Details

analyze5.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 15 to 11 computations (26.7% saved)

sample996.0ms (51.4%)

Results

982.0ms	8256×	body	128	valid
1.0ms	6×	body	128	invalid

preprocess40.0ms (2.1%)

Algorithm

2×	egg-herbie

Rules

492×	`fma-neg_binary64`
454×	`unsub-neg_binary64`
411×	`distribute-rgt-in_binary64`
374×	`fma-def_binary64`
353×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	25	20
3	36	20
4	53	20
5	81	20
6	128	20
7	323	20
8	664	20
9	1447	20
10	2776	20
11	4161	20
0	1	1

Stop Event

1×	saturated
1×	node limit

Calls

Call 1

Inputs
0

Outputs
0

Call 2

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

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

Compiler

Compiled 14 to 10 computations (28.6% saved)

simplify32.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

492×	`fma-neg_binary64`
454×	`unsub-neg_binary64`
411×	`distribute-rgt-in_binary64`
374×	`fma-def_binary64`
353×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	20
1	18	20
2	25	20
3	36	20
4	53	20
5	81	20
6	128	20
7	323	20
8	664	20
9	1447	20
10	2776	20
11	4161	20

Stop Event

1×	node limit

Counts

1 → 1

Calls

Call 1

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

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

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 42 to 30 computations (28.6% saved)

localize9.0ms (0.5%)

Local error

Found 3 expressions with local error:

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

series8.0ms (0.4%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
2.0ms	x	@	-inf	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
1.0ms	x	@	inf	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
1.0ms	x	@	inf	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
1.0ms	x	@	0	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
1.0ms	x	@	0	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))

rewrite68.0ms (3.5%)

Algorithm

1×	batch-egg-rewrite

Rules

399×	`fma-def_binary64`
203×	`fma-neg_binary64`
189×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`
182×	`log-div_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	50
1	225	50
2	3285	50

Stop Event

1×	node limit

Counts

3 → 167

Calls

Call 1

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

Outputs
((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x)))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x -2) (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) x)) (/.f64 (.f64 (-.f64 1 (.f64 x x)) (pow.f64 x -2)) (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x))) (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x))) 2) (cbrt.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x)) x) (/.f64 (sqrt.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (pow.f64 (-.f64 1 (.f64 x x)) 3/2) (pow.f64 x -3) (pow.f64 x -3)) (/.f64 1 (-.f64 (+.f64 (pow.f64 x -2) (.f64 (-.f64 1 (.f64 x x)) (pow.f64 x -2))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (-.f64 (pow.f64 x -2) (.f64 (-.f64 1 (.f64 x x)) (pow.f64 x -2))) (/.f64 1 (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (.f64 x x) (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (-.f64 (+.f64 (pow.f64 x -2) (.f64 (-.f64 1 (.f64 x x)) (pow.f64 x -2))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (.f64 x x))) (fma.f64 (pow.f64 (-.f64 1 (.f64 x x)) 3/2) (pow.f64 x -3) (pow.f64 x -3))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 1 (/.f64 (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) x) (-.f64 (pow.f64 x -2) (.f64 (-.f64 1 (.f64 x x)) (pow.f64 x -2)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (.f64 x x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 (-.f64 1 (.f64 x x)) 3/2) (pow.f64 x -3) (pow.f64 x -3)) (-.f64 (+.f64 (pow.f64 x -2) (.f64 (-.f64 1 (.f64 x x)) (pow.f64 x -2))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (pow.f64 (-.f64 1 (.f64 x x)) 3/2) (pow.f64 x -3) (pow.f64 x -3)) (fma.f64 (-.f64 1 (.f64 x x)) (pow.f64 x -2) (-.f64 (pow.f64 x -2) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (-.f64 (pow.f64 x -2) (.f64 (-.f64 1 (.f64 x x)) (pow.f64 x -2))) (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x)) (.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (fma.f64 (pow.f64 (-.f64 1 (.f64 x x)) 3/2) (pow.f64 x -3) (pow.f64 x -3))) (neg.f64 (-.f64 (+.f64 (pow.f64 x -2) (.f64 (-.f64 1 (.f64 x x)) (pow.f64 x -2))) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (neg.f64 (-.f64 (pow.f64 x -2) (.f64 (-.f64 1 (.f64 x x)) (pow.f64 x -2)))) (neg.f64 (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 (/.f64 x (sqrt.f64 (-.f64 1 (.f64 x x)))) x) (.f64 x (/.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 -1 (/.f64 x (sqrt.f64 (-.f64 1 (.f64 x x)))) (.f64 (neg.f64 x) 1)) (.f64 (neg.f64 x) (/.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))))))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 -1 x (.f64 (neg.f64 x) (sqrt.f64 (-.f64 1 (.f64 x x))))) (.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 -1 x (.f64 x (neg.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))) (.f64 x (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 -1 (neg.f64 x) (.f64 (neg.f64 x) (neg.f64 (sqrt.f64 (-.f64 1 (.f64 x x)))))) (.f64 (neg.f64 x) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (+.f64 x (.f64 (/.f64 x (sqrt.f64 (-.f64 1 (.f64 x x)))) 1)) (.f64 (/.f64 x (sqrt.f64 (-.f64 1 (.f64 x x)))) x))))) (#(struct:change #<rule egg-rr> (2) ((x /.f64 (fma.f64 (neg.f64 (sqrt.f64 (-.f64 1 (.f64 x 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pow.f64 (exp.f64 (cbrt.f64 (pow.f64 (log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x))) 2))) (cbrt.f64 (log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x)) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (/.f64 1 x))) (exp.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (exp.f64 (/.f64 1 x)) (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x)))))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (.f64 (+.f64 1 (expm1.f64 (/.f64 1 x))) (+.f64 1 (expm1.f64 (/.f64 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(#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 1 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) 1 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 1 x) (sqrt.f64 (-.f64 1 (.f64 x x))) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) (/.f64 1 x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x) 1 (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x)) (cbrt.f64 (.f64 (-.f64 1 (.f64 x x)) (pow.f64 x -2))) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x fma.f64 (cbrt.f64 (.f64 (-.f64 1 (.f64 x x)) (pow.f64 x -2))) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x)) (/.f64 1 x))))) 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Outputs

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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 x) (sqrt.f64 (-.f64 1 (*.f64 x x))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) (cbrt.f64 (*.f64 (-.f64 1 (*.f64 x x)) (pow.f64 x -2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (*.f64 (-.f64 1 (*.f64 x x)) (pow.f64 x -2))) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (*.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (*.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (/.f64 1 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (pow.f64 x -1/2) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (neg.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (/.f64 1 (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) 1) (/.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) 1) (/.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) x))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 1 (pow.f64 (cbrt.f64 x) 2)) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (pow.f64 (cbrt.f64 x) 2)) (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (pow.f64 (cbrt.f64 x) 2)) (/.f64 (pow.f64 (-.f64 1 (*.f64 x x)) 1/4) (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (/.f64 (cbrt.f64 (-.f64 1 (*.f64 x x))) (sqrt.f64 x)) (/.f64 (cbrt.f64 (sqrt.f64 (-.f64 1 (*.f64 x x)))) (sqrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (cbrt.f64 (pow.f64 x -2))) (/.f64 1 (cbrt.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (pow.f64 x -1/2)) (pow.f64 x -1/2))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) 2)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (/.f64 x (sqrt.f64 (-.f64 1 (*.f64 x x)))) -1)))) (#(struct:change #<rule egg-rr> (2) ((x neg.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) (neg.f64 x)))))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (*.f64 (-.f64 1 (*.f64 x x)) (pow.f64 x -2)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (exp.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (+.f64 1 (expm1.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x) 3))))) (#(struct:change #<rule egg-rr> (2) ((x log1p.f64 (expm1.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)) 1))))))

simplify40.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

535×	`times-frac_binary64`
354×	`fma-neg_binary64`
323×	`fma-def_binary64`
300×	`unswap-sqr_binary64`
275×	`associate-/r*_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	104	773
1	299	746
2	896	726
3	3285	719

Stop Event

1×	node limit

Counts

203 → 231

Calls

Call 1

Inputs
(/.f64 2 x)
(+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x)))
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (.f64 -1/2 x) (*.f64 2 (/.f64 1 x))))
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (.f64 -1/2 x) (+.f64 (.f64 2 (/.f64 1 x)) (.f64 -1/16 (pow.f64 x 5)))))
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (/.f64 1 x))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 x) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 2))))))
(-.f64 (+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 x) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 2)))))) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))
(*.f64 -1 (sqrt.f64 -1))
(+.f64 (/.f64 1 x) (*.f64 -1 (sqrt.f64 -1)))
(-.f64 (+.f64 (/.f64 1 x) (.f64 -1 (sqrt.f64 -1))) (.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 1 x) (+.f64 (.f64 -1 (sqrt.f64 -1)) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))) (.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 -1 (log.f64 x))))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -3/32 (pow.f64 x 4)) (*.f64 -1 (log.f64 x)))))
(+.f64 (.f64 -5/96 (pow.f64 x 6)) (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -3/32 (pow.f64 x 4)) (.f64 -1 (log.f64 x))))))
(log.f64 (sqrt.f64 -1))
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (log.f64 (sqrt.f64 -1)))
(-.f64 (+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (log.f64 (sqrt.f64 -1))) (.f64 1/6 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(-.f64 (+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (+.f64 (.f64 3/40 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (log.f64 (sqrt.f64 -1)))) (.f64 1/6 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(log.f64 (*.f64 -1 (sqrt.f64 -1)))
(-.f64 (log.f64 (.f64 -1 (sqrt.f64 -1))) (/.f64 1 (.f64 (sqrt.f64 -1) x)))
(-.f64 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 -1))) (.f64 1/6 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) (/.f64 1 (.f64 (sqrt.f64 -1) x)))
(-.f64 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 -1))) (.f64 1/6 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (.f64 3/40 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))))
(/.f64 1 x)
(+.f64 (*.f64 -1/2 x) (/.f64 1 x))
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (.f64 -1/2 x) (/.f64 1 x)))
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (.f64 -1/2 x) (+.f64 (/.f64 1 x) (*.f64 -1/16 (pow.f64 x 5)))))
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
(-.f64 (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 2))))) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))
(-.f64 (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 6)))))) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))
(*.f64 -1 (sqrt.f64 -1))
(-.f64 (.f64 -1 (sqrt.f64 -1)) (.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 -1 (sqrt.f64 -1)) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4))))) (.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
(-.f64 (+.f64 (.f64 -1 (sqrt.f64 -1)) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4))))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 6))))))

Outputs
(/.f64 2 x)
(+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x)))
(fma.f64 -1/2 x (/.f64 2 x))
(fma.f64 x -1/2 (/.f64 2 x))
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (.f64 -1/2 x) (*.f64 2 (/.f64 1 x))))
(fma.f64 -1/8 (pow.f64 x 3) (fma.f64 -1/2 x (/.f64 2 x)))
(fma.f64 -1/8 (pow.f64 x 3) (fma.f64 x -1/2 (/.f64 2 x)))
(fma.f64 x -1/2 (fma.f64 -1/8 (pow.f64 x 3) (/.f64 2 x)))
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (.f64 -1/2 x) (+.f64 (.f64 2 (/.f64 1 x)) (.f64 -1/16 (pow.f64 x 5)))))
(fma.f64 -1/8 (pow.f64 x 3) (+.f64 (fma.f64 -1/2 x (/.f64 2 x)) (*.f64 -1/16 (pow.f64 x 5))))
(fma.f64 -1/8 (pow.f64 x 3) (fma.f64 x -1/2 (fma.f64 -1/16 (pow.f64 x 5) (/.f64 2 x))))
(fma.f64 x -1/2 (fma.f64 -1/8 (pow.f64 x 3) (fma.f64 -1/16 (pow.f64 x 5) (/.f64 2 x))))
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (/.f64 1 x))
(+.f64 (/.f64 1 x) (sqrt.f64 -1))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 x) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 2))))))
(+.f64 (+.f64 (/.f64 1 x) (sqrt.f64 -1)) (/.f64 1/2 (.f64 (sqrt.f64 -1) (.f64 x x))))
(+.f64 (/.f64 1 x) (+.f64 (sqrt.f64 -1) (/.f64 1/2 (.f64 x (.f64 x (sqrt.f64 -1))))))
(+.f64 (/.f64 1 x) (+.f64 (sqrt.f64 -1) (/.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) x)))
(-.f64 (+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 x) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 2)))))) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))
(+.f64 (sqrt.f64 -1) (-.f64 (+.f64 (/.f64 1 x) (/.f64 1/2 (.f64 (sqrt.f64 -1) (.f64 x x)))) (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 x) (-.f64 (/.f64 1/2 (.f64 x (.f64 x (sqrt.f64 -1)))) (/.f64 (/.f64 1/8 (pow.f64 x 4)) (neg.f64 (sqrt.f64 -1))))))
(+.f64 (/.f64 1 x) (+.f64 (sqrt.f64 -1) (+.f64 (/.f64 (/.f64 1/2 (.f64 x (sqrt.f64 -1))) x) (/.f64 1/8 (.f64 (sqrt.f64 -1) (pow.f64 x 4))))))
(+.f64 (sqrt.f64 -1) (+.f64 (+.f64 (/.f64 1 x) (/.f64 (/.f64 1/2 (.f64 x (sqrt.f64 -1))) x)) (/.f64 1/8 (.f64 (sqrt.f64 -1) (pow.f64 x 4)))))
(*.f64 -1 (sqrt.f64 -1))
(neg.f64 (sqrt.f64 -1))
(+.f64 (/.f64 1 x) (*.f64 -1 (sqrt.f64 -1)))
(+.f64 (/.f64 1 x) (neg.f64 (sqrt.f64 -1)))
(-.f64 (/.f64 1 x) (sqrt.f64 -1))
(-.f64 (+.f64 (/.f64 1 x) (.f64 -1 (sqrt.f64 -1))) (.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
(+.f64 (/.f64 1 x) (-.f64 (neg.f64 (sqrt.f64 -1)) (/.f64 1/2 (.f64 (sqrt.f64 -1) (.f64 x x)))))
(+.f64 (-.f64 (/.f64 1 x) (sqrt.f64 -1)) (/.f64 -1/2 (.f64 x (.f64 x (sqrt.f64 -1)))))
(+.f64 (/.f64 1 x) (-.f64 (/.f64 (/.f64 -1/2 (sqrt.f64 -1)) (*.f64 x x)) (sqrt.f64 -1)))
(-.f64 (/.f64 1 x) (+.f64 (sqrt.f64 -1) (/.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) x)))
(-.f64 (+.f64 (/.f64 1 x) (+.f64 (.f64 -1 (sqrt.f64 -1)) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))) (.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
(+.f64 (/.f64 1 x) (-.f64 (fma.f64 -1 (sqrt.f64 -1) (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))) (/.f64 1/2 (.f64 (sqrt.f64 -1) (*.f64 x x)))))
(+.f64 (-.f64 (/.f64 1 x) (sqrt.f64 -1)) (fma.f64 1/8 (/.f64 (/.f64 -1 (sqrt.f64 -1)) (pow.f64 x 4)) (/.f64 -1/2 (.f64 x (.f64 x (sqrt.f64 -1))))))
(+.f64 (/.f64 -1/8 (.f64 (sqrt.f64 -1) (pow.f64 x 4))) (+.f64 (/.f64 1 x) (-.f64 (/.f64 (/.f64 -1/2 (sqrt.f64 -1)) (.f64 x x)) (sqrt.f64 -1))))
(+.f64 (/.f64 -1/8 (.f64 (sqrt.f64 -1) (pow.f64 x 4))) (-.f64 (/.f64 1 x) (+.f64 (sqrt.f64 -1) (/.f64 (/.f64 1/2 (.f64 x (sqrt.f64 -1))) x))))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 2) (neg.f64 (log.f64 x)))
(-.f64 (log.f64 2) (log.f64 x))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 -1 (log.f64 x))))
(+.f64 (log.f64 2) (fma.f64 -1/4 (*.f64 x x) (neg.f64 (log.f64 x))))
(+.f64 (log.f64 2) (-.f64 (.f64 x (.f64 x -1/4)) (log.f64 x)))
(-.f64 (fma.f64 x (*.f64 x -1/4) (log.f64 2)) (log.f64 x))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -3/32 (pow.f64 x 4)) (*.f64 -1 (log.f64 x)))))
(+.f64 (log.f64 2) (fma.f64 -1/4 (*.f64 x x) (fma.f64 -3/32 (pow.f64 x 4) (neg.f64 (log.f64 x)))))
(+.f64 (log.f64 2) (fma.f64 (*.f64 x x) -1/4 (fma.f64 (pow.f64 x 4) -3/32 (neg.f64 (log.f64 x)))))
(+.f64 (log.f64 2) (-.f64 (fma.f64 x (.f64 x -1/4) (.f64 (pow.f64 x 4) -3/32)) (log.f64 x)))
(fma.f64 x (*.f64 x -1/4) (fma.f64 (pow.f64 x 4) -3/32 (-.f64 (log.f64 2) (log.f64 x))))
(+.f64 (.f64 -5/96 (pow.f64 x 6)) (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -3/32 (pow.f64 x 4)) (.f64 -1 (log.f64 x))))))
(fma.f64 -5/96 (pow.f64 x 6) (+.f64 (log.f64 2) (fma.f64 -1/4 (*.f64 x x) (fma.f64 -3/32 (pow.f64 x 4) (neg.f64 (log.f64 x))))))
(+.f64 (fma.f64 (*.f64 x x) -1/4 (fma.f64 (pow.f64 x 4) -3/32 (neg.f64 (log.f64 x)))) (fma.f64 -5/96 (pow.f64 x 6) (log.f64 2)))
(-.f64 (fma.f64 x (.f64 x -1/4) (.f64 (pow.f64 x 4) -3/32)) (-.f64 (log.f64 x) (fma.f64 -5/96 (pow.f64 x 6) (log.f64 2))))
(fma.f64 -5/96 (pow.f64 x 6) (fma.f64 x (*.f64 x -1/4) (fma.f64 (pow.f64 x 4) -3/32 (-.f64 (log.f64 2) (log.f64 x)))))
(log.f64 (sqrt.f64 -1))
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (log.f64 (sqrt.f64 -1)))
(+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 1 (*.f64 x (sqrt.f64 -1))))
(-.f64 (+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (log.f64 (sqrt.f64 -1))) (.f64 1/6 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (-.f64 (log.f64 (sqrt.f64 -1)) (/.f64 1/6 (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3)))))
(+.f64 (log.f64 (sqrt.f64 -1)) (-.f64 (/.f64 1 (*.f64 x (sqrt.f64 -1))) (/.f64 (/.f64 1/6 (neg.f64 (sqrt.f64 -1))) (pow.f64 x 3))))
(+.f64 (log.f64 (sqrt.f64 -1)) (+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (/.f64 1/6 (.f64 (pow.f64 x 3) (sqrt.f64 -1)))))
(-.f64 (+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (+.f64 (.f64 3/40 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (log.f64 (sqrt.f64 -1)))) (.f64 1/6 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (-.f64 (+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 3/40 (.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)))) (/.f64 1/6 (*.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3)))))
(+.f64 (+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 3/40 (.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)))) (-.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (/.f64 (/.f64 1/6 (neg.f64 (sqrt.f64 -1))) (pow.f64 x 3))))
(+.f64 (log.f64 (sqrt.f64 -1)) (+.f64 (/.f64 3/40 (.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5))) (+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (/.f64 1/6 (*.f64 (pow.f64 x 3) (sqrt.f64 -1))))))
(+.f64 (log.f64 (sqrt.f64 -1)) (+.f64 (/.f64 3/40 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))) (+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (/.f64 1/6 (*.f64 (pow.f64 x 3) (sqrt.f64 -1))))))
(log.f64 (*.f64 -1 (sqrt.f64 -1)))
(log.f64 (neg.f64 (sqrt.f64 -1)))
(-.f64 (log.f64 (.f64 -1 (sqrt.f64 -1))) (/.f64 1 (.f64 (sqrt.f64 -1) x)))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (/.f64 1 (*.f64 x (sqrt.f64 -1))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (/.f64 -1 (*.f64 x (sqrt.f64 -1))))
(fma.f64 3 (log.f64 (sqrt.f64 -1)) (/.f64 -1 (*.f64 x (sqrt.f64 -1))))
(-.f64 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 -1))) (.f64 1/6 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) (/.f64 1 (.f64 (sqrt.f64 -1) x)))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (-.f64 (/.f64 1/6 (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3))) (/.f64 1 (.f64 x (sqrt.f64 -1)))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (fma.f64 1/6 (/.f64 (/.f64 -1 (sqrt.f64 -1)) (pow.f64 x 3)) (/.f64 -1 (*.f64 x (sqrt.f64 -1)))))
(-.f64 (/.f64 -1/6 (.f64 (pow.f64 x 3) (sqrt.f64 -1))) (-.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (log.f64 (neg.f64 (sqrt.f64 -1)))))
(+.f64 (/.f64 -1/6 (.f64 (pow.f64 x 3) (sqrt.f64 -1))) (fma.f64 3 (log.f64 (sqrt.f64 -1)) (/.f64 -1 (.f64 x (sqrt.f64 -1)))))
(-.f64 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 -1))) (.f64 1/6 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (.f64 3/40 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (-.f64 (/.f64 1/6 (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (/.f64 3/40 (*.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5))))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (-.f64 (fma.f64 1/6 (/.f64 (/.f64 -1 (sqrt.f64 -1)) (pow.f64 x 3)) (/.f64 -1 (.f64 x (sqrt.f64 -1)))) (/.f64 3/40 (.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)))))
(-.f64 (-.f64 (/.f64 -1/6 (.f64 (pow.f64 x 3) (sqrt.f64 -1))) (-.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (log.f64 (neg.f64 (sqrt.f64 -1))))) (/.f64 3/40 (*.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5))))
(+.f64 (/.f64 -1/6 (.f64 (pow.f64 x 3) (sqrt.f64 -1))) (+.f64 (fma.f64 3 (log.f64 (sqrt.f64 -1)) (/.f64 -1 (.f64 x (sqrt.f64 -1)))) (/.f64 -3/40 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))))
(/.f64 1 x)
(+.f64 (*.f64 -1/2 x) (/.f64 1 x))
(fma.f64 -1/2 x (/.f64 1 x))
(fma.f64 x -1/2 (/.f64 1 x))
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (.f64 -1/2 x) (/.f64 1 x)))
(fma.f64 -1/8 (pow.f64 x 3) (fma.f64 -1/2 x (/.f64 1 x)))
(fma.f64 -1/8 (pow.f64 x 3) (fma.f64 x -1/2 (/.f64 1 x)))
(fma.f64 x -1/2 (fma.f64 -1/8 (pow.f64 x 3) (/.f64 1 x)))
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (.f64 -1/2 x) (+.f64 (/.f64 1 x) (*.f64 -1/16 (pow.f64 x 5)))))
(fma.f64 -1/8 (pow.f64 x 3) (+.f64 (fma.f64 -1/2 x (/.f64 1 x)) (*.f64 -1/16 (pow.f64 x 5))))
(fma.f64 -1/8 (pow.f64 x 3) (fma.f64 x -1/2 (fma.f64 -1/16 (pow.f64 x 5) (/.f64 1 x))))
(fma.f64 x -1/2 (fma.f64 -1/8 (pow.f64 x 3) (fma.f64 -1/16 (pow.f64 x 5) (/.f64 1 x))))
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
(+.f64 (sqrt.f64 -1) (/.f64 1/2 (.f64 (sqrt.f64 -1) (.f64 x x))))
(+.f64 (sqrt.f64 -1) (/.f64 1/2 (.f64 x (.f64 x (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (/.f64 (/.f64 1/2 (*.f64 x (sqrt.f64 -1))) x))
(-.f64 (+.f64 (sqrt.f64 -1) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 2))))) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))
(-.f64 (+.f64 (sqrt.f64 -1) (/.f64 1/2 (.f64 (sqrt.f64 -1) (.f64 x x)))) (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4))))
(+.f64 (sqrt.f64 -1) (-.f64 (/.f64 1/2 (.f64 x (.f64 x (sqrt.f64 -1)))) (/.f64 (/.f64 1/8 (pow.f64 x 4)) (neg.f64 (sqrt.f64 -1)))))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 (/.f64 1/2 (.f64 x (sqrt.f64 -1))) x) (/.f64 1/8 (.f64 (sqrt.f64 -1) (pow.f64 x 4)))))
(-.f64 (+.f64 (sqrt.f64 -1) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (.f64 1/16 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 6)))))) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))
(-.f64 (+.f64 (+.f64 (sqrt.f64 -1) (/.f64 1/2 (.f64 (sqrt.f64 -1) (.f64 x x)))) (/.f64 1/16 (.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)))) (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4))))
(+.f64 (+.f64 (sqrt.f64 -1) (/.f64 1/2 (.f64 x (.f64 x (sqrt.f64 -1))))) (-.f64 (/.f64 1/16 (*.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5))) (/.f64 (/.f64 1/8 (pow.f64 x 4)) (neg.f64 (sqrt.f64 -1)))))
(+.f64 (/.f64 (/.f64 1/2 (.f64 x (sqrt.f64 -1))) x) (-.f64 (+.f64 (sqrt.f64 -1) (/.f64 (/.f64 1/16 (pow.f64 x 6)) (pow.f64 (sqrt.f64 -1) 5))) (/.f64 -1/8 (.f64 (sqrt.f64 -1) (pow.f64 x 4)))))
(+.f64 (/.f64 (/.f64 1/2 (.f64 x (sqrt.f64 -1))) x) (+.f64 (+.f64 (sqrt.f64 -1) (/.f64 (/.f64 1/16 (pow.f64 x 6)) (pow.f64 (sqrt.f64 -1) 5))) (/.f64 1/8 (.f64 (sqrt.f64 -1) (pow.f64 x 4)))))
(*.f64 -1 (sqrt.f64 -1))
(neg.f64 (sqrt.f64 -1))
(-.f64 (.f64 -1 (sqrt.f64 -1)) (.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
(-.f64 (neg.f64 (sqrt.f64 -1)) (/.f64 1/2 (.f64 (sqrt.f64 -1) (.f64 x x))))
(fma.f64 -1 (sqrt.f64 -1) (/.f64 -1/2 (.f64 x (.f64 x (sqrt.f64 -1)))))
(-.f64 (/.f64 (/.f64 -1/2 (sqrt.f64 -1)) (*.f64 x x)) (sqrt.f64 -1))
(-.f64 (+.f64 (.f64 -1 (sqrt.f64 -1)) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4))))) (.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
(-.f64 (fma.f64 -1 (sqrt.f64 -1) (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))) (/.f64 1/2 (.f64 (sqrt.f64 -1) (*.f64 x x))))
(+.f64 (-.f64 (/.f64 (/.f64 1/8 (pow.f64 x 4)) (neg.f64 (sqrt.f64 -1))) (sqrt.f64 -1)) (/.f64 -1/2 (.f64 x (.f64 x (sqrt.f64 -1)))))
(+.f64 (/.f64 -1/8 (.f64 (sqrt.f64 -1) (pow.f64 x 4))) (-.f64 (/.f64 (/.f64 -1/2 (sqrt.f64 -1)) (.f64 x x)) (sqrt.f64 -1)))
(-.f64 (+.f64 (.f64 -1 (sqrt.f64 -1)) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4))))) (+.f64 (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 2)))) (.f64 1/16 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 6))))))
(-.f64 (fma.f64 -1 (sqrt.f64 -1) (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))) (+.f64 (/.f64 1/2 (.f64 (sqrt.f64 -1) (.f64 x x))) (/.f64 1/16 (.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)))))
(+.f64 (-.f64 (/.f64 (/.f64 1/8 (pow.f64 x 4)) (neg.f64 (sqrt.f64 -1))) (sqrt.f64 -1)) (-.f64 (/.f64 -1/2 (.f64 x (.f64 x (sqrt.f64 -1)))) (/.f64 1/16 (*.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)))))
(+.f64 (/.f64 -1/8 (.f64 (sqrt.f64 -1) (pow.f64 x 4))) (+.f64 (-.f64 (/.f64 (/.f64 -1/2 (sqrt.f64 -1)) (.f64 x x)) (sqrt.f64 -1)) (/.f64 -1/16 (*.f64 (pow.f64 x 6) (pow.f64 (sqrt.f64 -1) 5)))))

prune215.0ms (11.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	230	1	231
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	230	2	232

Error

Counts

232 → 2

Alt Table

Status	Error	Program
▶	0.0b	(log.f64 (expm1.f64 (log1p.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 4696 to 3202 computations (31.8% saved)

localize12.0ms (0.6%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (expm1.f64 (log1p.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))
✓	0.0b	(log1p.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
	0.0b	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
✓	5.5b	(expm1.f64 (log1p.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))

series6.0ms (0.3%)

Counts

3 → 36

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	x	@	0	(log.f64 (expm1.f64 (log1p.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))
1.0ms	x	@	inf	(log1p.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
1.0ms	x	@	-inf	(log1p.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
0.0ms	x	@	0	(expm1.f64 (log1p.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))
0.0ms	x	@	0	(log1p.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

rewrite62.0ms (3.2%)

Algorithm

1×	batch-egg-rewrite

Rules

417×	`fma-def_binary64`
214×	`fma-neg_binary64`
204×	`expm1-udef_binary64`
203×	`log1p-udef_binary64`
178×	`log-pow_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	58
1	246	58
2	3494	58

Stop Event

1×	node limit

Counts

3 → 132

Calls

Call 1

Inputs
(expm1.f64 (log1p.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))
(log1p.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
(log.f64 (expm1.f64 (log1p.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))

Inputs

(expm1.f64 (log1p.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))))

(log1p.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

(log.f64 (expm1.f64 (log1p.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (/.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) x) (/.f64 1 x))))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 (fma.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1) 1) -1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (fma.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1) 1) 1)))) (#(struct:change #<rule egg-rr> (2) ((x -.f64 (/.f64 (pow.f64 x -2) (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) x)) (/.f64 (.f64 (-.f64 1 (.f64 x x)) (pow.f64 x -2)) (/.f64 (-.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))) x)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1)))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (.f64 x x)))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cbrt.f64 (.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1))) (pow.f64 (cbrt.f64 (.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (pow.f64 (cbrt.f64 (.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1))) 2) (cbrt.f64 (.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (.f64 x x))) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (/.f64 (sqrt.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x)) x) (/.f64 (sqrt.f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x)) x))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 x (sqrt.f64 (-.f64 1 (.f64 x x))) x) (pow.f64 x -2))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (fma.f64 (pow.f64 (-.f64 1 (.f64 x x)) 3/2) (pow.f64 x -3) (pow.f64 x -3)) (/.f64 1 (-.f64 (+.f64 (pow.f64 x -2) (.f64 (-.f64 1 (.f64 x x)) 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Outputs

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((#(struct:change #<rule egg-rr> (2) ((x -.f64 (exp.f64 (log1p.f64 (log1p.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (log1p.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (log1p.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (log1p.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))) (cbrt.f64 (pow.f64 (log1p.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))) 2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cbrt.f64 (pow.f64 (log1p.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))) 2)) (cbrt.f64 (log1p.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (sqrt.f64 (log1p.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))) (sqrt.f64 (log1p.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (log1p.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (pow.f64 (log1p.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))) 3) 1/3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (cbrt.f64 (log1p.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))) 3)))) (#(struct:change #<rule egg-rr> (2) ((x pow.f64 (sqrt.f64 (log1p.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))) 2)))) (#(struct:change #<rule egg-rr> (2) ((x sqrt.f64 (pow.f64 (log1p.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))) 2))))) (#(struct:change #<rule egg-rr> (2) ((x log.f64 (fma.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1) 1))))) (#(struct:change #<rule egg-rr> (2) ((x cbrt.f64 (pow.f64 (log1p.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1))) 3))))) (#(struct:change #<rule egg-rr> (2) ((x expm1.f64 (log1p.f64 (log1p.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (log.f64 (log1p.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))))))) (#(struct:change #<rule egg-rr> (2) ((x exp.f64 (*.f64 (log.f64 (log1p.f64 (*.f64 (/.f64 1 x) (+.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) 1)))) 1))))))

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simplify32.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

468×	`associate-/r*_binary64`
450×	`fma-def_binary64`
239×	`associate-+l+_binary64`
237×	`associate-r_binary64`
233×	`associate-l_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	973
1	435	894
2	1326	870

Stop Event

1×	node limit

Counts

168 → 199

Calls

Call 1

Inputs
(/.f64 2 x)
(+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x)))
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (.f64 -1/2 x) (*.f64 2 (/.f64 1 x))))
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (.f64 -1/2 x) (+.f64 (.f64 2 (/.f64 1 x)) (.f64 -1/16 (pow.f64 x 5)))))
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (/.f64 1 x))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 x) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 2))))))
(-.f64 (+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 x) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 2)))))) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))
(*.f64 -1 (sqrt.f64 -1))
(+.f64 (/.f64 1 x) (*.f64 -1 (sqrt.f64 -1)))
(-.f64 (+.f64 (/.f64 1 x) (.f64 -1 (sqrt.f64 -1))) (.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
(-.f64 (+.f64 (/.f64 1 x) (+.f64 (.f64 -1 (sqrt.f64 -1)) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))) (.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 x)))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (.f64 -1 (log.f64 x))))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (+.f64 (.f64 -3/8 (pow.f64 x 2)) (*.f64 -1 (log.f64 x)))))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (log.f64 2) (+.f64 (.f64 -3/8 (pow.f64 x 2)) (.f64 -1 (log.f64 x))))))
(log.f64 (+.f64 (sqrt.f64 -1) 1))
(+.f64 (log.f64 (+.f64 (sqrt.f64 -1) 1)) (/.f64 1 (*.f64 x (+.f64 (sqrt.f64 -1) 1))))
(+.f64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 -1) 1) x)) (+.f64 (.f64 1/2 (/.f64 (-.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) (+.f64 (sqrt.f64 -1) 1))) (/.f64 1 (pow.f64 (+.f64 (sqrt.f64 -1) 1) 2))) (pow.f64 x 2))) (log.f64 (+.f64 (sqrt.f64 -1) 1))))
(+.f64 (.f64 1/6 (/.f64 (-.f64 (.f64 2 (/.f64 1 (pow.f64 (+.f64 (sqrt.f64 -1) 1) 3))) (.f64 3 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 (+.f64 (sqrt.f64 -1) 1) 2))))) (pow.f64 x 3))) (+.f64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 -1) 1) x)) (+.f64 (.f64 1/2 (/.f64 (-.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) (+.f64 (sqrt.f64 -1) 1))) (/.f64 1 (pow.f64 (+.f64 (sqrt.f64 -1) 1) 2))) (pow.f64 x 2))) (log.f64 (+.f64 (sqrt.f64 -1) 1)))))
(log.f64 (+.f64 1 (*.f64 -1 (sqrt.f64 -1))))
(+.f64 (log.f64 (+.f64 1 (.f64 -1 (sqrt.f64 -1)))) (/.f64 1 (.f64 (+.f64 1 (*.f64 -1 (sqrt.f64 -1))) x)))
(+.f64 (log.f64 (+.f64 1 (.f64 -1 (sqrt.f64 -1)))) (+.f64 (/.f64 1 (.f64 (+.f64 1 (.f64 -1 (sqrt.f64 -1))) x)) (.f64 -1/2 (/.f64 (+.f64 (/.f64 1 (pow.f64 (+.f64 1 (.f64 -1 (sqrt.f64 -1))) 2)) (/.f64 1 (.f64 (sqrt.f64 -1) (+.f64 1 (*.f64 -1 (sqrt.f64 -1)))))) (pow.f64 x 2)))))
(+.f64 (log.f64 (+.f64 1 (.f64 -1 (sqrt.f64 -1)))) (+.f64 (/.f64 1 (.f64 (+.f64 1 (.f64 -1 (sqrt.f64 -1))) x)) (+.f64 (.f64 1/6 (/.f64 (+.f64 (.f64 3 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 (+.f64 1 (.f64 -1 (sqrt.f64 -1))) 2)))) (.f64 2 (/.f64 1 (pow.f64 (+.f64 1 (.f64 -1 (sqrt.f64 -1))) 3)))) (pow.f64 x 3))) (.f64 -1/2 (/.f64 (+.f64 (/.f64 1 (pow.f64 (+.f64 1 (.f64 -1 (sqrt.f64 -1))) 2)) (/.f64 1 (.f64 (sqrt.f64 -1) (+.f64 1 (*.f64 -1 (sqrt.f64 -1)))))) (pow.f64 x 2))))))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 -1 (log.f64 x))))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -3/32 (pow.f64 x 4)) (*.f64 -1 (log.f64 x)))))
(+.f64 (.f64 -5/96 (pow.f64 x 6)) (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -3/32 (pow.f64 x 4)) (.f64 -1 (log.f64 x))))))
(log.f64 (sqrt.f64 -1))
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (log.f64 (sqrt.f64 -1)))
(-.f64 (+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (log.f64 (sqrt.f64 -1))) (.f64 1/6 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(-.f64 (+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (+.f64 (.f64 3/40 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (log.f64 (sqrt.f64 -1)))) (.f64 1/6 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(log.f64 (*.f64 -1 (sqrt.f64 -1)))
(-.f64 (log.f64 (.f64 -1 (sqrt.f64 -1))) (/.f64 1 (.f64 (sqrt.f64 -1) x)))
(-.f64 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 -1))) (.f64 1/6 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) (/.f64 1 (.f64 (sqrt.f64 -1) x)))
(-.f64 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 -1))) (.f64 1/6 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (.f64 3/40 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))))

Outputs
(/.f64 2 x)
(+.f64 (.f64 -1/2 x) (.f64 2 (/.f64 1 x)))
(fma.f64 -1/2 x (/.f64 2 x))
(fma.f64 x -1/2 (/.f64 2 x))
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (.f64 -1/2 x) (*.f64 2 (/.f64 1 x))))
(fma.f64 -1/8 (pow.f64 x 3) (fma.f64 -1/2 x (/.f64 2 x)))
(fma.f64 -1/8 (pow.f64 x 3) (fma.f64 x -1/2 (/.f64 2 x)))
(fma.f64 x -1/2 (fma.f64 -1/8 (pow.f64 x 3) (/.f64 2 x)))
(+.f64 (.f64 -1/8 (pow.f64 x 3)) (+.f64 (.f64 -1/2 x) (+.f64 (.f64 2 (/.f64 1 x)) (.f64 -1/16 (pow.f64 x 5)))))
(fma.f64 -1/8 (pow.f64 x 3) (+.f64 (fma.f64 -1/2 x (/.f64 2 x)) (*.f64 -1/16 (pow.f64 x 5))))
(fma.f64 -1/8 (pow.f64 x 3) (fma.f64 x -1/2 (fma.f64 -1/16 (pow.f64 x 5) (/.f64 2 x))))
(sqrt.f64 -1)
(+.f64 (sqrt.f64 -1) (/.f64 1 x))
(+.f64 (/.f64 1 x) (sqrt.f64 -1))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 x) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 2))))))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 x) (/.f64 1/2 (.f64 (sqrt.f64 -1) (.f64 x x)))))
(+.f64 (/.f64 1 x) (+.f64 (sqrt.f64 -1) (/.f64 1/2 (.f64 (sqrt.f64 -1) (.f64 x x)))))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 x) (/.f64 1/2 (.f64 x (.f64 x (sqrt.f64 -1))))))
(-.f64 (+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1 x) (.f64 1/2 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 x 2)))))) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))
(+.f64 (sqrt.f64 -1) (-.f64 (+.f64 (/.f64 1 x) (/.f64 1/2 (.f64 (sqrt.f64 -1) (.f64 x x)))) (/.f64 1/8 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))
(+.f64 (sqrt.f64 -1) (+.f64 (/.f64 1/2 (.f64 (sqrt.f64 -1) (.f64 x x))) (-.f64 (/.f64 1 x) (/.f64 1/8 (*.f64 (pow.f64 x 4) (neg.f64 (sqrt.f64 -1)))))))
(+.f64 (/.f64 1 x) (+.f64 (/.f64 1/2 (.f64 x (.f64 x (sqrt.f64 -1)))) (+.f64 (sqrt.f64 -1) (/.f64 (/.f64 1/8 (sqrt.f64 -1)) (pow.f64 x 4)))))
(*.f64 -1 (sqrt.f64 -1))
(neg.f64 (sqrt.f64 -1))
(+.f64 (/.f64 1 x) (*.f64 -1 (sqrt.f64 -1)))
(+.f64 (/.f64 1 x) (neg.f64 (sqrt.f64 -1)))
(-.f64 (/.f64 1 x) (sqrt.f64 -1))
(-.f64 (+.f64 (/.f64 1 x) (.f64 -1 (sqrt.f64 -1))) (.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
(+.f64 (/.f64 1 x) (-.f64 (neg.f64 (sqrt.f64 -1)) (/.f64 1/2 (.f64 (sqrt.f64 -1) (.f64 x x)))))
(+.f64 (-.f64 (/.f64 1 x) (sqrt.f64 -1)) (/.f64 -1/2 (.f64 (sqrt.f64 -1) (.f64 x x))))
(-.f64 (/.f64 1 x) (-.f64 (sqrt.f64 -1) (/.f64 (/.f64 (/.f64 -1/2 (sqrt.f64 -1)) x) x)))
(-.f64 (+.f64 (/.f64 1 x) (+.f64 (.f64 -1 (sqrt.f64 -1)) (.f64 1/8 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))))) (.f64 1/2 (/.f64 1 (*.f64 (sqrt.f64 -1) (pow.f64 x 2)))))
(+.f64 (/.f64 1 x) (-.f64 (fma.f64 -1 (sqrt.f64 -1) (/.f64 1/8 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 4)))) (/.f64 1/2 (.f64 (sqrt.f64 -1) (*.f64 x x)))))
(+.f64 (/.f64 1 x) (+.f64 (-.f64 (/.f64 1/8 (.f64 (pow.f64 x 4) (neg.f64 (sqrt.f64 -1)))) (sqrt.f64 -1)) (/.f64 -1/2 (.f64 (sqrt.f64 -1) (*.f64 x x)))))
(+.f64 (/.f64 -1/8 (*.f64 (sqrt.f64 -1) (pow.f64 x 4))) (-.f64 (/.f64 1 x) (-.f64 (sqrt.f64 -1) (/.f64 (/.f64 (/.f64 -1/2 (sqrt.f64 -1)) x) x))))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 2) (neg.f64 (log.f64 x)))
(-.f64 (log.f64 2) (log.f64 x))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (.f64 -1 (log.f64 x))))
(fma.f64 1/2 x (+.f64 (log.f64 2) (neg.f64 (log.f64 x))))
(-.f64 (fma.f64 x 1/2 (log.f64 2)) (log.f64 x))
(+.f64 (.f64 1/2 x) (+.f64 (log.f64 2) (+.f64 (.f64 -3/8 (pow.f64 x 2)) (*.f64 -1 (log.f64 x)))))
(fma.f64 1/2 x (+.f64 (log.f64 2) (fma.f64 -3/8 (*.f64 x x) (neg.f64 (log.f64 x)))))
(+.f64 (-.f64 (.f64 (.f64 x x) -3/8) (log.f64 x)) (fma.f64 x 1/2 (log.f64 2)))
(-.f64 (fma.f64 x 1/2 (fma.f64 x (*.f64 x -3/8) (log.f64 2))) (log.f64 x))
(+.f64 (.f64 1/2 x) (+.f64 (.f64 1/6 (pow.f64 x 3)) (+.f64 (log.f64 2) (+.f64 (.f64 -3/8 (pow.f64 x 2)) (.f64 -1 (log.f64 x))))))
(fma.f64 1/2 x (fma.f64 1/6 (pow.f64 x 3) (+.f64 (log.f64 2) (fma.f64 -3/8 (*.f64 x x) (neg.f64 (log.f64 x))))))
(fma.f64 x 1/2 (+.f64 (-.f64 (.f64 (.f64 x x) -3/8) (log.f64 x)) (fma.f64 (pow.f64 x 3) 1/6 (log.f64 2))))
(fma.f64 x 1/2 (-.f64 (fma.f64 (pow.f64 x 3) 1/6 (fma.f64 x (*.f64 x -3/8) (log.f64 2))) (log.f64 x)))
(log.f64 (+.f64 (sqrt.f64 -1) 1))
(log.f64 (+.f64 1 (sqrt.f64 -1)))
(log1p.f64 (sqrt.f64 -1))
(+.f64 (log.f64 (+.f64 (sqrt.f64 -1) 1)) (/.f64 1 (*.f64 x (+.f64 (sqrt.f64 -1) 1))))
(+.f64 (log.f64 (+.f64 1 (sqrt.f64 -1))) (/.f64 1 (*.f64 x (+.f64 1 (sqrt.f64 -1)))))
(+.f64 (log1p.f64 (sqrt.f64 -1)) (/.f64 1 (fma.f64 x (sqrt.f64 -1) x)))
(+.f64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 -1) 1) x)) (+.f64 (.f64 1/2 (/.f64 (-.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) (+.f64 (sqrt.f64 -1) 1))) (/.f64 1 (pow.f64 (+.f64 (sqrt.f64 -1) 1) 2))) (pow.f64 x 2))) (log.f64 (+.f64 (sqrt.f64 -1) 1))))
(+.f64 (/.f64 1 (.f64 x (+.f64 1 (sqrt.f64 -1)))) (fma.f64 1/2 (/.f64 (-.f64 (/.f64 1 (.f64 (sqrt.f64 -1) (+.f64 1 (sqrt.f64 -1)))) (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 -1)) 2))) (*.f64 x x)) (log.f64 (+.f64 1 (sqrt.f64 -1)))))
(+.f64 (/.f64 1 (fma.f64 x (sqrt.f64 -1) x)) (fma.f64 1/2 (/.f64 (+.f64 (/.f64 1 (+.f64 -1 (sqrt.f64 -1))) (/.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 -1)) 2))) (*.f64 x x)) (log1p.f64 (sqrt.f64 -1))))
(+.f64 (log1p.f64 (sqrt.f64 -1)) (+.f64 (/.f64 1 (fma.f64 x (sqrt.f64 -1) x)) (/.f64 (+.f64 (/.f64 1/2 (+.f64 -1 (sqrt.f64 -1))) (/.f64 -1/2 (pow.f64 (+.f64 1 (sqrt.f64 -1)) 2))) (*.f64 x x))))
(+.f64 (.f64 1/6 (/.f64 (-.f64 (.f64 2 (/.f64 1 (pow.f64 (+.f64 (sqrt.f64 -1) 1) 3))) (.f64 3 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 (+.f64 (sqrt.f64 -1) 1) 2))))) (pow.f64 x 3))) (+.f64 (/.f64 1 (.f64 (+.f64 (sqrt.f64 -1) 1) x)) (+.f64 (.f64 1/2 (/.f64 (-.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) (+.f64 (sqrt.f64 -1) 1))) (/.f64 1 (pow.f64 (+.f64 (sqrt.f64 -1) 1) 2))) (pow.f64 x 2))) (log.f64 (+.f64 (sqrt.f64 -1) 1)))))
(fma.f64 1/6 (/.f64 (-.f64 (/.f64 2 (pow.f64 (+.f64 1 (sqrt.f64 -1)) 3)) (/.f64 3 (.f64 (sqrt.f64 -1) (pow.f64 (+.f64 1 (sqrt.f64 -1)) 2)))) (pow.f64 x 3)) (+.f64 (/.f64 1 (.f64 x (+.f64 1 (sqrt.f64 -1)))) (fma.f64 1/2 (/.f64 (-.f64 (/.f64 1 (.f64 (sqrt.f64 -1) (+.f64 1 (sqrt.f64 -1)))) (/.f64 1 (pow.f64 (+.f64 1 (sqrt.f64 -1)) 2))) (.f64 x x)) (log.f64 (+.f64 1 (sqrt.f64 -1))))))
(+.f64 (fma.f64 1/2 (/.f64 (+.f64 (/.f64 1 (+.f64 -1 (sqrt.f64 -1))) (/.f64 -1 (pow.f64 (+.f64 1 (sqrt.f64 -1)) 2))) (.f64 x x)) (log1p.f64 (sqrt.f64 -1))) (fma.f64 1/6 (/.f64 (+.f64 (/.f64 2 (pow.f64 (+.f64 1 (sqrt.f64 -1)) 3)) (/.f64 -3 (.f64 (+.f64 1 (sqrt.f64 -1)) (+.f64 -1 (sqrt.f64 -1))))) (pow.f64 x 3)) (/.f64 1 (fma.f64 x (sqrt.f64 -1) x))))
(+.f64 (log1p.f64 (sqrt.f64 -1)) (+.f64 (/.f64 1 (fma.f64 x (sqrt.f64 -1) x)) (+.f64 (/.f64 (+.f64 (/.f64 1/3 (pow.f64 (+.f64 1 (sqrt.f64 -1)) 3)) (/.f64 -1/2 (.f64 (+.f64 1 (sqrt.f64 -1)) (+.f64 -1 (sqrt.f64 -1))))) (pow.f64 x 3)) (/.f64 (+.f64 (/.f64 1/2 (+.f64 -1 (sqrt.f64 -1))) (/.f64 -1/2 (pow.f64 (+.f64 1 (sqrt.f64 -1)) 2))) (.f64 x x)))))
(log.f64 (+.f64 1 (*.f64 -1 (sqrt.f64 -1))))
(log1p.f64 (neg.f64 (sqrt.f64 -1)))
(+.f64 (log.f64 (+.f64 1 (.f64 -1 (sqrt.f64 -1)))) (/.f64 1 (.f64 (+.f64 1 (*.f64 -1 (sqrt.f64 -1))) x)))
(+.f64 (log1p.f64 (neg.f64 (sqrt.f64 -1))) (/.f64 1 (*.f64 x (+.f64 1 (neg.f64 (sqrt.f64 -1))))))
(+.f64 (log1p.f64 (neg.f64 (sqrt.f64 -1))) (/.f64 1 (*.f64 x (-.f64 1 (sqrt.f64 -1)))))
(+.f64 (log.f64 (+.f64 1 (.f64 -1 (sqrt.f64 -1)))) (+.f64 (/.f64 1 (.f64 (+.f64 1 (.f64 -1 (sqrt.f64 -1))) x)) (.f64 -1/2 (/.f64 (+.f64 (/.f64 1 (pow.f64 (+.f64 1 (.f64 -1 (sqrt.f64 -1))) 2)) (/.f64 1 (.f64 (sqrt.f64 -1) (+.f64 1 (*.f64 -1 (sqrt.f64 -1)))))) (pow.f64 x 2)))))
(+.f64 (log1p.f64 (neg.f64 (sqrt.f64 -1))) (+.f64 (/.f64 1 (.f64 x (+.f64 1 (neg.f64 (sqrt.f64 -1))))) (.f64 -1/2 (/.f64 (+.f64 (/.f64 1 (pow.f64 (+.f64 1 (neg.f64 (sqrt.f64 -1))) 2)) (/.f64 1 (.f64 (sqrt.f64 -1) (+.f64 1 (neg.f64 (sqrt.f64 -1)))))) (.f64 x x)))))
(+.f64 (log1p.f64 (neg.f64 (sqrt.f64 -1))) (fma.f64 -1/2 (/.f64 (+.f64 (/.f64 1 (pow.f64 (-.f64 1 (sqrt.f64 -1)) 2)) (/.f64 1 (+.f64 1 (sqrt.f64 -1)))) (.f64 x x)) (/.f64 1 (.f64 x (-.f64 1 (sqrt.f64 -1))))))
(+.f64 (+.f64 (log1p.f64 (neg.f64 (sqrt.f64 -1))) (/.f64 1 (.f64 x (-.f64 1 (sqrt.f64 -1))))) (/.f64 (+.f64 (/.f64 -1/2 (pow.f64 (-.f64 1 (sqrt.f64 -1)) 2)) (/.f64 -1/2 (+.f64 1 (sqrt.f64 -1)))) (.f64 x x)))
(+.f64 (log.f64 (+.f64 1 (.f64 -1 (sqrt.f64 -1)))) (+.f64 (/.f64 1 (.f64 (+.f64 1 (.f64 -1 (sqrt.f64 -1))) x)) (+.f64 (.f64 1/6 (/.f64 (+.f64 (.f64 3 (/.f64 1 (.f64 (sqrt.f64 -1) (pow.f64 (+.f64 1 (.f64 -1 (sqrt.f64 -1))) 2)))) (.f64 2 (/.f64 1 (pow.f64 (+.f64 1 (.f64 -1 (sqrt.f64 -1))) 3)))) (pow.f64 x 3))) (.f64 -1/2 (/.f64 (+.f64 (/.f64 1 (pow.f64 (+.f64 1 (.f64 -1 (sqrt.f64 -1))) 2)) (/.f64 1 (.f64 (sqrt.f64 -1) (+.f64 1 (*.f64 -1 (sqrt.f64 -1)))))) (pow.f64 x 2))))))
(+.f64 (log1p.f64 (neg.f64 (sqrt.f64 -1))) (+.f64 (/.f64 1 (.f64 x (+.f64 1 (neg.f64 (sqrt.f64 -1))))) (fma.f64 1/6 (/.f64 (+.f64 (/.f64 3 (.f64 (sqrt.f64 -1) (pow.f64 (+.f64 1 (neg.f64 (sqrt.f64 -1))) 2))) (/.f64 2 (pow.f64 (+.f64 1 (neg.f64 (sqrt.f64 -1))) 3))) (pow.f64 x 3)) (.f64 -1/2 (/.f64 (+.f64 (/.f64 1 (pow.f64 (+.f64 1 (neg.f64 (sqrt.f64 -1))) 2)) (/.f64 1 (.f64 (sqrt.f64 -1) (+.f64 1 (neg.f64 (sqrt.f64 -1)))))) (*.f64 x x))))))
(+.f64 (log1p.f64 (neg.f64 (sqrt.f64 -1))) (+.f64 (/.f64 1 (.f64 x (-.f64 1 (sqrt.f64 -1)))) (fma.f64 1/6 (/.f64 (+.f64 (/.f64 (/.f64 3 (sqrt.f64 -1)) (pow.f64 (-.f64 1 (sqrt.f64 -1)) 2)) (/.f64 2 (pow.f64 (-.f64 1 (sqrt.f64 -1)) 3))) (pow.f64 x 3)) (/.f64 (.f64 -1/2 (+.f64 (/.f64 1 (pow.f64 (-.f64 1 (sqrt.f64 -1)) 2)) (/.f64 1 (+.f64 1 (sqrt.f64 -1))))) (*.f64 x x)))))
(+.f64 (/.f64 1 (.f64 x (-.f64 1 (sqrt.f64 -1)))) (+.f64 (/.f64 (+.f64 (/.f64 -1/2 (pow.f64 (-.f64 1 (sqrt.f64 -1)) 2)) (/.f64 -1/2 (+.f64 1 (sqrt.f64 -1)))) (.f64 x x)) (+.f64 (/.f64 (+.f64 (/.f64 1/2 (+.f64 (+.f64 1 (sqrt.f64 -1)) (-.f64 1 (sqrt.f64 -1)))) (/.f64 1/3 (pow.f64 (-.f64 1 (sqrt.f64 -1)) 3))) (pow.f64 x 3)) (log1p.f64 (neg.f64 (sqrt.f64 -1))))))
(+.f64 (log.f64 2) (*.f64 -1 (log.f64 x)))
(+.f64 (log.f64 2) (neg.f64 (log.f64 x)))
(-.f64 (log.f64 2) (log.f64 x))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (.f64 -1 (log.f64 x))))
(+.f64 (log.f64 2) (fma.f64 -1/4 (*.f64 x x) (neg.f64 (log.f64 x))))
(+.f64 (log.f64 2) (fma.f64 (*.f64 x x) -1/4 (neg.f64 (log.f64 x))))
(-.f64 (fma.f64 x (*.f64 x -1/4) (log.f64 2)) (log.f64 x))
(+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -3/32 (pow.f64 x 4)) (*.f64 -1 (log.f64 x)))))
(+.f64 (log.f64 2) (fma.f64 -1/4 (*.f64 x x) (fma.f64 -3/32 (pow.f64 x 4) (neg.f64 (log.f64 x)))))
(+.f64 (log.f64 2) (fma.f64 (*.f64 x x) -1/4 (fma.f64 (pow.f64 x 4) -3/32 (neg.f64 (log.f64 x)))))
(+.f64 (log.f64 2) (-.f64 (fma.f64 x (.f64 x -1/4) (.f64 (pow.f64 x 4) -3/32)) (log.f64 x)))
(+.f64 (.f64 -5/96 (pow.f64 x 6)) (+.f64 (log.f64 2) (+.f64 (.f64 -1/4 (pow.f64 x 2)) (+.f64 (.f64 -3/32 (pow.f64 x 4)) (.f64 -1 (log.f64 x))))))
(fma.f64 -5/96 (pow.f64 x 6) (+.f64 (log.f64 2) (fma.f64 -1/4 (*.f64 x x) (fma.f64 -3/32 (pow.f64 x 4) (neg.f64 (log.f64 x))))))
(+.f64 (fma.f64 (*.f64 x x) -1/4 (fma.f64 (pow.f64 x 4) -3/32 (neg.f64 (log.f64 x)))) (fma.f64 -5/96 (pow.f64 x 6) (log.f64 2)))
(+.f64 (-.f64 (.f64 (pow.f64 x 4) -3/32) (log.f64 x)) (fma.f64 -5/96 (pow.f64 x 6) (fma.f64 x (.f64 x -1/4) (log.f64 2))))
(log.f64 (sqrt.f64 -1))
(+.f64 (/.f64 1 (*.f64 (sqrt.f64 -1) x)) (log.f64 (sqrt.f64 -1)))
(+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 1 (*.f64 x (sqrt.f64 -1))))
(+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 (/.f64 1 (sqrt.f64 -1)) x))
(-.f64 (+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (log.f64 (sqrt.f64 -1))) (.f64 1/6 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (-.f64 (log.f64 (sqrt.f64 -1)) (/.f64 1/6 (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3)))))
(+.f64 (log.f64 (sqrt.f64 -1)) (-.f64 (/.f64 (/.f64 1 (sqrt.f64 -1)) x) (/.f64 (/.f64 1/6 (pow.f64 x 3)) (neg.f64 (sqrt.f64 -1)))))
(+.f64 (log.f64 (sqrt.f64 -1)) (+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (/.f64 1/6 (.f64 (pow.f64 x 3) (sqrt.f64 -1)))))
(-.f64 (+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (+.f64 (.f64 3/40 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5)))) (log.f64 (sqrt.f64 -1)))) (.f64 1/6 (/.f64 1 (*.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3)))))
(+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (-.f64 (+.f64 (log.f64 (sqrt.f64 -1)) (/.f64 3/40 (.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)))) (/.f64 1/6 (*.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3)))))
(+.f64 (/.f64 (/.f64 1 (sqrt.f64 -1)) x) (+.f64 (log.f64 (sqrt.f64 -1)) (-.f64 (/.f64 3/40 (*.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5))) (/.f64 (/.f64 1/6 (pow.f64 x 3)) (neg.f64 (sqrt.f64 -1))))))
(+.f64 (log.f64 (sqrt.f64 -1)) (-.f64 (+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (/.f64 (/.f64 3/40 (pow.f64 (sqrt.f64 -1) 5)) (pow.f64 x 5))) (/.f64 -1/6 (.f64 (pow.f64 x 3) (sqrt.f64 -1)))))
(log.f64 (*.f64 -1 (sqrt.f64 -1)))
(log.f64 (neg.f64 (sqrt.f64 -1)))
(-.f64 (log.f64 (.f64 -1 (sqrt.f64 -1))) (/.f64 1 (.f64 (sqrt.f64 -1) x)))
(-.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (/.f64 1 (*.f64 x (sqrt.f64 -1))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (/.f64 -1 (*.f64 x (sqrt.f64 -1))))
(-.f64 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 -1))) (.f64 1/6 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) (/.f64 1 (.f64 (sqrt.f64 -1) x)))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (-.f64 (/.f64 1/6 (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3))) (/.f64 1 (.f64 x (sqrt.f64 -1)))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (fma.f64 1/6 (/.f64 (/.f64 -1 (sqrt.f64 -1)) (pow.f64 x 3)) (/.f64 -1 (*.f64 x (sqrt.f64 -1)))))
(+.f64 (/.f64 -1/6 (.f64 (pow.f64 x 3) (sqrt.f64 -1))) (+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (/.f64 -1 (.f64 x (sqrt.f64 -1)))))
(-.f64 (+.f64 (log.f64 (.f64 -1 (sqrt.f64 -1))) (.f64 1/6 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 3) (pow.f64 x 3))))) (+.f64 (/.f64 1 (.f64 (sqrt.f64 -1) x)) (.f64 3/40 (/.f64 1 (.f64 (pow.f64 (sqrt.f64 -1) 5) (pow.f64 x 5))))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (-.f64 (/.f64 1/6 (.f64 (pow.f64 x 3) (pow.f64 (sqrt.f64 -1) 3))) (+.f64 (/.f64 1 (.f64 x (sqrt.f64 -1))) (/.f64 3/40 (*.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5))))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (-.f64 (fma.f64 1/6 (/.f64 (/.f64 -1 (sqrt.f64 -1)) (pow.f64 x 3)) (/.f64 -1 (.f64 x (sqrt.f64 -1)))) (/.f64 3/40 (.f64 (pow.f64 x 5) (pow.f64 (sqrt.f64 -1) 5)))))
(+.f64 (log.f64 (neg.f64 (sqrt.f64 -1))) (+.f64 (/.f64 -1/6 (.f64 (pow.f64 x 3) (sqrt.f64 -1))) (-.f64 (/.f64 -1 (.f64 x (sqrt.f64 -1))) (/.f64 (/.f64 3/40 (pow.f64 (sqrt.f64 -1) 5)) (pow.f64 x 5)))))

prune315.0ms (16.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	305	0	305
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	305	2	307

Error

Counts

307 → 2

Alt Table

Status	Error	Program
✓	0.0b	(log.f64 (expm1.f64 (log1p.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))))
✓	0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

Compiler

Compiled 6448 to 4642 computations (28% saved)

regimes53.0ms (2.7%)

Accuracy

Total -0.0b remaining (-63%)

Threshold costs -0.0b (-63%)

Counts

17 → 1

Compiler

Compiled 228 to 159 computations (30.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	21
1	19	21
2	25	21
3	29	21
4	31	21

Stop Event

1×

saturated

Calls

Call 1

Inputs
(log1p.f64 (fma.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) -1))

Outputs
(log1p.f64 (fma.f64 (/.f64 1 x) (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x)))) -1))

end40.0ms (2.1%)

Stop Event

1×

done

Compiler

Compiled 58 to 42 computations (27.6% saved)

Details

analyze5.0ms (0.3%)

sample996.0ms (51.4%)

preprocess40.0ms (2.1%)

simplify32.0ms (1.6%)

prune2.0ms (0.1%)

localize9.0ms (0.5%)

series8.0ms (0.4%)

rewrite68.0ms (3.5%)

simplify40.0ms (2.1%)

prune215.0ms (11.1%)

localize12.0ms (0.6%)

series6.0ms (0.3%)

rewrite62.0ms (3.2%)

simplify32.0ms (1.6%)

prune315.0ms (16.3%)

regimes53.0ms (2.7%)

simplify2.0ms (0.1%)

end40.0ms (2.1%)

Profiling