Details

analyze502.0ms (8.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
50%	50%	0.1%	5
50%	50%	0.1%	6
50%	37.5%	12.6%	7
50%	37.5%	12.6%	8
50%	31.2%	18.8%	9
50%	31.2%	18.8%	10
50%	28.1%	22%	11
50%	28.1%	22%	12
50%	26.5%	23.5%	13
50%	26.5%	23.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample4.2s (70.9%)

Results

1.4s	2084×	body	1024	valid
1.1s	2020×	body	1024	invalid
608.0ms	4639×	body	128	valid
361.0ms	986×	body	512	valid
350.0ms	1049×	body	512	invalid
131.0ms	540×	body	256	valid
128.0ms	509×	body	256	invalid
98.0ms	691×	body	128	invalid
9.0ms	7×	body	2048	valid

Compiler

Compiled 28 to 22 computations (21.4% saved)

preprocess47.0ms (0.8%)

Algorithm

2×	egg-herbie

Rules

748×	`times-frac_binary64`
390×	`fma-def_binary64`
320×	`unswap-sqr_binary64`
302×	`associate-l_binary64`
234×	`associate-/l*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	36
1	49	36
2	131	36
3	256	34
4	373	34
5	672	34
6	1526	34
7	2651	34
8	3803	34
9	4549	34
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 13 to 10 computations (23.1% saved)

simplify33.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

529×	`associate-/l*_binary64`
430×	`unswap-sqr_binary64`
374×	`times-frac_binary64`
351×	`fma-def_binary64`
340×	`associate-/r/_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	11	18
1	28	18
2	70	18
3	134	17
4	194	17
5	347	17
6	783	17
7	1356	17
8	3975	17
9	4498	17

Stop Event

1×	node limit

Counts

1 → 2

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.0b

Counts

3 → 1

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 50 to 35 computations (30% saved)

localize11.0ms (0.2%)

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	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))

series16.0ms (0.3%)

Counts

2 → 32

Calls

9 calls:

3.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))	im	inf
3.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))	im	-inf
2.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))	re	0
2.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))	re	-inf
2.0ms	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))	re	inf

rewrite77.0ms (1.3%)

Algorithm

2×	egg-rewrite-iter-limit
2×	egg-rewrite
1×	batch-egg-rewrite

Rules

119×	`add-sqr-sqrt_binary64`
119×	`add-sqr-sqrt_binary64`
112×	`log1p-expm1-u_binary64`
112×	`expm1-log1p-u_binary64`
112×	`log1p-expm1-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	28
1	233	28
2	3763	28
0	6	10
1	126	10
2	2049	10
0	6	10
0	11	18
1	233	18
2	3740	18
0	11	18

Stop Event

1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	unsound

Counts

2 → 19

simplify35.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

705×	`fma-neg_binary64`
438×	`fma-def_binary64`
241×	`sub-neg_binary64`
190×	`distribute-rgt-out_binary64`
181×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	668
1	216	614
2	679	594
3	2964	554

Stop Event

1×	node limit

Counts

51 → 46

prune38.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	44	2	46
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	44	3	47

Error

Counts

47 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
	1.8b	(.f64 (.f64 1/2 (cos.f64 re)) (.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))))
▶	1.2b	(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4))) (cos.f64 re)))

Compiler

Compiled 963 to 471 computations (51.1% saved)

localize13.0ms (0.2%)

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))) (+.f64 (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4))) (cos.f64 re)))
✓	0.0b	(*.f64 (cos.f64 re) (pow.f64 im 4))
✓	0.1b	(.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))
✓	0.1b	(*.f64 (cos.f64 re) (pow.f64 im 2))

series68.0ms (1.1%)

Counts

4 → 22

Calls

24 calls:

9.0ms	(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4))) (cos.f64 re)))	re	inf
6.0ms	(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4))) (cos.f64 re)))	re	-inf
6.0ms	(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4))) (cos.f64 re)))	re	0
5.0ms	(.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))	re	-inf
4.0ms	(.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4)))	re	inf

rewrite65.0ms (1.1%)

Algorithm

1×	batch-egg-rewrite

Rules

291×	`expm1-udef_binary64`
291×	`log1p-udef_binary64`
164×	`add-sqr-sqrt_binary64`
163×	`log1p-expm1-u_binary64`
163×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	57
1	353	57
2	4450	57

Stop Event

1×	node limit

Counts

4 → 83

simplify27.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

676×	`fma-def_binary64`
469×	`associate-l_binary64`
420×	`associate-r_binary64`
409×	`cancel-sign-sub-inv_binary64`
334×	`associate--l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	81	678
1	267	628
2	1034	540

Stop Event

1×	node limit

Counts

105 → 120

prune114.0ms (1.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	120	3	123

Error

Counts

123 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
▶	1.8b	(.f64 (.f64 1/2 (cos.f64 re)) (.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))))
✓	1.2b	(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4))) (cos.f64 re)))

Compiler

Compiled 3595 to 2136 computations (40.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))
✓	0.0b	(.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))
✓	0.0b	(*.f64 (cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))
✓	1.0b	(cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))

series165.0ms (2.8%)

Counts

3 → 36

Calls

9 calls:

45.0ms	(*.f64 (cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))	im	inf
35.0ms	(*.f64 (cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))	im	-inf
29.0ms	(cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))	im	inf
26.0ms	(cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))	im	-inf
20.0ms	(*.f64 (cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))))	im	0

rewrite102.0ms (1.7%)

Algorithm

3×	egg-rewrite-iter-limit
3×	egg-rewrite
1×	batch-egg-rewrite

Rules

81×	`add-sqr-sqrt_binary64`
81×	`add-sqr-sqrt_binary64`
81×	`add-sqr-sqrt_binary64`
79×	`log1p-expm1-u_binary64`
79×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	180	36
2	2554	36
0	7	12
1	144	12
2	2256	12
0	7	12
0	8	15
1	165	15
2	2523	15
0	8	15
0	9	10
1	180	10
2	2554	10
0	9	10

Stop Event

1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	iter limit
1×	unsound
1×	unsound

Counts

3 → 28

simplify34.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

478×	`cancel-sign-sub-inv_binary64`
284×	`associate-/l/_binary64`
259×	`associate-/r/_binary64`
229×	`fma-neg_binary64`
175×	`fma-def_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	617
1	230	613
2	644	603
3	2520	595

Stop Event

1×	node limit

Counts

64 → 55

prune73.0ms (1.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	151	0	151
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	151	3	154

Error

Counts

154 → 3

Alt Table

Status	Error	Program
✓	0.0b	(.f64 (.f64 1/2 (cos.f64 re)) (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))
✓	1.8b	(.f64 (.f64 1/2 (cos.f64 re)) (.f64 (.f64 (cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im))) (cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))) (cbrt.f64 (+.f64 (exp.f64 (neg.f64 im)) (exp.f64 im)))))
✓	1.2b	(+.f64 (.f64 1/2 (.f64 (cos.f64 re) (pow.f64 im 2))) (+.f64 (.f64 1/24 (.f64 (cos.f64 re) (pow.f64 im 4))) (cos.f64 re)))

Compiler

Compiled 4928 to 1716 computations (65.2% saved)

regimes239.0ms (4%)

Accuracy

Total 0.0b remaining (57.6%)

Threshold costs 0.0b (57.6%)

Counts

37 → 1

Compiler

Compiled 4302 to 3000 computations (30.3% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	26
1	20	26
2	22	26
3	23	26

Stop Event

1×

saturated

end64.0ms (1.1%)

Stop Event

1×

done

Compiler

Compiled 101 to 64 computations (36.6% saved)

Details

analyze502.0ms (8.4%)

sample4.2s (70.9%)

preprocess47.0ms (0.8%)

simplify33.0ms (0.5%)

prune2.0ms (0%)

localize11.0ms (0.2%)

series16.0ms (0.3%)

rewrite77.0ms (1.3%)

simplify35.0ms (0.6%)

prune38.0ms (0.6%)

localize13.0ms (0.2%)

series68.0ms (1.1%)

rewrite65.0ms (1.1%)

simplify27.0ms (0.5%)

prune114.0ms (1.9%)

localize11.0ms (0.2%)

series165.0ms (2.8%)

rewrite102.0ms (1.7%)

simplify34.0ms (0.6%)

prune73.0ms (1.2%)

regimes239.0ms (4%)

simplify2.0ms (0%)

end64.0ms (1.1%)

Profiling