Details

analyze135.0ms (3.6%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
0%	0%	99.9%	0.1%	0%	0%	0%	1
0%	0%	99.9%	0.1%	0%	0%	0%	2
0%	0%	99.9%	0.1%	0%	0%	0%	3
0%	0%	99.9%	0.1%	0%	0%	0%	4
50%	50%	50%	0.1%	0%	0%	0%	5
50%	50%	50%	0.1%	0%	0%	0%	6
57.1%	50%	37.5%	0.1%	12.5%	0%	0%	7
57.1%	50%	37.5%	0.1%	12.5%	0%	0%	8
61.5%	50%	31.2%	0.1%	18.7%	0%	0%	9
61.5%	50%	31.2%	0.1%	18.7%	0%	0%	10
64%	50%	28.1%	0.1%	21.9%	0%	0%	11
64%	50%	28.1%	0.1%	21.9%	0%	0%	12

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample3.2s (83.8%)

Results

987.0ms	2039×	body	1024	valid
735.0ms	2101×	body	1024	infinite
689.0ms	5130×	body	256	valid
292.0ms	1085×	body	512	valid
246.0ms	1036×	body	512	infinite
194.0ms	1482×	body	256	infinite
2.0ms	2×	body	2048	valid

Bogosity

preprocess3.0ms (0.1%)

Algorithm

2×	egg-herbie

Rules

28×	`rational.json-simplify-2`
8×	`rational.json-simplify-31`
4×	`rational.json-simplify-1`
4×	`rational.json-simplify-9`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	70
1	29	70
2	39	70
3	47	70
0	2	2

Stop Event

1×	saturated
1×	saturated

Calls

Call 1

Inputs
0
1

Outputs
0
1

Call 2

Inputs
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(.f64 (.f64 1/2 (cos.f64 im)) (+.f64 (exp.f64 (neg.f64 re)) (exp.f64 re)))

Outputs
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(.f64 1/2 (.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) (cos.f64 re)))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))
(.f64 (.f64 1/2 (cos.f64 im)) (+.f64 (exp.f64 (neg.f64 re)) (exp.f64 re)))

Compiler

Compiled 15 to 12 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`rational.json-simplify-2`
4×	`rational.json-simplify-31`
2×	`rational.json-simplify-1`
2×	`rational.json-simplify-9`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	35
1	18	35
2	23	35
3	27	35

Stop Event

1×

saturated

Counts

1 → 3

Calls

Call 1

Inputs
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Outputs

(*.f64 (*.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

(*.f64 1/2 (*.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)) (cos.f64 re)))

(*.f64 1/2 (*.f64 (cos.f64 re) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))

eval1.0ms (0%)

Compiler: Compiled 35 to 16 computations (54.3% saved)

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

4 → 1

Alt Table

Click to see full alt table

Status	Error	Program
▶	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Compiler

Compiled 13 to 10 computations (23.1% saved)

localize15.0ms (0.4%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	0.0b	(cos.f64 re)

Compiler

Compiled 35 to 13 computations (62.9% saved)

series4.0ms (0.1%)

Counts

2 → 28

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	im	@	inf	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
1.0ms	re	@	-inf	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
1.0ms	re	@	inf	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
1.0ms	re	@	0	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
1.0ms	im	@	-inf	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

rewrite7.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

50×	`rational.json-simplify-2`
44×	`bool.json-1`
36×	`rational.json-1`
36×	`rational.json-2`
34×	`rational.json-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	40
1	61	40
2	106	40
3	129	40
4	143	40
5	146	40
6	148	40

Stop Event

1×

saturated

Counts

2 → 6

Calls

Call 1

Inputs
(cos.f64 re)
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (cos.f64 re) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (cos.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x .f64 (cos.f64 re) 1)))) (#(struct:change #<rule egg-rr> (2) ((x .f64 1 (cos.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x or (cos.f64 re) (cos.f64 re))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (cos.f64 re) (.f64 1/2 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (cos.f64 re) (.f64 1/2 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x or (.f64 (cos.f64 re) (.f64 1/2 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (.f64 (cos.f64 re) (.f64 1/2 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))))))))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (cos.f64 re) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (cos.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 re) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (cos.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x or (cos.f64 re) (cos.f64 re))))))

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (cos.f64 re) (*.f64 1/2 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (cos.f64 re) (*.f64 1/2 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))))))) (#(struct:change #<rule egg-rr> (2) ((x or (*.f64 (cos.f64 re) (*.f64 1/2 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (*.f64 (cos.f64 re) (*.f64 1/2 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))))))))

simplify22.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

168×	`rational.json-simplify-1`
104×	`rational.json-simplify-2`
102×	`rational.json-simplify-33`
32×	`rational.json-simplify-31`
6×	`rational.json-simplify-19`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	77	1338
1	141	1326
2	210	1326
3	277	1326
4	313	1326
5	314	1326

Stop Event

1×

saturated

Counts

34 → 40

Calls

Call 1

Inputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 re 2)))
(+.f64 (.f64 1/24 (pow.f64 re 4)) (+.f64 1 (.f64 -1/2 (pow.f64 re 2))))
(+.f64 (.f64 1/24 (pow.f64 re 4)) (+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 re 2)) (*.f64 -1/720 (pow.f64 re 6)))))
(*.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))
(+.f64 (.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (.f64 -1/4 (*.f64 (pow.f64 re 2) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))))
(+.f64 (.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (+.f64 (.f64 -1/4 (.f64 (pow.f64 re 2) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))) (.f64 1/48 (*.f64 (pow.f64 re 4) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))))
(+.f64 (.f64 -1/1440 (.f64 (pow.f64 re 6) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))) (+.f64 (.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (+.f64 (.f64 -1/4 (.f64 (pow.f64 re 2) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))) (.f64 1/48 (*.f64 (pow.f64 re 4) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))))))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(cos.f64 re)
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (cos.f64 re) (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (cos.f64 re) (+.f64 (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4))) (.f64 1/720 (.f64 (cos.f64 re) (pow.f64 im 6))))))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (*.f64 -1 im)))))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (*.f64 -1 im)))))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (*.f64 -1 im)))))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (*.f64 -1 im)))))
(+.f64 (cos.f64 re) 0)
(+.f64 0 (cos.f64 re))
(*.f64 (cos.f64 re) 1)
(*.f64 1 (cos.f64 re))
(+.f64 (.f64 (cos.f64 re) (.f64 1/2 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) 0)
(+.f64 0 (.f64 (cos.f64 re) (.f64 1/2 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))))

Outputs
1
(+.f64 1 (*.f64 -1/2 (pow.f64 re 2)))
(+.f64 (.f64 1/24 (pow.f64 re 4)) (+.f64 1 (.f64 -1/2 (pow.f64 re 2))))
(+.f64 (+.f64 1 (.f64 -1/2 (pow.f64 re 2))) (.f64 1/24 (pow.f64 re 4)))
(+.f64 (.f64 -1/2 (pow.f64 re 2)) (+.f64 1 (.f64 1/24 (pow.f64 re 4))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 re 2)) (.f64 1/24 (pow.f64 re 4))))
(+.f64 (.f64 1/24 (pow.f64 re 4)) (+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 re 2)) (*.f64 -1/720 (pow.f64 re 6)))))
(+.f64 1 (+.f64 (.f64 1/24 (pow.f64 re 4)) (+.f64 (.f64 -1/2 (pow.f64 re 2)) (*.f64 -1/720 (pow.f64 re 6)))))
(+.f64 1 (+.f64 (.f64 -1/2 (pow.f64 re 2)) (+.f64 (.f64 1/24 (pow.f64 re 4)) (*.f64 -1/720 (pow.f64 re 6)))))
(*.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))
(+.f64 (.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (.f64 -1/4 (*.f64 (pow.f64 re 2) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))))
(+.f64 (.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (*.f64 -1/4 (pow.f64 re 2))))
(+.f64 (.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (*.f64 (pow.f64 re 2) -1/4)))
(+.f64 (.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (+.f64 (.f64 -1/4 (.f64 (pow.f64 re 2) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))) (.f64 1/48 (*.f64 (pow.f64 re 4) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))))
(+.f64 (.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (+.f64 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (.f64 -1/4 (pow.f64 re 2))) (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (*.f64 1/48 (pow.f64 re 4)))))
(+.f64 (.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (+.f64 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (.f64 (pow.f64 re 2) -1/4)) (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (*.f64 (pow.f64 re 4) 1/48))))
(+.f64 (.f64 -1/1440 (.f64 (pow.f64 re 6) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))) (+.f64 (.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (+.f64 (.f64 -1/4 (.f64 (pow.f64 re 2) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))) (.f64 1/48 (*.f64 (pow.f64 re 4) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))))))
(+.f64 (+.f64 (.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (+.f64 (.f64 -1/4 (.f64 (pow.f64 re 2) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))) (.f64 1/48 (.f64 (pow.f64 re 4) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))))) (.f64 (pow.f64 re 6) (*.f64 -1/1440 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))))
(+.f64 (+.f64 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (.f64 -1/4 (pow.f64 re 2))) (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (.f64 1/48 (pow.f64 re 4)))) (+.f64 (.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (.f64 (pow.f64 re 6) (*.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) -1/1440))))
(+.f64 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (.f64 (pow.f64 re 4) 1/48)) (+.f64 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (.f64 (pow.f64 re 2) -1/4)) (+.f64 (.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (.f64 (pow.f64 re 6) (*.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) -1/1440)))))
(+.f64 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (.f64 (pow.f64 re 2) -1/4)) (+.f64 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (.f64 (pow.f64 re 4) 1/48)) (+.f64 (.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))) (.f64 (pow.f64 re 6) (*.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) -1/1440)))))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (cos.f64 re)))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (cos.f64 re)))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (cos.f64 re)))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (cos.f64 re)))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (cos.f64 re)))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (cos.f64 re)))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (cos.f64 re)))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (cos.f64 re)))
(cos.f64 re)
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(+.f64 (cos.f64 re) (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))))
(.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2))))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (cos.f64 re) (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (.f64 (cos.f64 re) (+.f64 1 (.f64 1/24 (pow.f64 im 4)))))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (cos.f64 re) (+.f64 (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4))) (.f64 1/720 (.f64 (cos.f64 re) (pow.f64 im 6))))))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (.f64 (cos.f64 re) (+.f64 1 (.f64 1/24 (pow.f64 im 4)))) (.f64 1/720 (.f64 (cos.f64 re) (pow.f64 im 6)))))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (.f64 (cos.f64 re) (+.f64 1 (.f64 1/24 (pow.f64 im 4)))) (.f64 (cos.f64 re) (.f64 1/720 (pow.f64 im 6)))))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (cos.f64 re)))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (cos.f64 re)))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (cos.f64 re)))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im)))))
(.f64 1/2 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (cos.f64 re)))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (*.f64 -1 im)))))
(.f64 1/2 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (cos.f64 re)))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (*.f64 -1 im)))))
(.f64 1/2 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (cos.f64 re)))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (*.f64 -1 im)))))
(.f64 1/2 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (cos.f64 re)))
(.f64 1/2 (.f64 (cos.f64 re) (+.f64 (exp.f64 im) (exp.f64 (*.f64 -1 im)))))
(.f64 1/2 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (cos.f64 re)))
(+.f64 (cos.f64 re) 0)
(+.f64 0 (cos.f64 re))
(+.f64 (cos.f64 re) 0)
(*.f64 (cos.f64 re) 1)
(*.f64 1 (cos.f64 re))
(*.f64 1 (cos.f64 re))
(+.f64 (.f64 (cos.f64 re) (.f64 1/2 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) 0)
(+.f64 0 (.f64 1/2 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (cos.f64 re))))
(+.f64 0 (.f64 (cos.f64 re) (.f64 1/2 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))))
(+.f64 0 (.f64 1/2 (.f64 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))) (cos.f64 re))))

eval15.0ms (0.4%)

Compiler: Compiled 891 to 449 computations (49.6% saved)

prune7.0ms (0.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	36	4	40
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	5	41

Error

0.0b

Counts

41 → 5

Alt Table

Click to see full alt table

Status	Error	Program
▶	1.0b	(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
▶	1.0b	(.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2))))
▶	30.0b	(*.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))
▶	1.3b	(cos.f64 re)

Compiler

Compiled 52 to 40 computations (23.1% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.0b	(cos.f64 re)

Compiler

Compiled 5 to 3 computations (40% saved)

localize8.0ms (0.2%)

Compiler: Compiled 25 to 9 computations (64% saved)

localize14.0ms (0.4%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 1/2 (pow.f64 im 2))
	0.0b	(cos.f64 re)
✓	0.0b	(.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2))))

Compiler

Compiled 34 to 25 computations (26.5% saved)

series4.0ms (0.1%)

Counts

2 → 16

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	im	@	inf	(*.f64 1/2 (pow.f64 im 2))
1.0ms	re	@	inf	(.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2))))
0.0ms	im	@	inf	(.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2))))
0.0ms	re	@	0	(.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2))))
0.0ms	im	@	0	(.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2))))

rewrite6.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

32×	`bool.json-1`
28×	`rational.json-simplify-2`
26×	`rational.json-simplify-1`
24×	`rational.json-1`
24×	`rational.json-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	42
1	58	42
2	87	42
3	93	42

Stop Event

1×

saturated

Counts

2 → 4

Calls

Call 1

Inputs
(.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2))))
(*.f64 1/2 (pow.f64 im 2))

Outputs
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2)))) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2)))))))) (#(struct:change #<rule egg-rr> (2) ((x or (.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2)))) (.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2)))))))))
((#(struct:change #<rule egg-rr> (2) ((x +.f64 (.f64 1/2 (pow.f64 im 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (.f64 1/2 (pow.f64 im 2)))))) (#(struct:change #<rule egg-rr> (2) ((x or (.f64 1/2 (pow.f64 im 2)) (.f64 1/2 (pow.f64 im 2)))))))

Outputs

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

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

simplify17.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

226×	`rational.json-simplify-1`
214×	`rational.json-simplify-33`
56×	`rational.json-simplify-2`
18×	`rational.json-simplify-31`
8×	`rational.json-simplify-19`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	784
1	78	694
2	130	694
3	201	694
4	284	694
5	328	694
6	333	694

Stop Event

1×

saturated

Counts

20 → 24

Calls

Call 1

Inputs
(+.f64 1 (*.f64 1/2 (pow.f64 im 2)))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 -1/2 (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (pow.f64 re 2)))))
(+.f64 1 (+.f64 (.f64 1/24 (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (pow.f64 re 4))) (+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 -1/2 (.f64 (+.f64 1 (*.f64 1/2 (pow.f64 im 2))) (pow.f64 re 2))))))
(+.f64 1 (+.f64 (.f64 1/24 (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (pow.f64 re 4))) (+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (.f64 -1/2 (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (pow.f64 re 2))) (.f64 -1/720 (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (pow.f64 re 6)))))))
(cos.f64 re)
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2)))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2)))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(+.f64 (.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2)))) 0)
(+.f64 0 (.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2)))))
(+.f64 (*.f64 1/2 (pow.f64 im 2)) 0)
(+.f64 0 (*.f64 1/2 (pow.f64 im 2)))

Outputs
(+.f64 1 (*.f64 1/2 (pow.f64 im 2)))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 -1/2 (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (pow.f64 re 2)))))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (.f64 -1/2 (pow.f64 re 2)))))
(.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (+.f64 1 (*.f64 -1/2 (pow.f64 re 2))))
(+.f64 1 (+.f64 (.f64 1/24 (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (pow.f64 re 4))) (+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 -1/2 (.f64 (+.f64 1 (*.f64 1/2 (pow.f64 im 2))) (pow.f64 re 2))))))
(+.f64 1 (+.f64 (+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (.f64 -1/2 (pow.f64 re 2)))) (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (*.f64 1/24 (pow.f64 re 4)))))
(+.f64 (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (+.f64 1 (.f64 -1/2 (pow.f64 re 2)))) (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (.f64 1/24 (pow.f64 re 4))))
(+.f64 (.f64 -1/2 (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (pow.f64 re 2))) (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (+.f64 1 (.f64 1/24 (pow.f64 re 4)))))
(+.f64 1 (+.f64 (.f64 1/24 (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (pow.f64 re 4))) (+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (.f64 -1/2 (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (pow.f64 re 2))) (.f64 -1/720 (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (pow.f64 re 6)))))))
(+.f64 1 (+.f64 (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (.f64 1/24 (pow.f64 re 4))) (+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (.f64 -1/2 (pow.f64 re 2))) (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (.f64 -1/720 (pow.f64 re 6)))))))
(+.f64 (+.f64 (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (+.f64 1 (.f64 -1/2 (pow.f64 re 2)))) (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (.f64 1/24 (pow.f64 re 4)))) (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (*.f64 -1/720 (pow.f64 re 6))))
(+.f64 (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (.f64 1/24 (pow.f64 re 4))) (+.f64 (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (+.f64 1 (.f64 -1/2 (pow.f64 re 2)))) (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (*.f64 -1/720 (pow.f64 re 6)))))
(+.f64 (+.f64 (.f64 -1/2 (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (pow.f64 re 2))) (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (+.f64 1 (.f64 1/24 (pow.f64 re 4))))) (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (*.f64 -1/720 (pow.f64 re 6))))
(cos.f64 re)
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(+.f64 (cos.f64 re) (.f64 1/2 (.f64 (pow.f64 im 2) (cos.f64 re))))
(.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (cos.f64 re))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(+.f64 (cos.f64 re) (.f64 1/2 (.f64 (pow.f64 im 2) (cos.f64 re))))
(.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (cos.f64 re))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(+.f64 (cos.f64 re) (.f64 1/2 (.f64 (pow.f64 im 2) (cos.f64 re))))
(.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (cos.f64 re))
(.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2)))
(.f64 1/2 (.f64 (pow.f64 im 2) (cos.f64 re)))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(+.f64 (cos.f64 re) (.f64 1/2 (.f64 (pow.f64 im 2) (cos.f64 re))))
(.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (cos.f64 re))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(+.f64 (cos.f64 re) (.f64 1/2 (.f64 (pow.f64 im 2) (cos.f64 re))))
(.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (cos.f64 re))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(+.f64 (cos.f64 re) (.f64 1/2 (.f64 (pow.f64 im 2) (cos.f64 re))))
(.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (cos.f64 re))
(.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2)))
(.f64 1/2 (.f64 (pow.f64 im 2) (cos.f64 re)))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(+.f64 (cos.f64 re) (.f64 1/2 (.f64 (pow.f64 im 2) (cos.f64 re))))
(.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (cos.f64 re))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(+.f64 (cos.f64 re) (.f64 1/2 (.f64 (pow.f64 im 2) (cos.f64 re))))
(.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (cos.f64 re))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
(+.f64 (cos.f64 re) (.f64 1/2 (.f64 (pow.f64 im 2) (cos.f64 re))))
(.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (cos.f64 re))
(+.f64 (.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2)))) 0)
(+.f64 (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (cos.f64 re)) 0)
(+.f64 0 (.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2)))))
(+.f64 (.f64 (+.f64 1 (.f64 1/2 (pow.f64 im 2))) (cos.f64 re)) 0)
(+.f64 (*.f64 1/2 (pow.f64 im 2)) 0)
(+.f64 0 (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (*.f64 1/2 (pow.f64 im 2)) 0)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
✓	0.0b	(.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2)))
	0.0b	(cos.f64 re)
✓	0.1b	(*.f64 (cos.f64 re) (pow.f64 im 2))

Compiler

Compiled 36 to 21 computations (41.7% saved)

series3.0ms (0.1%)

Counts

3 → 15

Calls

18 calls:

Time	Variable		Point	Expression
0.0ms	re	@	0	(.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2)))
0.0ms	im	@	inf	(*.f64 (cos.f64 re) (pow.f64 im 2))
0.0ms	re	@	0	(*.f64 (cos.f64 re) (pow.f64 im 2))
0.0ms	re	@	-inf	(.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2)))
0.0ms	re	@	inf	(.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2)))

rewrite8.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

42×	`rational.json-simplify-2`
40×	`bool.json-1`
34×	`rational.json-simplify-1`
32×	`rational.json-1`
32×	`rational.json-2`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	73
1	57	69
2	98	69
3	119	69
4	124	69
5	125	69

Stop Event

1×

saturated

Counts

3 → 8

Calls

Call 1

Inputs
(*.f64 (cos.f64 re) (pow.f64 im 2))
(.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2)))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x +.f64 (*.f64 (cos.f64 re) (pow.f64 im 2)) 0)))) (#(struct:change #<rule egg-rr> (2) ((x +.f64 0 (*.f64 (cos.f64 re) (pow.f64 im 2)))))) (#(struct:change #<rule egg-rr> (2) ((x or (*.f64 (cos.f64 re) (pow.f64 im 2)) (*.f64 (cos.f64 re) (pow.f64 im 2)))))))

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

((#(struct:change #<rule egg-rr> (2) ((x *.f64 (cos.f64 re) (+.f64 1 (*.f64 (pow.f64 im 2) 1/2)))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (*.f64 (cos.f64 re) (+.f64 1 (*.f64 (pow.f64 im 2) 1/2))) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (*.f64 (cos.f64 re) (+.f64 1 (*.f64 (pow.f64 im 2) 1/2))))))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 1 (*.f64 (pow.f64 im 2) 1/2)) (cos.f64 re))))) (#(struct:change #<rule egg-rr> (2) ((x or (*.f64 (cos.f64 re) (+.f64 1 (*.f64 (pow.f64 im 2) 1/2))) (*.f64 (cos.f64 re) (+.f64 1 (*.f64 (pow.f64 im 2) 1/2))))))))

simplify42.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

524×	`rational.json-simplify-31`
494×	`rational.json-simplify-2`
336×	`rational.json-simplify-1`
260×	`rational.json-simplify-33`
24×	`rational.json-simplify-27`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	73	1015
1	150	1015
2	253	997
3	381	997
4	506	997
5	587	997
6	650	997
7	733	997
8	826	997
9	966	997
10	1022	997
11	1022	997
12	1032	997

Stop Event

1×

saturated

Counts

23 → 58

Calls

Call 1

Inputs
(pow.f64 im 2)
(+.f64 (pow.f64 im 2) (.f64 -1/2 (.f64 (pow.f64 re 2) (pow.f64 im 2))))
(+.f64 (.f64 1/24 (.f64 (pow.f64 re 4) (pow.f64 im 2))) (+.f64 (pow.f64 im 2) (.f64 -1/2 (.f64 (pow.f64 re 2) (pow.f64 im 2)))))
(+.f64 (.f64 1/24 (.f64 (pow.f64 re 4) (pow.f64 im 2))) (+.f64 (pow.f64 im 2) (+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (pow.f64 im 2))) (.f64 -1/720 (.f64 (pow.f64 re 6) (pow.f64 im 2))))))
(*.f64 1/2 (pow.f64 im 2))
(+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 -1/4 (*.f64 (pow.f64 re 2) (pow.f64 im 2))))
(+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (.f64 1/48 (.f64 (pow.f64 re 4) (pow.f64 im 2))) (.f64 -1/4 (*.f64 (pow.f64 re 2) (pow.f64 im 2)))))
(+.f64 (.f64 -1/1440 (.f64 (pow.f64 re 6) (pow.f64 im 2))) (+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (.f64 1/48 (.f64 (pow.f64 re 4) (pow.f64 im 2))) (.f64 -1/4 (*.f64 (pow.f64 re 2) (pow.f64 im 2))))))
(+.f64 1 (*.f64 1/2 (pow.f64 im 2)))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 (-.f64 (*.f64 -1/4 (pow.f64 im 2)) 1/2) (pow.f64 re 2))))
(+.f64 1 (+.f64 (.f64 (pow.f64 re 4) (+.f64 1/24 (.f64 1/48 (pow.f64 im 2)))) (+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 (-.f64 (*.f64 -1/4 (pow.f64 im 2)) 1/2) (pow.f64 re 2)))))
(+.f64 1 (+.f64 (.f64 (pow.f64 re 4) (+.f64 1/24 (.f64 1/48 (pow.f64 im 2)))) (+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (.f64 (-.f64 (.f64 -1/4 (pow.f64 im 2)) 1/2) (pow.f64 re 2)) (.f64 (-.f64 (*.f64 -1/1440 (pow.f64 im 2)) 1/720) (pow.f64 re 6))))))
(cos.f64 re)
(.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2)))
(.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2)))
(+.f64 (*.f64 (cos.f64 re) (pow.f64 im 2)) 0)
(+.f64 0 (*.f64 (cos.f64 re) (pow.f64 im 2)))
(+.f64 (.f64 (cos.f64 re) (.f64 (pow.f64 im 2) 1/2)) 0)
(+.f64 0 (.f64 (cos.f64 re) (.f64 (pow.f64 im 2) 1/2)))
(.f64 (cos.f64 re) (+.f64 1 (.f64 (pow.f64 im 2) 1/2)))
(.f64 (.f64 (cos.f64 re) (+.f64 1 (*.f64 (pow.f64 im 2) 1/2))) 1)
(.f64 1 (.f64 (cos.f64 re) (+.f64 1 (*.f64 (pow.f64 im 2) 1/2))))
(.f64 (+.f64 1 (.f64 (pow.f64 im 2) 1/2)) (cos.f64 re))

Outputs
(pow.f64 im 2)
(+.f64 (pow.f64 im 2) (.f64 -1/2 (.f64 (pow.f64 re 2) (pow.f64 im 2))))
(+.f64 (pow.f64 im 2) (.f64 -1/2 (.f64 (pow.f64 im 2) (pow.f64 re 2))))
(+.f64 (pow.f64 im 2) (.f64 (pow.f64 im 2) (.f64 -1/2 (pow.f64 re 2))))
(.f64 (pow.f64 im 2) (+.f64 1 (.f64 -1/2 (pow.f64 re 2))))
(+.f64 (.f64 1/24 (.f64 (pow.f64 re 4) (pow.f64 im 2))) (+.f64 (pow.f64 im 2) (.f64 -1/2 (.f64 (pow.f64 re 2) (pow.f64 im 2)))))
(+.f64 (+.f64 (pow.f64 im 2) (.f64 -1/2 (.f64 (pow.f64 im 2) (pow.f64 re 2)))) (.f64 1/24 (.f64 (pow.f64 im 2) (pow.f64 re 4))))
(+.f64 (.f64 (pow.f64 im 2) (.f64 -1/2 (pow.f64 re 2))) (+.f64 (pow.f64 im 2) (.f64 (pow.f64 re 4) (.f64 (pow.f64 im 2) 1/24))))
(+.f64 (.f64 (pow.f64 im 2) (+.f64 1 (.f64 -1/2 (pow.f64 re 2)))) (.f64 (pow.f64 re 4) (.f64 (pow.f64 im 2) 1/24)))
(+.f64 (.f64 1/24 (.f64 (pow.f64 re 4) (pow.f64 im 2))) (+.f64 (pow.f64 im 2) (+.f64 (.f64 -1/2 (.f64 (pow.f64 re 2) (pow.f64 im 2))) (.f64 -1/720 (.f64 (pow.f64 re 6) (pow.f64 im 2))))))
(+.f64 (.f64 1/24 (.f64 (pow.f64 im 2) (pow.f64 re 4))) (+.f64 (pow.f64 im 2) (+.f64 (.f64 -1/2 (.f64 (pow.f64 im 2) (pow.f64 re 2))) (.f64 -1/720 (.f64 (pow.f64 im 2) (pow.f64 re 6))))))
(+.f64 (+.f64 (.f64 (pow.f64 im 2) (.f64 -1/2 (pow.f64 re 2))) (.f64 (pow.f64 im 2) (.f64 -1/720 (pow.f64 re 6)))) (+.f64 (pow.f64 im 2) (.f64 (pow.f64 re 4) (.f64 (pow.f64 im 2) 1/24))))
(+.f64 (.f64 (pow.f64 re 4) (.f64 (pow.f64 im 2) 1/24)) (+.f64 (.f64 (pow.f64 im 2) (+.f64 1 (.f64 -1/2 (pow.f64 re 2)))) (.f64 (pow.f64 im 2) (.f64 -1/720 (pow.f64 re 6)))))
(+.f64 (.f64 (pow.f64 im 2) (.f64 -1/2 (pow.f64 re 2))) (+.f64 (.f64 (pow.f64 re 4) (.f64 (pow.f64 im 2) 1/24)) (.f64 (pow.f64 im 2) (+.f64 1 (.f64 -1/720 (pow.f64 re 6))))))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 (pow.f64 im 2) 1/2)
(+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 -1/4 (*.f64 (pow.f64 re 2) (pow.f64 im 2))))
(+.f64 (.f64 (pow.f64 im 2) 1/2) (.f64 (pow.f64 re 2) (*.f64 (pow.f64 im 2) -1/4)))
(+.f64 (.f64 (pow.f64 im 2) 1/2) (.f64 (pow.f64 im 2) (*.f64 (pow.f64 re 2) -1/4)))
(+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (.f64 1/48 (.f64 (pow.f64 re 4) (pow.f64 im 2))) (.f64 -1/4 (*.f64 (pow.f64 re 2) (pow.f64 im 2)))))
(+.f64 (.f64 (pow.f64 im 2) 1/2) (+.f64 (.f64 (pow.f64 re 2) (.f64 (pow.f64 im 2) -1/4)) (.f64 (pow.f64 re 4) (*.f64 (pow.f64 im 2) 1/48))))
(+.f64 (.f64 (pow.f64 im 2) 1/2) (+.f64 (.f64 (pow.f64 im 2) (.f64 (pow.f64 re 2) -1/4)) (.f64 (pow.f64 im 2) (*.f64 (pow.f64 re 4) 1/48))))
(+.f64 (.f64 -1/1440 (.f64 (pow.f64 re 6) (pow.f64 im 2))) (+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (.f64 1/48 (.f64 (pow.f64 re 4) (pow.f64 im 2))) (.f64 -1/4 (*.f64 (pow.f64 re 2) (pow.f64 im 2))))))
(+.f64 (+.f64 (.f64 (pow.f64 im 2) 1/2) (+.f64 (.f64 (pow.f64 re 2) (.f64 (pow.f64 im 2) -1/4)) (.f64 (pow.f64 re 4) (.f64 (pow.f64 im 2) 1/48)))) (.f64 (pow.f64 re 6) (*.f64 (pow.f64 im 2) -1/1440)))
(+.f64 (+.f64 (.f64 (pow.f64 im 2) (.f64 (pow.f64 re 2) -1/4)) (.f64 (pow.f64 im 2) (.f64 (pow.f64 re 4) 1/48))) (+.f64 (.f64 (pow.f64 im 2) 1/2) (.f64 (pow.f64 im 2) (*.f64 (pow.f64 re 6) -1/1440))))
(+.f64 (.f64 (pow.f64 im 2) 1/2) (+.f64 (+.f64 (.f64 (pow.f64 im 2) (.f64 (pow.f64 re 2) -1/4)) (.f64 (pow.f64 im 2) (.f64 (pow.f64 re 4) 1/48))) (.f64 (pow.f64 im 2) (*.f64 (pow.f64 re 6) -1/1440))))
(+.f64 (.f64 (pow.f64 im 2) 1/2) (+.f64 (.f64 (pow.f64 im 2) (.f64 (pow.f64 re 4) 1/48)) (+.f64 (.f64 (pow.f64 im 2) (.f64 (pow.f64 re 2) -1/4)) (.f64 (pow.f64 im 2) (*.f64 (pow.f64 re 6) -1/1440)))))
(+.f64 1 (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (*.f64 (pow.f64 im 2) 1/2) 1)
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 (-.f64 (*.f64 -1/4 (pow.f64 im 2)) 1/2) (pow.f64 re 2))))
(+.f64 1 (+.f64 (.f64 (pow.f64 im 2) 1/2) (.f64 (pow.f64 re 2) (+.f64 -1/2 (*.f64 (pow.f64 im 2) -1/4)))))
(+.f64 (.f64 (pow.f64 re 2) (+.f64 -1/2 (.f64 (pow.f64 im 2) -1/4))) (+.f64 (*.f64 (pow.f64 im 2) 1/2) 1))
(+.f64 1 (+.f64 (.f64 (pow.f64 re 4) (+.f64 1/24 (.f64 1/48 (pow.f64 im 2)))) (+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 (-.f64 (*.f64 -1/4 (pow.f64 im 2)) 1/2) (pow.f64 re 2)))))
(+.f64 1 (+.f64 (+.f64 (.f64 (pow.f64 im 2) 1/2) (.f64 (pow.f64 re 2) (+.f64 -1/2 (.f64 (pow.f64 im 2) -1/4)))) (.f64 (pow.f64 re 4) (+.f64 1/24 (*.f64 (pow.f64 im 2) 1/48)))))
(+.f64 (+.f64 (+.f64 1 (.f64 (pow.f64 re 4) (+.f64 1/24 (.f64 (pow.f64 im 2) 1/48)))) (.f64 (pow.f64 re 2) (+.f64 -1/2 (.f64 (pow.f64 im 2) -1/4)))) (*.f64 (pow.f64 im 2) 1/2))
(+.f64 (.f64 (pow.f64 im 2) 1/2) (+.f64 (.f64 (pow.f64 re 2) (+.f64 -1/2 (.f64 (pow.f64 im 2) -1/4))) (+.f64 1 (.f64 (pow.f64 re 4) (+.f64 1/24 (*.f64 (pow.f64 im 2) 1/48))))))
(+.f64 1 (+.f64 (.f64 (pow.f64 re 4) (+.f64 1/24 (.f64 1/48 (pow.f64 im 2)))) (+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (.f64 (-.f64 (.f64 -1/4 (pow.f64 im 2)) 1/2) (pow.f64 re 2)) (.f64 (-.f64 (*.f64 -1/1440 (pow.f64 im 2)) 1/720) (pow.f64 re 6))))))
(+.f64 1 (+.f64 (.f64 (pow.f64 re 4) (+.f64 1/24 (.f64 (pow.f64 im 2) 1/48))) (+.f64 (.f64 (pow.f64 im 2) 1/2) (+.f64 (.f64 (pow.f64 re 2) (+.f64 -1/2 (.f64 (pow.f64 im 2) -1/4))) (.f64 (pow.f64 re 6) (+.f64 -1/720 (*.f64 (pow.f64 im 2) -1/1440)))))))
(+.f64 (+.f64 (+.f64 (+.f64 1 (.f64 (pow.f64 re 4) (+.f64 1/24 (.f64 (pow.f64 im 2) 1/48)))) (.f64 (pow.f64 re 2) (+.f64 -1/2 (.f64 (pow.f64 im 2) -1/4)))) (.f64 (pow.f64 im 2) 1/2)) (.f64 (pow.f64 re 6) (+.f64 -1/720 (*.f64 (pow.f64 im 2) -1/1440))))
(+.f64 (.f64 (pow.f64 im 2) 1/2) (+.f64 (+.f64 (.f64 (pow.f64 re 2) (+.f64 -1/2 (.f64 (pow.f64 im 2) -1/4))) (+.f64 1 (.f64 (pow.f64 re 4) (+.f64 1/24 (.f64 (pow.f64 im 2) 1/48))))) (.f64 (pow.f64 re 6) (+.f64 -1/720 (*.f64 (pow.f64 im 2) -1/1440)))))
(+.f64 (.f64 (pow.f64 im 2) 1/2) (+.f64 (.f64 (pow.f64 re 6) (+.f64 -1/720 (.f64 (pow.f64 im 2) -1/1440))) (+.f64 (.f64 (pow.f64 re 2) (+.f64 -1/2 (.f64 (pow.f64 im 2) -1/4))) (+.f64 1 (.f64 (pow.f64 re 4) (+.f64 1/24 (*.f64 (pow.f64 im 2) 1/48)))))))
(cos.f64 re)
(.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2)))
(.f64 (.f64 (pow.f64 im 2) 1/2) (cos.f64 re))
(.f64 (pow.f64 im 2) (.f64 1/2 (cos.f64 re)))
(.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2)))
(.f64 (.f64 (pow.f64 im 2) 1/2) (cos.f64 re))
(.f64 (pow.f64 im 2) (.f64 1/2 (cos.f64 re)))
(+.f64 (*.f64 (cos.f64 re) (pow.f64 im 2)) 0)
(+.f64 (*.f64 (pow.f64 im 2) (cos.f64 re)) 0)
(+.f64 0 (*.f64 (cos.f64 re) (pow.f64 im 2)))
(+.f64 (*.f64 (pow.f64 im 2) (cos.f64 re)) 0)
(+.f64 (.f64 (cos.f64 re) (.f64 (pow.f64 im 2) 1/2)) 0)
(+.f64 0 (.f64 (.f64 (pow.f64 im 2) 1/2) (cos.f64 re)))
(+.f64 0 (.f64 (pow.f64 im 2) (.f64 1/2 (cos.f64 re))))
(+.f64 0 (.f64 (cos.f64 re) (.f64 (pow.f64 im 2) 1/2)))
(+.f64 0 (.f64 (.f64 (pow.f64 im 2) 1/2) (cos.f64 re)))
(+.f64 0 (.f64 (pow.f64 im 2) (.f64 1/2 (cos.f64 re))))
(.f64 (cos.f64 re) (+.f64 1 (.f64 (pow.f64 im 2) 1/2)))
(.f64 (cos.f64 re) (+.f64 (.f64 (pow.f64 im 2) 1/2) 1))
(.f64 (.f64 (cos.f64 re) (+.f64 1 (*.f64 (pow.f64 im 2) 1/2))) 1)
(.f64 1 (.f64 (cos.f64 re) (+.f64 (*.f64 (pow.f64 im 2) 1/2) 1)))
(.f64 1 (.f64 (cos.f64 re) (+.f64 1 (*.f64 (pow.f64 im 2) 1/2))))
(.f64 1 (.f64 (cos.f64 re) (+.f64 (*.f64 (pow.f64 im 2) 1/2) 1)))
(.f64 (+.f64 1 (.f64 (pow.f64 im 2) 1/2)) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 (.f64 (pow.f64 im 2) 1/2) 1))

eval54.0ms (1.4%)

Compiler: Compiled 2712 to 2114 computations (22.1% saved)

prune20.0ms (0.5%)

Pruning

8 alts after pruning (3 fresh and 5 done)

	Pruned	Kept	Total
New	131	3	134
Fresh	0	0	0
Picked	0	1	1
Done	0	4	4
Total	131	8	139

Error

0.0b

Counts

139 → 8

Alt Table

Click to see full alt table

Status	Error	Program
▶	1.2b	(+.f64 (*.f64 (pow.f64 im 2) 1/2) (cos.f64 re))
▶	30.6b	(+.f64 (*.f64 (pow.f64 im 2) 1/2) 1)
✓	1.0b	(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	1.0b	(.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2))))
✓	30.0b	(*.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))
✓	1.3b	(cos.f64 re)
	30.8b	1

Compiler

Compiled 74 to 59 computations (20.3% saved)

localize8.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (pow.f64 im 2) 1/2)

Compiler

Compiled 21 to 17 computations (19% saved)

series0.0ms (0%)

Counts

1 → 12

Calls

3 calls:

Time	Variable		Point	Expression
0.0ms	im	@	0	(*.f64 (pow.f64 im 2) 1/2)
0.0ms	im	@	inf	(*.f64 (pow.f64 im 2) 1/2)
0.0ms	im	@	-inf	(*.f64 (pow.f64 im 2) 1/2)

rewrite5.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

22×	`bool.json-1`
16×	`rational.json-simplify-2`
14×	`rational.json-1`
14×	`rational.json-2`
14×	`rational.json-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	33	13
2	55	13
3	60	13

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(*.f64 (pow.f64 im 2) 1/2)

Outputs

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

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`rational.json-simplify-2`
2×	`rational.json-simplify-1`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	194
1	11	194

Stop Event

1×

saturated

Counts

14 → 4

Calls

Call 1

Inputs
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(+.f64 (*.f64 (pow.f64 im 2) 1/2) 0)
(+.f64 0 (*.f64 (pow.f64 im 2) 1/2))

Outputs
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(*.f64 1/2 (pow.f64 im 2))
(+.f64 (*.f64 (pow.f64 im 2) 1/2) 0)
(+.f64 (*.f64 1/2 (pow.f64 im 2)) 0)
(+.f64 0 (*.f64 (pow.f64 im 2) 1/2))
(+.f64 (*.f64 1/2 (pow.f64 im 2)) 0)

localize13.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (pow.f64 im 2) 1/2)
✓	0.0b	(+.f64 (*.f64 (pow.f64 im 2) 1/2) (cos.f64 re))
	0.0b	(cos.f64 re)

Compiler

Compiled 24 to 16 computations (33.3% saved)

series1.0ms (0%)

Counts

1 → 24

Calls

6 calls:

Time	Variable		Point	Expression
0.0ms	re	@	0	(+.f64 (*.f64 (pow.f64 im 2) 1/2) (cos.f64 re))
0.0ms	im	@	0	(+.f64 (*.f64 (pow.f64 im 2) 1/2) (cos.f64 re))
0.0ms	re	@	inf	(+.f64 (*.f64 (pow.f64 im 2) 1/2) (cos.f64 re))
0.0ms	im	@	inf	(+.f64 (*.f64 (pow.f64 im 2) 1/2) (cos.f64 re))
0.0ms	re	@	-inf	(+.f64 (*.f64 (pow.f64 im 2) 1/2) (cos.f64 re))

rewrite5.0ms (0.1%)

Algorithm

1×	batch-egg-rewrite

Rules

30×	`bool.json-1`
24×	`rational.json-simplify-2`
24×	`rational.json-simplify-1`
22×	`rational.json-1`
22×	`rational.json-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	23
1	50	23
2	80	23
3	85	23

Stop Event

1×

saturated

Counts

1 → 2

Calls

Call 1

Inputs
(+.f64 (*.f64 (pow.f64 im 2) 1/2) (cos.f64 re))

Outputs

((#(struct:change #<rule egg-rr> (2) ((x *.f64 (+.f64 (*.f64 (pow.f64 im 2) 1/2) (cos.f64 re)) 1)))) (#(struct:change #<rule egg-rr> (2) ((x *.f64 1 (+.f64 (*.f64 (pow.f64 im 2) 1/2) (cos.f64 re)))))) (#(struct:change #<rule egg-rr> (2) ((x or (+.f64 (*.f64 (pow.f64 im 2) 1/2) (cos.f64 re)) (+.f64 (*.f64 (pow.f64 im 2) 1/2) (cos.f64 re)))))))

simplify16.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

200×	`rational.json-simplify-1`
174×	`rational.json-simplify-33`
10×	`rational.json-simplify-2`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	664
1	54	664
2	84	664
3	145	664
4	216	664
5	243	664
6	244	664

Stop Event

1×

saturated

Counts

26 → 18

Calls

Call 1

Inputs
(cos.f64 re)
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(*.f64 1/2 (pow.f64 im 2))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(*.f64 1/2 (pow.f64 im 2))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 1 (*.f64 1/2 (pow.f64 im 2)))
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 -1/2 (pow.f64 re 2))))
(+.f64 (.f64 1/24 (pow.f64 re 4)) (+.f64 1 (+.f64 (.f64 1/2 (pow.f64 im 2)) (*.f64 -1/2 (pow.f64 re 2)))))
(+.f64 (.f64 1/24 (pow.f64 re 4)) (+.f64 1 (+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (.f64 -1/2 (pow.f64 re 2)) (.f64 -1/720 (pow.f64 re 6))))))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(.f64 (+.f64 (.f64 (pow.f64 im 2) 1/2) (cos.f64 re)) 1)
(.f64 1 (+.f64 (.f64 (pow.f64 im 2) 1/2) (cos.f64 re)))

Outputs
(cos.f64 re)
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(*.f64 1/2 (pow.f64 im 2))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(*.f64 1/2 (pow.f64 im 2))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 1 (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (*.f64 1/2 (pow.f64 im 2)) 1)
(+.f64 1 (+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 -1/2 (pow.f64 re 2))))
(+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 1 (.f64 -1/2 (pow.f64 re 2))))
(+.f64 (.f64 1/24 (pow.f64 re 4)) (+.f64 1 (+.f64 (.f64 1/2 (pow.f64 im 2)) (*.f64 -1/2 (pow.f64 re 2)))))
(+.f64 (+.f64 1 (+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 -1/2 (pow.f64 re 2)))) (*.f64 1/24 (pow.f64 re 4)))
(+.f64 (+.f64 (.f64 1/2 (pow.f64 im 2)) (.f64 -1/2 (pow.f64 re 2))) (+.f64 1 (*.f64 1/24 (pow.f64 re 4))))
(+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (.f64 -1/2 (pow.f64 re 2)) (+.f64 1 (*.f64 1/24 (pow.f64 re 4)))))
(+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (.f64 1/24 (pow.f64 re 4)) (+.f64 1 (*.f64 -1/2 (pow.f64 re 2)))))
(+.f64 (.f64 1/24 (pow.f64 re 4)) (+.f64 1 (+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (.f64 -1/2 (pow.f64 re 2)) (.f64 -1/720 (pow.f64 re 6))))))
(+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (+.f64 (.f64 -1/2 (pow.f64 re 2)) (.f64 -1/720 (pow.f64 re 6))) (+.f64 1 (.f64 1/24 (pow.f64 re 4)))))
(+.f64 (.f64 1/2 (pow.f64 im 2)) (+.f64 (.f64 -1/720 (pow.f64 re 6)) (+.f64 (.f64 1/24 (pow.f64 re 4)) (+.f64 1 (.f64 -1/2 (pow.f64 re 2))))))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(+.f64 (cos.f64 re) (*.f64 1/2 (pow.f64 im 2)))
(.f64 (+.f64 (.f64 (pow.f64 im 2) 1/2) (cos.f64 re)) 1)
(.f64 1 (+.f64 (cos.f64 re) (.f64 1/2 (pow.f64 im 2))))
(.f64 1 (+.f64 (.f64 (pow.f64 im 2) 1/2) (cos.f64 re)))
(.f64 1 (+.f64 (cos.f64 re) (.f64 1/2 (pow.f64 im 2))))

eval12.0ms (0.3%)

Compiler: Compiled 540 to 438 computations (18.9% saved)

prune9.0ms (0.2%)

Pruning

9 alts after pruning (2 fresh and 7 done)

	Pruned	Kept	Total
New	38	1	39
Fresh	0	1	1
Picked	0	1	1
Done	0	6	6
Total	38	9	47

Error

0.0b

Counts

47 → 9

Alt Table

Click to see full alt table

Status	Error	Program
✓	1.2b	(+.f64 (*.f64 (pow.f64 im 2) 1/2) (cos.f64 re))
✓	30.6b	(+.f64 (*.f64 (pow.f64 im 2) 1/2) 1)
✓	1.0b	(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	1.0b	(.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2))))
▶	61.6b	(*.f64 1/2 (pow.f64 im 2))
✓	30.0b	(*.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))
✓	1.3b	(cos.f64 re)
	30.8b	1

Compiler

Compiled 81 to 65 computations (19.8% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.0b	(*.f64 1/2 (pow.f64 im 2))

Compiler

Compiled 13 to 10 computations (23.1% saved)

eval1.0ms (0%)

Compiler: Compiled 16 to 14 computations (12.5% saved)

prune5.0ms (0.1%)

Pruning

9 alts after pruning (1 fresh and 8 done)

	Pruned	Kept	Total
New	2	0	2
Fresh	0	1	1
Picked	0	1	1
Done	0	7	7
Total	2	9	11

Error

0.0b

Counts

11 → 9

Alt Table

Click to see full alt table

Status	Error	Program
✓	1.2b	(+.f64 (*.f64 (pow.f64 im 2) 1/2) (cos.f64 re))
✓	30.6b	(+.f64 (*.f64 (pow.f64 im 2) 1/2) 1)
✓	1.0b	(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	1.0b	(.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2))))
✓	61.6b	(*.f64 1/2 (pow.f64 im 2))
✓	30.0b	(*.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))
✓	1.3b	(cos.f64 re)
	30.8b	1

Compiler

Compiled 81 to 65 computations (19.8% saved)

regimes37.0ms (1%)

Counts

9 → 1

Calls

Call 1

Inputs
1
(cos.f64 re)
(*.f64 1/2 (pow.f64 im 2))
(+.f64 (*.f64 (pow.f64 im 2) 1/2) 1)
(*.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))
(+.f64 (*.f64 (pow.f64 im 2) 1/2) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2))))
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (cos.f64 re))

Outputs
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

Calls

6 calls:

12.0ms	re
5.0ms	im
5.0ms	(cos.f64 re)
5.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
5.0ms	(*.f64 1/2 (cos.f64 re))

Results

Error	Segments	Branch
0.0b	1	`re`
0.0b	1	`im`
0.0b	1	`(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))`
0.0b	1	`(*.f64 1/2 (cos.f64 re))`
0.0b	1	`(cos.f64 re)`
0.0b	1	`(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))`

Compiler

Compiled 102 to 70 computations (31.4% saved)

regimes17.0ms (0.4%)

Counts

7 → 1

Calls

Call 1

Inputs
1
(cos.f64 re)
(*.f64 1/2 (pow.f64 im 2))
(+.f64 (*.f64 (pow.f64 im 2) 1/2) 1)
(*.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))
(+.f64 (*.f64 (pow.f64 im 2) 1/2) (cos.f64 re))
(.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2))))

Outputs
(.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2))))

Calls

3 calls:

6.0ms	re
4.0ms	im
4.0ms	(cos.f64 re)

Results

Error	Segments	Branch
1.0b	1	`re`
1.0b	1	`im`
1.0b	1	`(cos.f64 re)`

Compiler

Compiled 53 to 39 computations (26.4% saved)

regimes16.0ms (0.4%)

Counts

6 → 1

Calls

Call 1

Inputs
1
(cos.f64 re)
(*.f64 1/2 (pow.f64 im 2))
(+.f64 (*.f64 (pow.f64 im 2) 1/2) 1)
(*.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))
(+.f64 (*.f64 (pow.f64 im 2) 1/2) (cos.f64 re))

Outputs
(+.f64 (*.f64 (pow.f64 im 2) 1/2) (cos.f64 re))

Calls

3 calls:

6.0ms	im
4.0ms	re
4.0ms	(cos.f64 re)

Results

Error	Segments	Branch
1.2b	1	`re`
1.2b	1	`im`
1.2b	1	`(cos.f64 re)`

Compiler

Compiled 43 to 32 computations (25.6% saved)

regimes15.0ms (0.4%)

Accuracy

Total -60.5b remaining (-4525.3%)

Threshold costs -60.5b (-4525.3%)

Counts

5 → 1

Calls

Call 1

Inputs
1
(cos.f64 re)
(*.f64 1/2 (pow.f64 im 2))
(+.f64 (*.f64 (pow.f64 im 2) 1/2) 1)
(*.f64 1/2 (+.f64 (exp.f64 im) (exp.f64 (neg.f64 im))))

Outputs
(cos.f64 re)

Calls

3 calls:

6.0ms	re
4.0ms	im
4.0ms	(cos.f64 re)

Results

Error	Segments	Branch
1.3b	1	`re`
1.3b	1	`im`
1.3b	1	`(cos.f64 re)`

Compiler

Compiled 35 to 27 computations (22.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	93

Stop Event

1×	fuel
1×	saturated

Calls

Call 1

Inputs
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2))))
(+.f64 (*.f64 (pow.f64 im 2) 1/2) (cos.f64 re))
(cos.f64 re)
1

Outputs
(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
(.f64 (cos.f64 re) (+.f64 1 (.f64 1/2 (pow.f64 im 2))))
(+.f64 (*.f64 (pow.f64 im 2) 1/2) (cos.f64 re))
(cos.f64 re)
1

Compiler

Compiled 42 to 34 computations (19% saved)

soundness0.0ms (0%)

end32.0ms (0.9%)

Compiler: Compiled 34 to 23 computations (32.4% saved)

Details

analyze135.0ms (3.6%)

sample3.2s (83.8%)

preprocess3.0ms (0.1%)

simplify4.0ms (0.1%)

eval1.0ms (0%)

prune1.0ms (0%)

localize15.0ms (0.4%)

series4.0ms (0.1%)

rewrite7.0ms (0.2%)

simplify22.0ms (0.6%)

eval15.0ms (0.4%)

prune7.0ms (0.2%)

localize3.0ms (0.1%)

localize8.0ms (0.2%)

localize14.0ms (0.4%)

series4.0ms (0.1%)

rewrite6.0ms (0.2%)

simplify17.0ms (0.4%)

localize13.0ms (0.4%)

series3.0ms (0.1%)

rewrite8.0ms (0.2%)

simplify42.0ms (1.1%)

eval54.0ms (1.4%)

prune20.0ms (0.5%)

localize8.0ms (0.2%)

series0.0ms (0%)

rewrite5.0ms (0.1%)

simplify5.0ms (0.1%)

localize13.0ms (0.3%)

series1.0ms (0%)

rewrite5.0ms (0.1%)

simplify16.0ms (0.4%)

eval12.0ms (0.3%)

prune9.0ms (0.2%)

localize5.0ms (0.1%)

eval1.0ms (0%)

prune5.0ms (0.1%)

regimes37.0ms (1%)

regimes17.0ms (0.4%)

regimes16.0ms (0.4%)

regimes15.0ms (0.4%)

simplify3.0ms (0.1%)

soundness0.0ms (0%)

end32.0ms (0.9%)

Profiling