Details

analyze301.0ms (4.1%)

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
0%	0%	100%	0%	0%	0%	0%	2
0%	0%	100%	0%	0%	0%	0%	3
16.7%	12.5%	62.5%	0%	0%	25%	0%	4
30%	18.7%	43.7%	0%	0%	37.5%	0%	5
38.9%	21.9%	34.4%	0%	0%	43.7%	0%	6
44.1%	23.4%	29.7%	0%	0%	46.9%	0%	7
47%	24.2%	27.3%	0%	0%	48.4%	0%	8
48.5%	24.6%	26.2%	0%	0%	49.2%	0%	9
49.2%	24.8%	25.6%	0%	0%	49.6%	0%	10
49.6%	24.9%	25.3%	0%	0%	49.8%	0%	11
49.8%	24.9%	25.1%	0%	0%	49.9%	0%	12

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample4.0s (54.3%)

Results

2.1s	8256×	body	256	valid
1.5s	7343×	body	256	infinite
201.0ms	1034×	body	256	invalid

Bogosity

preprocess16.0ms (0.2%)

Algorithm

2×	egg-herbie

Rules

4×	`rational_best-simplify-1`
2×	`rational_best-simplify-74`
2×	`rational_best-simplify-19`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	14	27
2	15	27
0	1	1

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0

Outputs
0

Call 2

Inputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Outputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify13.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

4×	`rational_best-simplify-1`
2×	`rational_best-simplify-74`
2×	`rational_best-simplify-19`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	27
1	14	27
2	15	27

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Outputs
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))

eval1.0ms (0%)

Compiler: Compiled 19 to 12 computations (36.8% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

33.0b

Counts

3 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	33.0b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))

Compiler

Compiled 10 to 7 computations (30% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
✓	0.0b	(-.f64 (*.f64 x x) 1)
✓	30.7b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

Compiler

Compiled 34 to 17 computations (50% saved)

series2.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(sqrt.f64 (-.f64 (*.f64 x x) 1))
0.0ms	x	@	inf	(sqrt.f64 (-.f64 (*.f64 x x) 1))
0.0ms	x	@	-inf	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
0.0ms	x	@	inf	(-.f64 (*.f64 x x) 1)
0.0ms	x	@	0	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))

rewrite107.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

888×	`rational_best-simplify-80`
876×	`rational_best-simplify-57`
710×	`rational_best-simplify-78`
610×	`rational_best-simplify-43`
460×	`rational_best-5`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	53
1	75	53
2	246	53
3	996	53
4	4612	53

Stop Event

1×	node limit

Counts

3 → 82

Calls

Call 1

Inputs
(sqrt.f64 (-.f64 (*.f64 x x) 1))
(-.f64 (*.f64 x x) 1)
(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))

Outputs
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(#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))) (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (*.f64 (/.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (/.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))) (*.f64 (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (/.f64 1 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))) (*.f64 (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))) (*.f64 (*.f64 (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))) (*.f64 (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (/.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))) (*.f64 (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))) (*.f64 (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (neg.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))) 2) -2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))))

simplify321.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

1814×	`rational_best-simplify-54`
1374×	`rational_best-simplify-2`
980×	`rational_best-simplify-78`
970×	`rational_best-simplify-80`
896×	`rational_best-simplify-94`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	219	2532
1	427	2524
2	1634	2524
3	5238	2524

Stop Event

1×	node limit

Counts

118 → 145

Calls

Call 1

Inputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(*.f64 -1 x)
(+.f64 (.f64 -1 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 -1 x))))
-1
(-.f64 (pow.f64 x 2) 1)
(-.f64 (pow.f64 x 2) 1)
(-.f64 (pow.f64 x 2) 1)
(pow.f64 x 2)
(-.f64 (pow.f64 x 2) 1)
(-.f64 (pow.f64 x 2) 1)
(-.f64 (pow.f64 x 2) 1)
(pow.f64 x 2)
(-.f64 (pow.f64 x 2) 1)
(-.f64 (pow.f64 x 2) 1)
(-.f64 (pow.f64 x 2) 1)
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) x)
(+.f64 (sqrt.f64 -1) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) x))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) x)))
(*.f64 2 x)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(/.f64 1/2 x)
(+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/2 (/.f64 1 x))))
(+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 5/128 (/.f64 1 (pow.f64 x 7))))))
(+.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 0)
(+.f64 0 (sqrt.f64 (+.f64 (*.f64 x x) -1)))
(-.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 0)
(-.f64 0 (neg.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1))))
(.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))
(.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) 1)
(.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))))
(.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1)))))
(.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (+.f64 (.f64 x x) -1)))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))
(.f64 (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))
(.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (sqrt.f64 (+.f64 (*.f64 x x) -1)))
(.f64 (/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1)))) (sqrt.f64 (+.f64 (.f64 x x) -1)))
(.f64 (/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))))))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))))))
(.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))
(.f64 (/.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))))
(.f64 (/.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))))) (.f64 (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))))))
(.f64 (/.f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))))))
(.f64 (/.f64 (/.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))))
(.f64 (/.f64 (/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1)))) (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))
(/.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 1)
(/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (*.f64 x x) -1))))
(/.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) 2) 2)
(/.f64 (.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 x x) -1))) 2) -2)
(pow.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 1)
(neg.f64 (neg.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1))))
(+.f64 (*.f64 x x) -1)
(+.f64 (+.f64 (*.f64 x x) -1) 0)
(+.f64 0 (+.f64 (*.f64 x x) -1))
(+.f64 -1 (*.f64 x x))
(.f64 1 (+.f64 (.f64 x x) -1))
(.f64 (+.f64 (.f64 x x) -1) 1)
(.f64 (+.f64 (.f64 x x) -1) (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))
(.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (/.f64 1 (+.f64 (*.f64 x x) -1))))
(.f64 (+.f64 (.f64 x x) -1) (/.f64 1 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))))
(.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (+.f64 (.f64 x x) -1))
(.f64 (/.f64 1 (+.f64 (.f64 x x) -1)) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))
(.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 1 (+.f64 (*.f64 x x) -1)))
(.f64 (.f64 (+.f64 (.f64 x x) -1) (/.f64 1 (+.f64 (.f64 x x) -1))) (+.f64 (*.f64 x x) -1))
(.f64 (/.f64 1 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (+.f64 (.f64 x x) -1))
(.f64 (/.f64 1 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (+.f64 (.f64 x x) -1) (.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))))
(.f64 (/.f64 (/.f64 1 (+.f64 (.f64 x x) -1)) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))))
(.f64 (/.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (+.f64 (.f64 x x) -1)) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))
(.f64 (/.f64 (.f64 (+.f64 (.f64 x x) -1) (/.f64 1 (+.f64 (.f64 x x) -1))) (+.f64 (.f64 x x) -1)) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))
(.f64 (/.f64 (/.f64 (/.f64 1 (+.f64 (.f64 x x) -1)) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))))) (.f64 (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))) (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))))
(.f64 (/.f64 (/.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (+.f64 (.f64 x x) -1)) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))))
(.f64 (/.f64 (/.f64 (.f64 (+.f64 (.f64 x x) -1) (/.f64 1 (+.f64 (.f64 x x) -1))) (+.f64 (.f64 x x) -1)) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))))
(.f64 (/.f64 (/.f64 1 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (+.f64 (.f64 x x) -1)) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))
(/.f64 (+.f64 (*.f64 x x) -1) 1)
(/.f64 (+.f64 (.f64 x x) -1) (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))
(/.f64 (+.f64 (*.f64 x (+.f64 x x)) -2) 2)
(/.f64 (-.f64 2 (*.f64 x (+.f64 x x))) -2)
(pow.f64 (+.f64 (*.f64 x x) -1) 1)
(neg.f64 (-.f64 1 (*.f64 x x)))
(-.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) 0)
(-.f64 0 (neg.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(.f64 1 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))
(.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) 1)
(.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))
(.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))))
(.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))))
(.f64 (/.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))
(.f64 (/.f64 1 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(.f64 (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 1 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(.f64 (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))
(.f64 (/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))
(.f64 (/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (/.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))))
(.f64 (/.f64 (/.f64 1 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))))
(.f64 (/.f64 (/.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(.f64 (/.f64 (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))
(.f64 (/.f64 (/.f64 (/.f64 1 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))))) (.f64 (.f64 (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))
(.f64 (/.f64 (/.f64 (/.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))))
(.f64 (/.f64 (/.f64 (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))))
(.f64 (/.f64 (/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(/.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) 1)
(/.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(/.f64 (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) 2) 2)
(/.f64 (.f64 (neg.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) 2) -2)
(pow.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) 1)
(neg.f64 (neg.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))

Outputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
(+.f64 (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (sqrt.f64 -1))))))
(+.f64 (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (sqrt.f64 -1))) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (sqrt.f64 -1))))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
(-.f64 x (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 -1 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 -1 x))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (neg.f64 x))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (neg.f64 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 -1 x))))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (neg.f64 x))))
-1
(-.f64 (pow.f64 x 2) 1)
(+.f64 (pow.f64 x 2) -1)
(+.f64 -1 (pow.f64 x 2))
(-.f64 (pow.f64 x 2) 1)
(+.f64 (pow.f64 x 2) -1)
(+.f64 -1 (pow.f64 x 2))
(-.f64 (pow.f64 x 2) 1)
(+.f64 (pow.f64 x 2) -1)
(+.f64 -1 (pow.f64 x 2))
(pow.f64 x 2)
(-.f64 (pow.f64 x 2) 1)
(+.f64 (pow.f64 x 2) -1)
(+.f64 -1 (pow.f64 x 2))
(-.f64 (pow.f64 x 2) 1)
(+.f64 (pow.f64 x 2) -1)
(+.f64 -1 (pow.f64 x 2))
(-.f64 (pow.f64 x 2) 1)
(+.f64 (pow.f64 x 2) -1)
(+.f64 -1 (pow.f64 x 2))
(pow.f64 x 2)
(-.f64 (pow.f64 x 2) 1)
(+.f64 (pow.f64 x 2) -1)
(+.f64 -1 (pow.f64 x 2))
(-.f64 (pow.f64 x 2) 1)
(+.f64 (pow.f64 x 2) -1)
(+.f64 -1 (pow.f64 x 2))
(-.f64 (pow.f64 x 2) 1)
(+.f64 (pow.f64 x 2) -1)
(+.f64 -1 (pow.f64 x 2))
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) x)
(+.f64 (sqrt.f64 -1) (+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) x))
(+.f64 (sqrt.f64 -1) (+.f64 x (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) x))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) x)))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (+.f64 x (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))))
(+.f64 (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (+.f64 x (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))) (+.f64 x (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))))
(*.f64 2 x)
(*.f64 x 2)
(-.f64 (.f64 2 x) (.f64 1/2 (/.f64 1 x)))
(-.f64 (.f64 x 2) (.f64 1/2 (/.f64 1 x)))
(-.f64 (.f64 2 x) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
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(.f64 (/.f64 (/.f64 (/.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))))
(+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(.f64 (/.f64 (/.f64 (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))))))
(+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(.f64 (/.f64 (/.f64 1 (/.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))))) (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(/.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) 1)
(+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(/.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(/.f64 (.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1))) 2) 2)
(+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(/.f64 (.f64 (neg.f64 (+.f64 x (sqrt.f64 (+.f64 (.f64 x x) -1)))) 2) -2)
(+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(pow.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1))) 1)
(+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(neg.f64 (neg.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(+.f64 x (sqrt.f64 (+.f64 -1 (*.f64 x x))))

eval54.0ms (0.7%)

Compiler: Compiled 3546 to 2293 computations (35.3% saved)

prune20.0ms (0.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	142	3	145
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	142	4	146

Error

0.0b

Counts

146 → 4

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.5b	(log.f64 (-.f64 (.f64 x 2) (.f64 1/2 (/.f64 1 x))))
▶	47.3b	(log.f64 (+.f64 x (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))))
✓	33.0b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
▶	0.8b	(log.f64 (+.f64 x x))

Compiler

Compiled 51 to 35 computations (31.4% saved)

localize4.0ms (0.1%)

Compiler: Compiled 9 to 3 computations (66.7% saved)

localize35.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))
✓	13.3b	(sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))
✓	30.7b	(sqrt.f64 (+.f64 (*.f64 x x) -1))
✓	30.9b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))

Compiler

Compiled 117 to 64 computations (45.3% saved)

series1.0ms (0%)

Counts

4 → 48

Calls

12 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))
0.0ms	x	@	inf	(.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))
0.0ms	x	@	0	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))
0.0ms	x	@	inf	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))
0.0ms	x	@	-inf	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))

rewrite141.0ms (1.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1114×	`rational_best-simplify-57`
670×	`rational_best-simplify-44`
622×	`rational_best-simplify-43`
606×	`rational_best-simplify-54`
576×	`rational_best-5`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	13	192
1	107	192
2	329	100
3	1381	100
4	6275	100

Stop Event

1×	node limit

Counts

4 → 161

Calls

Call 1

Inputs
(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))
(sqrt.f64 (+.f64 (*.f64 x x) -1))
(sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))
(.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (+.f64 (.f64 x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (sqrt.f64 (+.f64 (.f64 x x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (sqrt.f64 (+.f64 (.f64 x x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (+.f64 (*.f64 x x) -1))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (sqrt.f64 (+.f64 (.f64 x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (sqrt.f64 (+.f64 (.f64 x x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) 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egg-rr> (2) ((x .f64 (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (+.f64 (.f64 x x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (+.f64 (.f64 x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))) (/.f64 1 (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))) (sqrt.f64 (.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1)))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))) (sqrt.f64 (.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (+.f64 (.f64 x x) -1)))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))) (sqrt.f64 (.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (/.f64 1 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1)))) (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))))) (sqrt.f64 (.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (.f64 (.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (+.f64 (.f64 x x) -1) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))))
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simplify303.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

1718×	`rational_best-simplify-132`
1032×	`rational_best-simplify-2`
920×	`rational_best-simplify-49`
748×	`rational_best-simplify-50`
548×	`rational_best-simplify-80`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	386	7599
1	791	7557
2	1597	7539
3	3583	7441
4	7980	7441

Stop Event

1×	node limit

Counts

209 → 218

Calls

Call 1

Inputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(*.f64 -1 x)
(+.f64 (.f64 -1 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 -1 x))))
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(*.f64 -1 x)
(+.f64 (.f64 -1 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 -1 x))))
-1
(-.f64 (pow.f64 x 2) 1)
(-.f64 (pow.f64 x 2) 1)
(-.f64 (pow.f64 x 2) 1)
(pow.f64 x 2)
(-.f64 (pow.f64 x 2) 1)
(-.f64 (pow.f64 x 2) 1)
(-.f64 (pow.f64 x 2) 1)
(pow.f64 x 2)
(-.f64 (pow.f64 x 2) 1)
(-.f64 (pow.f64 x 2) 1)
(-.f64 (pow.f64 x 2) 1)
1
(+.f64 (*.f64 -2 (pow.f64 x 2)) 1)
(+.f64 (*.f64 -2 (pow.f64 x 2)) (+.f64 1 (pow.f64 x 4)))
(+.f64 (*.f64 -2 (pow.f64 x 2)) (+.f64 1 (pow.f64 x 4)))
(pow.f64 x 4)
(+.f64 (*.f64 -2 (pow.f64 x 2)) (pow.f64 x 4))
(+.f64 (*.f64 -2 (pow.f64 x 2)) (+.f64 1 (pow.f64 x 4)))
(+.f64 (*.f64 -2 (pow.f64 x 2)) (+.f64 1 (pow.f64 x 4)))
(pow.f64 x 4)
(+.f64 (*.f64 -2 (pow.f64 x 2)) (pow.f64 x 4))
(+.f64 (*.f64 -2 (pow.f64 x 2)) (+.f64 1 (pow.f64 x 4)))
(+.f64 (*.f64 -2 (pow.f64 x 2)) (+.f64 1 (pow.f64 x 4)))
(+.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 0)
(+.f64 0 (sqrt.f64 (+.f64 (*.f64 x x) -1)))
(-.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 0)
(-.f64 0 (neg.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1))))
(/.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 1)
(/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (*.f64 x x) -1))))
(/.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) 2) 2)
(pow.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 1)
(neg.f64 (neg.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1))))
(sqrt.f64 (+.f64 (*.f64 x x) -1))
(+.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 0)
(+.f64 0 (sqrt.f64 (+.f64 (*.f64 x x) -1)))
(-.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1)) 0)
(-.f64 0 (neg.f64 (sqrt.f64 (+.f64 (*.f64 x x) -1))))
(.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))
(.f64 (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))
(.f64 (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (.f64 x x) -1)))))
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(fabs.f64 (.f64 (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (/.f64 1 (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))) (/.f64 (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (fabs.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (*.f64 x x) -1))))))))
(fabs.f64 (-.f64 0 (/.f64 (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (fabs.f64 (/.f64 (sqrt.f64 (+.f64 (.f64 x x) -1)) (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))
(+.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)) 0)
(+.f64 0 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))
(-.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)) 0)
(-.f64 0 (neg.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))
(/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)) 1)
(/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))
(/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x (+.f64 x x)) -2)) 2)
(pow.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)) 1)
(neg.f64 (neg.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))
(fabs.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))
(fabs.f64 (neg.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))
(fabs.f64 (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))))
(fabs.f64 (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (neg.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))))
(fabs.f64 (neg.f64 (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))))
(fabs.f64 (.f64 (-.f64 1 (.f64 x x)) (+.f64 (*.f64 x x) -1)))
(fabs.f64 (.f64 (fabs.f64 (+.f64 (.f64 x x) -1)) (+.f64 (*.f64 x x) -1)))
(fabs.f64 (.f64 (/.f64 (+.f64 (.f64 x x) -1) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))) (+.f64 (*.f64 x x) -1)))
(fabs.f64 (.f64 (+.f64 (.f64 x x) -1) (-.f64 1 (*.f64 x x))))
(fabs.f64 (.f64 (fabs.f64 (+.f64 (.f64 x x) -1)) (-.f64 1 (*.f64 x x))))
(fabs.f64 (.f64 (/.f64 (+.f64 (.f64 x x) -1) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))) (-.f64 1 (*.f64 x x))))
(fabs.f64 (.f64 (+.f64 (.f64 x x) -1) (fabs.f64 (+.f64 (*.f64 x x) -1))))
(fabs.f64 (.f64 (-.f64 1 (.f64 x x)) (fabs.f64 (+.f64 (*.f64 x x) -1))))
(fabs.f64 (.f64 (/.f64 (+.f64 (.f64 x x) -1) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))) (fabs.f64 (+.f64 (*.f64 x x) -1))))
(fabs.f64 (.f64 (+.f64 (.f64 x x) -1) (/.f64 (+.f64 (.f64 x x) -1) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))))
(fabs.f64 (.f64 (-.f64 1 (.f64 x x)) (/.f64 (+.f64 (.f64 x x) -1) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))))
(fabs.f64 (.f64 (fabs.f64 (+.f64 (.f64 x x) -1)) (/.f64 (+.f64 (.f64 x x) -1) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))))
(fabs.f64 (.f64 (/.f64 (+.f64 (.f64 x x) -1) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))) (/.f64 (+.f64 (.f64 x x) -1) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))))
(fabs.f64 (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (neg.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))))
(fabs.f64 (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))))))
(fabs.f64 (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (+.f64 (.f64 x x) -1) (fabs.f64 (+.f64 (*.f64 x x) -1)))))
(fabs.f64 (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (fabs.f64 (/.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))))))
(fabs.f64 (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (-.f64 1 (.f64 x x)) (fabs.f64 (+.f64 (*.f64 x x) -1)))))
(fabs.f64 (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (+.f64 (.f64 x (+.f64 x x)) -2) (.f64 (fabs.f64 (+.f64 (.f64 x x) -1)) 2))))
(fabs.f64 (/.f64 (neg.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))))
(fabs.f64 (/.f64 (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))))
(fabs.f64 (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (neg.f64 (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))))
(fabs.f64 (.f64 (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))))
(fabs.f64 (.f64 (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (neg.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))))
(fabs.f64 (.f64 (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))))))
(fabs.f64 (.f64 (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 1 (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (neg.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))))))
(fabs.f64 (.f64 1 (.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (neg.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))))
(fabs.f64 (.f64 1 (.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))))))
(fabs.f64 (.f64 1 (.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (neg.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))))))
(fabs.f64 (.f64 (.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))
(fabs.f64 (.f64 (.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (/.f64 1 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (neg.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))))))
(fabs.f64 (.f64 (.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (/.f64 1 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))))))
(fabs.f64 (.f64 (.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (/.f64 1 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (neg.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))))))
(fabs.f64 (.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (.f64 (/.f64 1 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (neg.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))))
(fabs.f64 (.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (.f64 (/.f64 1 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))))))
(fabs.f64 (.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (.f64 (/.f64 1 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (neg.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))))))
(fabs.f64 (.f64 1 (.f64 (/.f64 1 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (+.f64 (.f64 x x) -1) (.f64 (neg.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (+.f64 (.f64 x x) -1))))))
(fabs.f64 (.f64 1 (.f64 (/.f64 1 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (+.f64 (.f64 x x) -1) (.f64 (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))) (+.f64 (.f64 x x) -1))))))
(fabs.f64 (.f64 1 (.f64 (/.f64 1 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (neg.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))))))))
(fabs.f64 (-.f64 0 (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (neg.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))))

Outputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (sqrt.f64 -1))))))
(+.f64 (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (sqrt.f64 -1))) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (sqrt.f64 -1))))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (sqrt.f64 -1))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
(-.f64 x (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 -1 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 -1 x))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (neg.f64 x))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (neg.f64 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 -1 x))))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (neg.f64 x))))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (*.f64 1/8 (/.f64 1 (pow.f64 x 3))) (neg.f64 x))))
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (sqrt.f64 -1))))))
(+.f64 (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (sqrt.f64 -1))) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (sqrt.f64 -1))))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (sqrt.f64 -1))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
(-.f64 x (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 -1 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 -1 x))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (neg.f64 x))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (neg.f64 x)))
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(fabs.f64 (.f64 (-.f64 1 (.f64 x x)) (/.f64 (+.f64 -1 (.f64 x x)) (fabs.f64 (/.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))))))
(fabs.f64 (.f64 (+.f64 (.f64 x x) -1) (fabs.f64 (+.f64 (*.f64 x x) -1))))
(fabs.f64 (.f64 (+.f64 -1 (.f64 x x)) (fabs.f64 (+.f64 -1 (*.f64 x x)))))
(fabs.f64 (.f64 (-.f64 1 (.f64 x x)) (fabs.f64 (+.f64 (*.f64 x x) -1))))
(fabs.f64 (.f64 (-.f64 1 (.f64 x x)) (fabs.f64 (+.f64 -1 (*.f64 x x)))))
(fabs.f64 (.f64 (/.f64 (+.f64 (.f64 x x) -1) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))) (fabs.f64 (+.f64 (*.f64 x x) -1))))
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(.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))
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(.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))
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(.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))
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(.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))
(fabs.f64 (.f64 1 (.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (neg.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))))
(.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))
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(.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))
(fabs.f64 (.f64 1 (.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (neg.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))))))
(.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))
(fabs.f64 (.f64 (.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))
(.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))
(fabs.f64 (.f64 (.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (/.f64 1 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (neg.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))))))
(.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))
(fabs.f64 (.f64 (.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (/.f64 1 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))))))
(.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))
(fabs.f64 (.f64 (.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (/.f64 1 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (neg.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))))))
(.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))
(fabs.f64 (.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (.f64 (/.f64 1 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (neg.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))))
(fabs.f64 (.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (.f64 (neg.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x)))) (/.f64 1 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))))))
(fabs.f64 (.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (.f64 (/.f64 1 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x)))) (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x))))))
(fabs.f64 (.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (/.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (neg.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x)))))))
(fabs.f64 (.f64 (+.f64 -1 (.f64 x x)) (.f64 (+.f64 -1 (.f64 x x)) (-.f64 (/.f64 0 (+.f64 -1 (.f64 x x))) (/.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))))))
(fabs.f64 (.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (.f64 (/.f64 1 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))))))
(fabs.f64 (.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (.f64 (neg.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x)))) (/.f64 1 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))))))
(fabs.f64 (.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (.f64 (/.f64 1 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x)))) (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x))))))
(fabs.f64 (.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (/.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (neg.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x)))))))
(fabs.f64 (.f64 (+.f64 -1 (.f64 x x)) (.f64 (+.f64 -1 (.f64 x x)) (-.f64 (/.f64 0 (+.f64 -1 (.f64 x x))) (/.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))))))
(fabs.f64 (.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (.f64 (/.f64 1 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (neg.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1)))))))
(fabs.f64 (.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (.f64 (neg.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x)))) (/.f64 1 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))))))
(fabs.f64 (.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (.f64 (/.f64 1 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x)))) (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x))))))
(fabs.f64 (.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (/.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (neg.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x)))))))
(fabs.f64 (.f64 (+.f64 -1 (.f64 x x)) (.f64 (+.f64 -1 (.f64 x x)) (-.f64 (/.f64 0 (+.f64 -1 (.f64 x x))) (/.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))))))
(fabs.f64 (.f64 1 (.f64 (/.f64 1 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (+.f64 (.f64 x x) -1) (.f64 (neg.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (+.f64 (.f64 x x) -1))))))
(fabs.f64 (.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (.f64 (neg.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x)))) (/.f64 1 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))))))
(fabs.f64 (.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (.f64 (/.f64 1 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x)))) (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x))))))
(fabs.f64 (.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (/.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (neg.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x)))))))
(fabs.f64 (.f64 (+.f64 -1 (.f64 x x)) (.f64 (+.f64 -1 (.f64 x x)) (-.f64 (/.f64 0 (+.f64 -1 (.f64 x x))) (/.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))))))
(fabs.f64 (.f64 1 (.f64 (/.f64 1 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1))) (.f64 (+.f64 (.f64 x x) -1) (.f64 (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (fabs.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)))) (+.f64 (.f64 x x) -1))))))
(fabs.f64 (.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (.f64 (neg.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x)))) (/.f64 1 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))))))
(fabs.f64 (.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (.f64 (/.f64 1 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x)))) (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x))))))
(fabs.f64 (.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (/.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (neg.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x)))))))
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(fabs.f64 (.f64 1 (.f64 (/.f64 1 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x)))) (.f64 (neg.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x)))) (/.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (fabs.f64 (/.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x)))))))))
(fabs.f64 (.f64 (/.f64 1 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x)))) (.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (neg.f64 (/.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (fabs.f64 (/.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))))))))
(fabs.f64 (.f64 (/.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (fabs.f64 (/.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))))) (.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (/.f64 -1 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))))))
(fabs.f64 (.f64 (/.f64 (.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))) (fabs.f64 (/.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (.f64 x x))))) (-.f64 (/.f64 0 (+.f64 -1 (.f64 x x))) (/.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x))))))
(fabs.f64 (-.f64 0 (/.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (.f64 x x) -1)) (neg.f64 (/.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))))
(.f64 (+.f64 -1 (.f64 x x)) (+.f64 -1 (*.f64 x x)))

localize15.0ms (0.2%)

Compiler: Compiled 35 to 27 computations (22.9% saved)

eval108.0ms (1.5%)

Compiler: Compiled 8270 to 5033 computations (39.1% saved)

prune30.0ms (0.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	217	1	218
Fresh	0	0	0
Picked	0	1	1
Done	1	2	3
Total	218	4	222

Error

0.0b

Counts

222 → 4

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(log.f64 (-.f64 (.f64 x 2) (.f64 1/2 (/.f64 1 x))))
▶	33.0b	(log.f64 (+.f64 x (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (-.f64 (pow.f64 x 2) 1))))
✓	33.0b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
✓	0.8b	(log.f64 (+.f64 x x))

Compiler

Compiled 44 to 33 computations (25% saved)

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (pow.f64 x 2) 1)
✓	0.0b	(/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))
	30.7b	(sqrt.f64 (+.f64 (*.f64 x x) -1))
✓	30.9b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (-.f64 (pow.f64 x 2) 1))

Compiler

Compiled 82 to 54 computations (34.1% saved)

series2.0ms (0%)

Counts

3 → 27

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))
0.0ms	x	@	inf	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (-.f64 (pow.f64 x 2) 1))
0.0ms	x	@	-inf	(-.f64 (pow.f64 x 2) 1)
0.0ms	x	@	-inf	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (-.f64 (pow.f64 x 2) 1))
0.0ms	x	@	-inf	(/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))

rewrite117.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

1230×	`rational_best-simplify-57`
690×	`rational_best-simplify-44`
630×	`rational_best-5`
628×	`rational_best-4`
628×	`rational_best-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	77
1	114	77
2	338	77
3	1366	77
4	6307	77

Stop Event

1×	node limit

Counts

3 → 52

Calls

Call 1

Inputs
(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (-.f64 (pow.f64 x 2) 1))
(/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))
(-.f64 (pow.f64 x 2) 1)

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (-.f64 (*.f64 2 (pow.f64 x 2)) 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2)))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))) (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (*.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 -1 (pow.f64 x 2))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (pow.f64 x 2) -1)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (+.f64 -1 (pow.f64 x 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (+.f64 -1 (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 -1 (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1 (pow.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1 (pow.f64 x 2)) (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1 (pow.f64 x 2)) (*.f64 (+.f64 -1 (pow.f64 x 2)) (/.f64 1 (+.f64 -1 (pow.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 -1 (pow.f64 x 2)) (/.f64 1 (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))) (+.f64 -1 (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (+.f64 -1 (pow.f64 x 2))) (*.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))) (/.f64 1 (+.f64 -1 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (+.f64 -1 (pow.f64 x 2)) (/.f64 1 (+.f64 -1 (pow.f64 x 2)))) (+.f64 -1 (pow.f64 x 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2)))) (*.f64 (+.f64 -1 (pow.f64 x 2)) (*.f64 (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))) (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (+.f64 -1 (pow.f64 x 2))) (*.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2)))) (*.f64 (+.f64 -1 (pow.f64 x 2)) (*.f64 (+.f64 -1 (pow.f64 x 2)) (*.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))) (+.f64 -1 (pow.f64 x 2))) (*.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (*.f64 (+.f64 -1 (pow.f64 x 2)) (/.f64 1 (+.f64 -1 (pow.f64 x 2)))) (+.f64 -1 (pow.f64 x 2))) (*.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (/.f64 1 (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2)))) (+.f64 -1 (pow.f64 x 2))) (*.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (pow.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 -1 (pow.f64 x 2)) (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (*.f64 2 (pow.f64 x 2)) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (+.f64 -1 (pow.f64 x 2)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (-.f64 1 (pow.f64 x 2)))))))

simplify191.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

914×	`rational_best-simplify-80`
832×	`rational_best-simplify-78`
820×	`rational_best-simplify-49`
780×	`rational_best-simplify-24`
736×	`rational_best-simplify-94`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	176	2285
1	349	2265
2	927	2265
3	3158	2265
4	7135	2265

Stop Event

1×	node limit

Counts

79 → 115

Calls

Call 1

Inputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(*.f64 -1 x)
(+.f64 (.f64 -1 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 -1 x))))
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 4)) (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (*.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) (pow.f64 (sqrt.f64 -1) 2))) 1) (pow.f64 x 6)) (sqrt.f64 -1))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 4)) (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))))
(/.f64 1 x)
(+.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x))
(+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (.f64 3/8 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (.f64 5/16 (/.f64 1 (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (*.f64 3/8 (/.f64 1 (pow.f64 x 5))))))
(/.f64 -1 x)
(neg.f64 (+.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)))
(neg.f64 (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (.f64 3/8 (/.f64 1 (pow.f64 x 5))))))
(neg.f64 (+.f64 (.f64 5/16 (/.f64 1 (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (*.f64 3/8 (/.f64 1 (pow.f64 x 5)))))))
-1
(pow.f64 x 2)
(pow.f64 x 2)
(+.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 0)
(+.f64 0 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 0)
(-.f64 0 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2)))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 1)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) (/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2)))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (-.f64 (*.f64 2 (pow.f64 x 2)) 2)) 2)
(pow.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 1)
(neg.f64 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2)))))
(+.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 0)
(+.f64 0 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))
(-.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 0)
(-.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) 1)
(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))
(.f64 (/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))))))
(.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))))
(.f64 (/.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(.f64 (/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))))
(.f64 (/.f64 (/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(pow.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 1)
(neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(+.f64 -1 (pow.f64 x 2))
(+.f64 (pow.f64 x 2) -1)
(+.f64 (+.f64 -1 (pow.f64 x 2)) 0)
(+.f64 0 (+.f64 -1 (pow.f64 x 2)))
(*.f64 1 (+.f64 -1 (pow.f64 x 2)))
(*.f64 (+.f64 -1 (pow.f64 x 2)) 1)
(*.f64 (+.f64 -1 (pow.f64 x 2)) (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))
(.f64 (+.f64 -1 (pow.f64 x 2)) (.f64 (+.f64 -1 (pow.f64 x 2)) (/.f64 1 (+.f64 -1 (pow.f64 x 2)))))
(*.f64 (+.f64 -1 (pow.f64 x 2)) (/.f64 1 (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2)))))
(*.f64 (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))) (+.f64 -1 (pow.f64 x 2)))
(.f64 (/.f64 1 (+.f64 -1 (pow.f64 x 2))) (.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))
(.f64 (.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))) (/.f64 1 (+.f64 -1 (pow.f64 x 2))))
(.f64 (.f64 (+.f64 -1 (pow.f64 x 2)) (/.f64 1 (+.f64 -1 (pow.f64 x 2)))) (+.f64 -1 (pow.f64 x 2)))
(.f64 (/.f64 1 (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2)))) (.f64 (+.f64 -1 (pow.f64 x 2)) (*.f64 (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))) (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))))
(.f64 (/.f64 (/.f64 1 (+.f64 -1 (pow.f64 x 2))) (.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2)))) (.f64 (+.f64 -1 (pow.f64 x 2)) (.f64 (+.f64 -1 (pow.f64 x 2)) (*.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))))
(.f64 (/.f64 (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))) (+.f64 -1 (pow.f64 x 2))) (.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))
(.f64 (/.f64 (.f64 (+.f64 -1 (pow.f64 x 2)) (/.f64 1 (+.f64 -1 (pow.f64 x 2)))) (+.f64 -1 (pow.f64 x 2))) (*.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))
(.f64 (/.f64 (/.f64 1 (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2)))) (+.f64 -1 (pow.f64 x 2))) (.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))
(/.f64 (+.f64 -1 (pow.f64 x 2)) 1)
(/.f64 (+.f64 -1 (pow.f64 x 2)) (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))
(/.f64 (-.f64 (*.f64 2 (pow.f64 x 2)) 2) 2)
(pow.f64 (+.f64 -1 (pow.f64 x 2)) 1)
(neg.f64 (-.f64 1 (pow.f64 x 2)))

Outputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
(+.f64 (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (.f64 1/16 (/.f64 (pow.f64 x 6) (sqrt.f64 -1)))) (+.f64 (sqrt.f64 -1) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
(+.f64 (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (sqrt.f64 -1))) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
(+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (sqrt.f64 -1))) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
(-.f64 x (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 1/2 (/.f64 1 x)) (*.f64 1/16 (/.f64 1 (pow.f64 x 5))))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 -1 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 -1 x))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (neg.f64 x))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (neg.f64 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 -1 x))))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (+.f64 (*.f64 1/16 (/.f64 1 (pow.f64 x 5))) (neg.f64 x))))
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (sqrt.f64 -1) (*.f64 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) -1/2))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 4)) (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (*.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (.f64 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) -1/2) (+.f64 (sqrt.f64 -1) (.f64 -1/2 (/.f64 (*.f64 (pow.f64 x 4) (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2))) (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) -1/2) (.f64 -1/2 (/.f64 (*.f64 (pow.f64 x 4) (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2))) (sqrt.f64 -1)))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) (pow.f64 (sqrt.f64 -1) 2))) 1) (pow.f64 x 6)) (sqrt.f64 -1))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 4)) (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))))
(+.f64 (+.f64 (sqrt.f64 -1) (.f64 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) -1/2)) (+.f64 (.f64 -1/2 (/.f64 (.f64 (pow.f64 x 4) (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2))) (sqrt.f64 -1))) (.f64 -1/2 (/.f64 (.f64 (pow.f64 x 6) (+.f64 1 (.f64 1/2 (/.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) 1)))) (sqrt.f64 -1)))))
(+.f64 (+.f64 (sqrt.f64 -1) (.f64 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) -1/2)) (.f64 -1/2 (+.f64 (/.f64 (.f64 (pow.f64 x 6) (+.f64 1 (.f64 1/2 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2))))) (sqrt.f64 -1)) (/.f64 (*.f64 (pow.f64 x 4) (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2))) (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) -1/2) (.f64 -1/2 (+.f64 (/.f64 (.f64 (pow.f64 x 4) (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2))) (sqrt.f64 -1)) (/.f64 (.f64 (pow.f64 x 6) (+.f64 1 (*.f64 1/2 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2))))) (sqrt.f64 -1))))))
(/.f64 1 x)
(+.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 1 (pow.f64 x 3))))
(+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (.f64 3/8 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (.f64 (/.f64 1 (pow.f64 x 5)) 3/8)))
(+.f64 (/.f64 1 x) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (.f64 (/.f64 1 (pow.f64 x 5)) 3/8)))
(+.f64 (.f64 5/16 (/.f64 1 (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (*.f64 3/8 (/.f64 1 (pow.f64 x 5))))))
(+.f64 (+.f64 (/.f64 1 x) (.f64 (/.f64 1 (pow.f64 x 5)) 3/8)) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (*.f64 5/16 (/.f64 1 (pow.f64 x 7)))))
(+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (+.f64 (/.f64 1 x) (.f64 (/.f64 1 (pow.f64 x 5)) 3/8)) (*.f64 5/16 (/.f64 1 (pow.f64 x 7)))))
(+.f64 (/.f64 1 x) (+.f64 (.f64 (/.f64 1 (pow.f64 x 5)) 3/8) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (*.f64 5/16 (/.f64 1 (pow.f64 x 7))))))
(+.f64 (/.f64 1 x) (+.f64 (.f64 5/16 (/.f64 1 (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (*.f64 (/.f64 1 (pow.f64 x 5)) 3/8))))
(/.f64 -1 x)
(neg.f64 (+.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)))
(neg.f64 (+.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 1 (pow.f64 x 3)))))
(neg.f64 (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (.f64 3/8 (/.f64 1 (pow.f64 x 5))))))
(neg.f64 (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (.f64 (/.f64 1 (pow.f64 x 5)) 3/8))))
(neg.f64 (+.f64 (/.f64 1 x) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (.f64 (/.f64 1 (pow.f64 x 5)) 3/8))))
(neg.f64 (+.f64 (.f64 5/16 (/.f64 1 (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (*.f64 3/8 (/.f64 1 (pow.f64 x 5)))))))
(neg.f64 (+.f64 (+.f64 (/.f64 1 x) (.f64 (/.f64 1 (pow.f64 x 5)) 3/8)) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (*.f64 5/16 (/.f64 1 (pow.f64 x 7))))))
(neg.f64 (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (+.f64 (/.f64 1 x) (.f64 (/.f64 1 (pow.f64 x 5)) 3/8)) (*.f64 5/16 (/.f64 1 (pow.f64 x 7))))))
(neg.f64 (+.f64 (/.f64 1 x) (+.f64 (.f64 (/.f64 1 (pow.f64 x 5)) 3/8) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (*.f64 5/16 (/.f64 1 (pow.f64 x 7)))))))
(neg.f64 (+.f64 (/.f64 1 x) (+.f64 (.f64 5/16 (/.f64 1 (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (*.f64 (/.f64 1 (pow.f64 x 5)) 3/8)))))
-1
(pow.f64 x 2)
(pow.f64 x 2)
(+.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 0)
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (+.f64 -1 (pow.f64 x 2)))
(+.f64 0 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (+.f64 -1 (pow.f64 x 2)))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 0)
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (+.f64 -1 (pow.f64 x 2)))
(-.f64 0 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2)))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (+.f64 -1 (pow.f64 x 2)))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 1)
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (+.f64 -1 (pow.f64 x 2)))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) (/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2)))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (+.f64 -1 (pow.f64 x 2)))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (-.f64 (*.f64 2 (pow.f64 x 2)) 2)) 2)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (-.f64 (*.f64 2 (pow.f64 x 2)) 2)) 2)
(pow.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 1)
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (+.f64 -1 (pow.f64 x 2)))
(neg.f64 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2)))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (+.f64 -1 (pow.f64 x 2)))
(+.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 0)
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(+.f64 0 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(-.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 0)
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(-.f64 0 (neg.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) 1)
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))))
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))))
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(.f64 (/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))))))
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))))
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(.f64 (/.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(.f64 (/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))))
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(.f64 (/.f64 (/.f64 1 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(pow.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 1)
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(neg.f64 (neg.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(+.f64 -1 (pow.f64 x 2))
(+.f64 (pow.f64 x 2) -1)
(+.f64 -1 (pow.f64 x 2))
(+.f64 (+.f64 -1 (pow.f64 x 2)) 0)
(+.f64 -1 (pow.f64 x 2))
(+.f64 0 (+.f64 -1 (pow.f64 x 2)))
(+.f64 -1 (pow.f64 x 2))
(*.f64 1 (+.f64 -1 (pow.f64 x 2)))
(+.f64 -1 (pow.f64 x 2))
(*.f64 (+.f64 -1 (pow.f64 x 2)) 1)
(+.f64 -1 (pow.f64 x 2))
(*.f64 (+.f64 -1 (pow.f64 x 2)) (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))
(+.f64 -1 (pow.f64 x 2))
(.f64 (+.f64 -1 (pow.f64 x 2)) (.f64 (+.f64 -1 (pow.f64 x 2)) (/.f64 1 (+.f64 -1 (pow.f64 x 2)))))
(+.f64 -1 (pow.f64 x 2))
(*.f64 (+.f64 -1 (pow.f64 x 2)) (/.f64 1 (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2)))))
(+.f64 -1 (pow.f64 x 2))
(*.f64 (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))) (+.f64 -1 (pow.f64 x 2)))
(+.f64 -1 (pow.f64 x 2))
(.f64 (/.f64 1 (+.f64 -1 (pow.f64 x 2))) (.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))
(+.f64 -1 (pow.f64 x 2))
(.f64 (.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))) (/.f64 1 (+.f64 -1 (pow.f64 x 2))))
(+.f64 -1 (pow.f64 x 2))
(.f64 (.f64 (+.f64 -1 (pow.f64 x 2)) (/.f64 1 (+.f64 -1 (pow.f64 x 2)))) (+.f64 -1 (pow.f64 x 2)))
(+.f64 -1 (pow.f64 x 2))
(.f64 (/.f64 1 (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2)))) (.f64 (+.f64 -1 (pow.f64 x 2)) (*.f64 (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))) (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))))
(+.f64 -1 (pow.f64 x 2))
(.f64 (/.f64 (/.f64 1 (+.f64 -1 (pow.f64 x 2))) (.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2)))) (.f64 (+.f64 -1 (pow.f64 x 2)) (.f64 (+.f64 -1 (pow.f64 x 2)) (*.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))))
(+.f64 -1 (pow.f64 x 2))
(.f64 (/.f64 (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))) (+.f64 -1 (pow.f64 x 2))) (.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))
(+.f64 -1 (pow.f64 x 2))
(.f64 (/.f64 (.f64 (+.f64 -1 (pow.f64 x 2)) (/.f64 1 (+.f64 -1 (pow.f64 x 2)))) (+.f64 -1 (pow.f64 x 2))) (*.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))
(+.f64 -1 (pow.f64 x 2))
(.f64 (/.f64 (/.f64 1 (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2)))) (+.f64 -1 (pow.f64 x 2))) (.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))
(+.f64 -1 (pow.f64 x 2))
(/.f64 (+.f64 -1 (pow.f64 x 2)) 1)
(+.f64 -1 (pow.f64 x 2))
(/.f64 (+.f64 -1 (pow.f64 x 2)) (/.f64 (+.f64 -1 (pow.f64 x 2)) (+.f64 -1 (pow.f64 x 2))))
(+.f64 -1 (pow.f64 x 2))
(/.f64 (-.f64 (*.f64 2 (pow.f64 x 2)) 2) 2)
(-.f64 (/.f64 (*.f64 2 (pow.f64 x 2)) 2) 1)
(+.f64 -1 (/.f64 (*.f64 2 (pow.f64 x 2)) 2))
(pow.f64 (+.f64 -1 (pow.f64 x 2)) 1)
(+.f64 -1 (pow.f64 x 2))
(neg.f64 (-.f64 1 (pow.f64 x 2)))
(+.f64 -1 (pow.f64 x 2))

eval71.0ms (1%)

Compiler: Compiled 4579 to 3397 computations (25.8% saved)

prune20.0ms (0.3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	143	1	144
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	143	5	148

Error

Counts

148 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(log.f64 (-.f64 (.f64 x 2) (.f64 1/2 (/.f64 1 x))))
✓	33.0b	(log.f64 (+.f64 x (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (-.f64 (pow.f64 x 2) 1))))
▶	45.4b	(log.f64 (+.f64 x (.f64 (.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))) (-.f64 (pow.f64 x 2) 1))))
✓	33.0b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
✓	0.8b	(log.f64 (+.f64 x x))

Compiler

Compiled 118 to 85 computations (28% saved)

localize119.0ms (1.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))
	30.7b	(sqrt.f64 (+.f64 (*.f64 x x) -1))
✓	30.9b	(.f64 (.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))) (-.f64 (pow.f64 x 2) 1))
✓	46.1b	(.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))))

Compiler

Compiled 404 to 271 computations (32.9% saved)

series2.0ms (0%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
0.0ms	x	@	0	(.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))))
0.0ms	x	@	-inf	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))
0.0ms	x	@	inf	(.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))
0.0ms	x	@	inf	(.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))))
0.0ms	x	@	-inf	(.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))))

rewrite64.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

1316×	`rational_best-simplify-47`
1196×	`rational_best-5`
1194×	`rational_best-4`
1194×	`rational_best-2`
1194×	`rational_best-3`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	463
1	165	115
2	546	115
3	2352	115

Stop Event

1×	node limit

Counts

3 → 29

Calls

Call 1

Inputs

(*.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))

(*.f64 (*.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))) (*.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))) (-.f64 (pow.f64 x 2) 1))

(*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 2) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) (/.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (-.f64 (*.f64 2 (pow.f64 x 2)) 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 1)))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 2)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 0 (neg.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))))) (#(struct:change #<rule egg-rr> (2) ((x fabs.f64 (-.f64 0 (/.f64 (*.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))))))))

simplify203.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

1190×	`rational_best-simplify-2`
1146×	`rational_best-simplify-132`
1126×	`rational_best-simplify-82`
1016×	`rational_best-simplify-83`
616×	`rational_best-simplify-80`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	156	2819
1	300	2791
2	507	2783
3	1107	2775
4	2839	2775
5	6234	2775

Stop Event

1×	node limit

Counts

65 → 120

Calls

Call 1

Inputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 4)) (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (*.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) (pow.f64 (sqrt.f64 -1) 2))) 1) (pow.f64 x 6)) (sqrt.f64 -1))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 4)) (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))))
(/.f64 1 x)
(+.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x))
(+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (.f64 3/8 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (.f64 5/16 (/.f64 1 (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (*.f64 3/8 (/.f64 1 (pow.f64 x 5))))))
(/.f64 -1 x)
(neg.f64 (+.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)))
(neg.f64 (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (.f64 3/8 (/.f64 1 (pow.f64 x 5))))))
(neg.f64 (+.f64 (.f64 5/16 (/.f64 1 (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (*.f64 3/8 (/.f64 1 (pow.f64 x 5)))))))
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(*.f64 -1 x)
(+.f64 (.f64 -1 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 -1 x))))
-1
(-.f64 (*.f64 -1 (pow.f64 x 2)) 1)
(-.f64 (+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 4))) 1)
(-.f64 (+.f64 (.f64 -1 (pow.f64 x 6)) (+.f64 (.f64 -1 (pow.f64 x 2)) (*.f64 -1 (pow.f64 x 4)))) 1)
(/.f64 1 (pow.f64 x 2))
(+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2)))
(+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 6))))
(+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 1 (pow.f64 x 8)) (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 6)))))
(/.f64 1 (pow.f64 x 2))
(+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2)))
(+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 6))))
(+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 1 (pow.f64 x 8)) (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 6)))))
(+.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 0)
(+.f64 0 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))
(-.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 0)
(/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))
(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 1)
(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) 2) 2)
(pow.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 1)
(+.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 0)
(+.f64 0 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 0)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 1)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) (/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2)))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (-.f64 (*.f64 2 (pow.f64 x 2)) 2)) 2)
(pow.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 1)
(+.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) 0)
(+.f64 0 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) 0)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) 1)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) 2)) 2)
(pow.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) 1)
(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(fabs.f64 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))
(fabs.f64 (/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))
(fabs.f64 (/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))
(fabs.f64 (-.f64 0 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))
(fabs.f64 (-.f64 0 (/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))))

Outputs
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 4)) (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (*.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (+.f64 (sqrt.f64 -1) (.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (.f64 -1/2 (/.f64 (*.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 4)) (sqrt.f64 -1))))
(+.f64 (sqrt.f64 -1) (.f64 -1/2 (+.f64 (/.f64 (.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 4)) (sqrt.f64 -1)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (.f64 -1/2 (+.f64 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) (/.f64 (.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 4)) (sqrt.f64 -1)))))
(+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 (.f64 1/2 (/.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) (pow.f64 (sqrt.f64 -1) 2))) 1) (pow.f64 x 6)) (sqrt.f64 -1))) (+.f64 (.f64 -1/2 (/.f64 (.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 4)) (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))))
(+.f64 (+.f64 (+.f64 (sqrt.f64 -1) (.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (.f64 -1/2 (/.f64 (.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 4)) (sqrt.f64 -1)))) (.f64 -1/2 (/.f64 (.f64 (+.f64 1 (.f64 1/2 (/.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) 1))) (pow.f64 x 6)) (sqrt.f64 -1))))
(+.f64 (+.f64 (sqrt.f64 -1) (.f64 -1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))) (.f64 -1/2 (+.f64 (/.f64 (.f64 (+.f64 1 (.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) 1/2)) (pow.f64 x 6)) (sqrt.f64 -1)) (/.f64 (*.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 4)) (sqrt.f64 -1)))))
(+.f64 (+.f64 (sqrt.f64 -1) (.f64 -1/2 (+.f64 (/.f64 (.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 4)) (sqrt.f64 -1)) (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))) (.f64 -1/2 (/.f64 (.f64 (+.f64 1 (*.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) 1/2)) (pow.f64 x 6)) (sqrt.f64 -1))))
(+.f64 (sqrt.f64 -1) (.f64 -1/2 (+.f64 (+.f64 (/.f64 (.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 4)) (sqrt.f64 -1)) (/.f64 (.f64 (+.f64 1 (.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) 1/2)) (pow.f64 x 6)) (sqrt.f64 -1))) (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (.f64 -1/2 (+.f64 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) (+.f64 (/.f64 (.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) (pow.f64 x 4)) (sqrt.f64 -1)) (/.f64 (.f64 (+.f64 1 (.f64 (+.f64 1 (pow.f64 (/.f64 -1/2 (sqrt.f64 -1)) 2)) 1/2)) (pow.f64 x 6)) (sqrt.f64 -1))))))
(/.f64 1 x)
(+.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x))
(+.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 1 (pow.f64 x 3))))
(+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (.f64 3/8 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (/.f64 1 x) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (.f64 3/8 (/.f64 1 (pow.f64 x 5)))))
(+.f64 (.f64 5/16 (/.f64 1 (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (*.f64 3/8 (/.f64 1 (pow.f64 x 5))))))
(+.f64 (+.f64 (/.f64 1 x) (.f64 3/8 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (*.f64 5/16 (/.f64 1 (pow.f64 x 7)))))
(+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (+.f64 (/.f64 1 x) (.f64 3/8 (/.f64 1 (pow.f64 x 5)))) (*.f64 5/16 (/.f64 1 (pow.f64 x 7)))))
(+.f64 (/.f64 1 x) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 3/8 (/.f64 1 (pow.f64 x 5))) (*.f64 5/16 (/.f64 1 (pow.f64 x 7))))))
(+.f64 (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (.f64 3/8 (/.f64 1 (pow.f64 x 5)))) (+.f64 (/.f64 1 x) (*.f64 5/16 (/.f64 1 (pow.f64 x 7)))))
(/.f64 -1 x)
(neg.f64 (+.f64 (*.f64 1/2 (/.f64 1 (pow.f64 x 3))) (/.f64 1 x)))
(neg.f64 (+.f64 (/.f64 1 x) (*.f64 1/2 (/.f64 1 (pow.f64 x 3)))))
(neg.f64 (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (.f64 3/8 (/.f64 1 (pow.f64 x 5))))))
(neg.f64 (+.f64 (/.f64 1 x) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (.f64 3/8 (/.f64 1 (pow.f64 x 5))))))
(neg.f64 (+.f64 (.f64 5/16 (/.f64 1 (pow.f64 x 7))) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 x) (*.f64 3/8 (/.f64 1 (pow.f64 x 5)))))))
(neg.f64 (+.f64 (+.f64 (/.f64 1 x) (.f64 3/8 (/.f64 1 (pow.f64 x 5)))) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (*.f64 5/16 (/.f64 1 (pow.f64 x 7))))))
(neg.f64 (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (+.f64 (/.f64 1 x) (.f64 3/8 (/.f64 1 (pow.f64 x 5)))) (*.f64 5/16 (/.f64 1 (pow.f64 x 7))))))
(neg.f64 (+.f64 (/.f64 1 x) (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (+.f64 (.f64 3/8 (/.f64 1 (pow.f64 x 5))) (*.f64 5/16 (/.f64 1 (pow.f64 x 7)))))))
(neg.f64 (+.f64 (+.f64 (.f64 1/2 (/.f64 1 (pow.f64 x 3))) (.f64 3/8 (/.f64 1 (pow.f64 x 5)))) (+.f64 (/.f64 1 x) (*.f64 5/16 (/.f64 1 (pow.f64 x 7))))))
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (*.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))))
(+.f64 (sqrt.f64 -1) (*.f64 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) 1/2))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)))))
(+.f64 (.f64 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) 1/2) (+.f64 (sqrt.f64 -1) (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) 1/2) (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
(+.f64 (+.f64 (sqrt.f64 -1) (.f64 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) 1/2)) (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 (pow.f64 x 2) (sqrt.f64 -1))) (*.f64 1/16 (/.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))))))
(+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (sqrt.f64 -1))) (+.f64 (sqrt.f64 -1) (*.f64 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) 1/2))))
(+.f64 (+.f64 (sqrt.f64 -1) (.f64 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) 1/2)) (+.f64 (.f64 1/16 (/.f64 (pow.f64 x 6) (sqrt.f64 -1))) (*.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (+.f64 (.f64 -1/8 (/.f64 (pow.f64 x 4) (sqrt.f64 -1))) (+.f64 (.f64 (/.f64 (pow.f64 x 2) (sqrt.f64 -1)) 1/2) (*.f64 1/16 (/.f64 (pow.f64 x 6) (sqrt.f64 -1))))))
x
(-.f64 x (*.f64 1/2 (/.f64 1 x)))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 1/8 (/.f64 1 (pow.f64 x 3)))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 (/.f64 1 (pow.f64 x 3)) 1/8)))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (*.f64 1/8 (/.f64 1 (pow.f64 x 3))))))
(-.f64 x (+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 (/.f64 1 (pow.f64 x 3)) 1/8) (*.f64 (/.f64 1 (pow.f64 x 5)) 1/16))))
(*.f64 -1 x)
(neg.f64 x)
(+.f64 (.f64 -1 x) (.f64 1/2 (/.f64 1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (.f64 -1 x))
(+.f64 (*.f64 1/2 (/.f64 1 x)) (neg.f64 x))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (*.f64 -1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 (/.f64 1 (pow.f64 x 3)) 1/8) (*.f64 -1 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 (/.f64 1 (pow.f64 x 3)) 1/8) (neg.f64 x)))
(+.f64 (.f64 (/.f64 1 (pow.f64 x 3)) 1/8) (+.f64 (.f64 1/2 (/.f64 1 x)) (neg.f64 x)))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 1/16 (/.f64 1 (pow.f64 x 5))) (+.f64 (.f64 1/8 (/.f64 1 (pow.f64 x 3))) (.f64 -1 x))))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 (/.f64 1 (pow.f64 x 5)) 1/16) (+.f64 (.f64 (/.f64 1 (pow.f64 x 3)) 1/8) (.f64 -1 x))))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 (/.f64 1 (pow.f64 x 3)) 1/8) (+.f64 (neg.f64 x) (*.f64 (/.f64 1 (pow.f64 x 5)) 1/16))))
(+.f64 (.f64 1/2 (/.f64 1 x)) (+.f64 (.f64 (/.f64 1 (pow.f64 x 3)) 1/8) (+.f64 (*.f64 (/.f64 1 (pow.f64 x 5)) 1/16) (neg.f64 x))))
-1
(-.f64 (*.f64 -1 (pow.f64 x 2)) 1)
(+.f64 (*.f64 -1 (pow.f64 x 2)) -1)
(+.f64 -1 (neg.f64 (pow.f64 x 2)))
(-.f64 (+.f64 (.f64 -1 (pow.f64 x 2)) (.f64 -1 (pow.f64 x 4))) 1)
(+.f64 (*.f64 -1 (+.f64 (pow.f64 x 4) (pow.f64 x 2))) -1)
(+.f64 -1 (*.f64 -1 (+.f64 (pow.f64 x 2) (pow.f64 x 4))))
(+.f64 -1 (neg.f64 (+.f64 (pow.f64 x 2) (pow.f64 x 4))))
(-.f64 (+.f64 (.f64 -1 (pow.f64 x 6)) (+.f64 (.f64 -1 (pow.f64 x 2)) (*.f64 -1 (pow.f64 x 4)))) 1)
(+.f64 (+.f64 (.f64 -1 (+.f64 (pow.f64 x 4) (pow.f64 x 2))) (.f64 -1 (pow.f64 x 6))) -1)
(+.f64 -1 (*.f64 -1 (+.f64 (pow.f64 x 6) (+.f64 (pow.f64 x 2) (pow.f64 x 4)))))
(+.f64 -1 (*.f64 -1 (+.f64 (pow.f64 x 2) (+.f64 (pow.f64 x 4) (pow.f64 x 6)))))
(+.f64 -1 (neg.f64 (+.f64 (pow.f64 x 2) (+.f64 (pow.f64 x 4) (pow.f64 x 6)))))
(/.f64 1 (pow.f64 x 2))
(+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2)))
(+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 4)))
(+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 6))))
(+.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (/.f64 1 (pow.f64 x 6)) (/.f64 1 (pow.f64 x 4))))
(+.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 6))))
(+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 1 (pow.f64 x 8)) (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 6)))))
(+.f64 (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 6))) (+.f64 (/.f64 1 (pow.f64 x 8)) (/.f64 1 (pow.f64 x 4))))
(+.f64 (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 6))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 8))))
(+.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (/.f64 1 (pow.f64 x 6)) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 8)))))
(+.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 1 (pow.f64 x 6)) (/.f64 1 (pow.f64 x 8)))))
(+.f64 (/.f64 1 (pow.f64 x 6)) (+.f64 (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 4))) (/.f64 1 (pow.f64 x 8))))
(/.f64 1 (pow.f64 x 2))
(+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 2)))
(+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 4)))
(+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 6))))
(+.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (/.f64 1 (pow.f64 x 6)) (/.f64 1 (pow.f64 x 4))))
(+.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 6))))
(+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 1 (pow.f64 x 8)) (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 6)))))
(+.f64 (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 6))) (+.f64 (/.f64 1 (pow.f64 x 8)) (/.f64 1 (pow.f64 x 4))))
(+.f64 (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 6))) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 8))))
(+.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (/.f64 1 (pow.f64 x 6)) (+.f64 (/.f64 1 (pow.f64 x 4)) (/.f64 1 (pow.f64 x 8)))))
(+.f64 (/.f64 1 (pow.f64 x 2)) (+.f64 (/.f64 1 (pow.f64 x 4)) (+.f64 (/.f64 1 (pow.f64 x 6)) (/.f64 1 (pow.f64 x 8)))))
(+.f64 (/.f64 1 (pow.f64 x 6)) (+.f64 (+.f64 (/.f64 1 (pow.f64 x 2)) (/.f64 1 (pow.f64 x 4))) (/.f64 1 (pow.f64 x 8))))
(+.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 0)
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(+.f64 0 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(-.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 0)
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 1)
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))
(/.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (/.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x))))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x)))))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) 2) 2)
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(pow.f64 (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))) 1)
(/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x))))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 0)
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (+.f64 -1 (pow.f64 x 2)))
(+.f64 0 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (+.f64 -1 (pow.f64 x 2)))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 0)
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (+.f64 -1 (pow.f64 x 2)))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 1)
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (+.f64 -1 (pow.f64 x 2)))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) (/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2)))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (+.f64 -1 (pow.f64 x 2)))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (-.f64 (*.f64 2 (pow.f64 x 2)) 2)) 2)
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (-.f64 (*.f64 2 (pow.f64 x 2)) 2)) 2)
(pow.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (+.f64 -1 (pow.f64 x 2))) 1)
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (+.f64 -1 (pow.f64 x 2)))
(+.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) 0)
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(+.f64 0 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(-.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) 0)
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) 1)
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) 2)) 2)
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(pow.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))) 1)
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(fabs.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(fabs.f64 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(fabs.f64 (/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(fabs.f64 (/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (neg.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(fabs.f64 (-.f64 0 (neg.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
(fabs.f64 (-.f64 0 (/.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (fabs.f64 (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1))))))))
(.f64 (/.f64 1 (sqrt.f64 (+.f64 -1 (.f64 x x)))) (/.f64 1 (sqrt.f64 (+.f64 -1 (*.f64 x x)))))

eval420.0ms (5.7%)

Compiler: Compiled 31500 to 21533 computations (31.6% saved)

prune167.0ms (2.3%)

Pruning

5 alts after pruning (0 fresh and 5 done)

	Pruned	Kept	Total
New	401	0	401
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	401	5	406

Error

Counts

406 → 5

Alt Table

Click to see full alt table

Status	Error	Program
✓	0.5b	(log.f64 (-.f64 (.f64 x 2) (.f64 1/2 (/.f64 1 x))))
✓	33.0b	(log.f64 (+.f64 x (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (-.f64 (pow.f64 x 2) 1))))
✓	45.4b	(log.f64 (+.f64 x (.f64 (.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))) (-.f64 (pow.f64 x 2) 1))))
✓	33.0b	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
✓	0.8b	(log.f64 (+.f64 x x))

Compiler

Compiled 118 to 85 computations (28% saved)

regimes76.0ms (1%)

Accuracy

Total -47.5b remaining (-9457.5%)

Threshold costs -47.5b (-9457.5%)

Counts

6 → 1

Calls

Call 1

Inputs
(log.f64 (+.f64 x x))
(log.f64 (-.f64 (.f64 x 2) (.f64 1/2 (/.f64 1 x))))
(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
(log.f64 (+.f64 x (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (-.f64 (pow.f64 x 2) 1))))
(log.f64 (+.f64 x (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (sqrt.f64 (.f64 (+.f64 (.f64 x x) -1) (+.f64 (*.f64 x x) -1))))))
(log.f64 (+.f64 x (.f64 (.f64 (/.f64 (/.f64 1 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))))) (.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1)))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 (.f64 x x) -1))) (/.f64 1 (sqrt.f64 (+.f64 (*.f64 x x) -1)))))) (-.f64 (pow.f64 x 2) 1))))

Outputs
(log.f64 (-.f64 (.f64 x 2) (.f64 1/2 (/.f64 1 x))))

Calls

3 calls:

65.0ms	x
4.0ms	(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))
4.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))

Results

Error	Segments	Branch
0.5b	1	`x`
0.5b	1	`(log.f64 (+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1))))`
0.5b	1	`(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))`

Compiler

Compiled 159 to 107 computations (32.7% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	40

Stop Event

1×	done
1×	saturated

Calls

Call 1

Inputs
(log.f64 (-.f64 (.f64 x 2) (.f64 1/2 (/.f64 1 x))))
(log.f64 (+.f64 x x))

Outputs
(log.f64 (-.f64 (.f64 x 2) (.f64 1/2 (/.f64 1 x))))
(log.f64 (+.f64 x x))

Compiler

Compiled 16 to 12 computations (25% saved)

soundness368.0ms (5%)

Algorithm

1×	egg-herbie

Rules

1814×	`rational_best-simplify-54`
1374×	`rational_best-simplify-2`
980×	`rational_best-simplify-78`
970×	`rational_best-simplify-80`
896×	`rational_best-simplify-94`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	219	2532
1	427	2524
2	1634	2524
3	5238	2524

Stop Event

1×	node limit

Compiler

Compiled 21 to 17 computations (19% saved)

end17.0ms (0.2%)

Compiler: Compiled 15 to 11 computations (26.7% saved)

Details

analyze301.0ms (4.1%)

sample4.0s (54.3%)

preprocess16.0ms (0.2%)

simplify13.0ms (0.2%)

eval1.0ms (0%)

prune1.0ms (0%)

localize14.0ms (0.2%)

series2.0ms (0%)

rewrite107.0ms (1.5%)

simplify321.0ms (4.4%)

eval54.0ms (0.7%)

prune20.0ms (0.3%)

localize4.0ms (0.1%)

localize35.0ms (0.5%)

series1.0ms (0%)

rewrite141.0ms (1.9%)

simplify303.0ms (4.1%)

localize15.0ms (0.2%)

eval108.0ms (1.5%)

prune30.0ms (0.4%)

localize30.0ms (0.4%)

series2.0ms (0%)

rewrite117.0ms (1.6%)

simplify191.0ms (2.6%)

eval71.0ms (1%)

prune20.0ms (0.3%)

localize119.0ms (1.6%)

series2.0ms (0%)

rewrite64.0ms (0.9%)

simplify203.0ms (2.8%)

eval420.0ms (5.7%)

prune167.0ms (2.3%)

regimes76.0ms (1%)

simplify2.0ms (0%)

soundness368.0ms (5%)

end17.0ms (0.2%)

Profiling