343.0ms (3%)

simplify333.0ms (2.9%)

eval34.0ms (0.3%)

prune64.0ms (0.6%)

simplify237.0ms (2.1%)

localize358.0ms (3.1%)

series64.0ms (0.6%)

rewrite1.6s (13.9%)

simplify254.0ms (2.2%)

eval146.0ms (1.3%)

prune175.0ms (1.5%)

simplify172.0ms (1.5%)

localize216.0ms (1.9%)

series41.0ms (0.4%)

rewrite320.0ms (2.8%)

simplify294.0ms (2.6%)

eval187.0ms (1.6%)

prune334.0ms (2.9%)

simplify205.0ms (1.8%)

localize367.0ms (3.2%)

series18.0ms (0.2%)

rewrite355.0ms (3.1%)

simplify271.0ms (2.4%)

eval114.0ms (1%)

prune113.0ms (1%)

regimes26.0ms (0.2%)

regimes17.0ms (0.1%)

regimes9.0ms (0.1%)

regimes28.0ms (0.2%)

regimes7.0ms (0.1%)

regimes5.0ms (0%)

regimes5.0ms (0%)

regimes4.0ms (0%)

regimes5.0ms (0%)

regimes4.0ms (0%)

regimes2.0ms (0%)

regimes1.0ms (0%)

bsearch0.0ms (0%)

bsearch13.0ms (0.1%)

bsearch13.0ms (0.1%)

bsearch15.0ms (0.1%)

bsearch13.0ms (0.1%)

bsearch14.0ms (0.1%)

bsearch12.0ms (0.1%)

bsearch14.0ms (0.1%)

simplify38.0ms (0.3%)

soundness3.0s (25.8%)

preprocess115.0ms (1%)

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