Details

analyze476.0ms (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
25%	74.9%	0.1%	5
31.2%	68.7%	0.1%	6
43.7%	51.5%	4.8%	7
48.4%	46.8%	4.8%	8
55.4%	37.5%	7.1%	9
58.1%	34.7%	7.1%	10
61.9%	29.9%	8.3%	11
63.3%	28.4%	8.3%	12
65.2%	25.9%	8.9%	13
66%	25.1%	8.9%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample3.9s (69.1%)

Results

2.5s	2541×	body	8192	exit
1.0s	7594×	body	128	valid
153.0ms	228×	body	1024	valid
110.0ms	258×	body	512	valid
45.0ms	176×	body	256	valid
11.0ms	76×	body	128	invalid

Compiler

Compiled 24 to 18 computations (25% saved)

preprocess38.0ms (0.7%)

Algorithm

2×	egg-herbie

Rules

732×	`times-frac_binary64`
438×	`associate-/r/_binary64`
300×	`fma-def_binary64`
232×	`unswap-sqr_binary64`
157×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	32	22
2	45	22
3	71	22
4	101	22
5	150	22
6	231	22
7	320	22
8	425	22
9	543	22
10	635	22
11	675	22
12	823	22
13	1264	22
14	2823	22
0	2	2

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 11 to 8 computations (27.3% saved)

simplify35.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

369×	`times-frac_binary64`
363×	`associate-l_binary64`
285×	`associate-/l/_binary64`
280×	`associate-/l*_binary64`
262×	`associate-/r*_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	19	11
2	30	11
3	47	11
4	66	11
5	100	11
6	154	11
7	205	11
8	273	11
9	352	11
10	414	11
11	440	11
12	519	11
13	747	11
14	1549	11
15	4642	11

Stop Event

1×	node limit

Counts

1 → 2

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

Compiler

Compiled 36 to 22 computations (38.9% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	0.2b	(log1p.f64 (exp.f64 x))

series230.0ms (4.1%)

Counts

2 → 36

Calls

9 calls:

99.0ms	(log1p.f64 (exp.f64 x))	x	inf
67.0ms	(log1p.f64 (exp.f64 x))	x	-inf
18.0ms	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))	y	0
13.0ms	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))	x	inf
11.0ms	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))	x	-inf

rewrite66.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

733×	`expm1-log1p-u_binary64`
732×	`log1p-expm1-u_binary64`
659×	`prod-diff_binary64`
111×	`egg-rr`
76×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	147	16
2	1998	16

Stop Event

1×	node limit

Counts

2 → 111

simplify44.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

537×	`fma-def_binary64`
237×	`distribute-lft-out_binary64`
196×	`sub-neg_binary64`
194×	`*-commutative_binary64`
188×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	30	356
1	81	350
2	201	337
3	652	321
4	2594	321
5	4861	321

Stop Event

1×	node limit

Counts

147 → 130

prune71.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	128	2	130
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	128	3	131

Error

0.2b

Counts

131 → 3

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
	11.3b	(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))
▶	9.4b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))

Compiler

Compiled 2842 to 864 computations (69.6% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))

series12.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

3.0ms	(fma.f64 x (-.f64 1/2 y) (log.f64 2))	y	-inf
2.0ms	(fma.f64 x (-.f64 1/2 y) (log.f64 2))	x	0
2.0ms	(fma.f64 x (-.f64 1/2 y) (log.f64 2))	y	0
2.0ms	(fma.f64 x (-.f64 1/2 y) (log.f64 2))	y	inf
2.0ms	(fma.f64 x (-.f64 1/2 y) (log.f64 2))	x	-inf

rewrite37.0ms (0.6%)

Algorithm

1×	batch-egg-rewrite

Rules

775×	`log1p-expm1-u_binary64`
775×	`expm1-log1p-u_binary64`
117×	`prod-diff_binary64`
84×	`add-sqr-sqrt_binary64`
80×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	170	10
2	2008	10

Stop Event

1×	node limit

Counts

1 → 23

simplify30.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

336×	`fma-def_binary64`
260×	`fma-neg_binary64`
76×	`cancel-sign-sub-inv_binary64`
51×	`sub-neg_binary64`
41×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	17	308
1	40	252
2	85	216
3	161	216
4	287	216
5	436	216
6	659	216
7	970	216
8	1247	216
9	1272	216
10	1273	216

Stop Event

1×

saturated

Counts

47 → 33

prune31.0ms (0.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	33	3	36

Error

0.2b

Counts

36 → 3

Alt Table

Status	Error	Program
	17.1b	(/.f64 (-.f64 (.f64 (.f64 x (-.f64 1/2 y)) (.f64 x (-.f64 1/2 y))) (pow.f64 (log.f64 2) 2)) (-.f64 (.f64 x (-.f64 1/2 y)) (log.f64 2)))
✓	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
▶	11.3b	(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))

Compiler

Compiled 436 to 335 computations (23.2% saved)

localize11.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))

series10.0ms (0.2%)

Counts

1 → 24

Calls

6 calls:

2.0ms	(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))	y	0
2.0ms	(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))	y	inf
2.0ms	(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))	y	-inf
1.0ms	(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))	x	0
1.0ms	(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))	x	-inf

rewrite44.0ms (0.8%)

Algorithm

1×	batch-egg-rewrite

Rules

423×	`prod-diff_binary64`
409×	`log-prod_binary64`
225×	`fma-def_binary64`
181×	`expm1-udef_binary64`
180×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	14
1	208	14
2	2466	14

Stop Event

1×	node limit

Counts

1 → 27

simplify29.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

716×	`fma-neg_binary64`
547×	`cancel-sign-sub-inv_binary64`
410×	`fma-def_binary64`
238×	`associate-l_binary64`
223×	`distribute-rgt-neg-in_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	19	424
1	49	370
2	109	349
3	286	282
4	825	282
5	2321	282

Stop Event

1×	node limit

Counts

51 → 40

prune27.0ms (0.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	40	0	40
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	40	3	43

Error

0.2b

Counts

43 → 3

Alt Table

Status	Error	Program
▶	17.1b	(/.f64 (-.f64 (.f64 (.f64 x (-.f64 1/2 y)) (.f64 x (-.f64 1/2 y))) (pow.f64 (log.f64 2) 2)) (-.f64 (.f64 x (-.f64 1/2 y)) (log.f64 2)))
✓	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	11.3b	(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))

Compiler

Compiled 656 to 491 computations (25.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (.f64 (.f64 x (-.f64 1/2 y)) (*.f64 x (-.f64 1/2 y))) (pow.f64 (log.f64 2) 2))
✓	0.2b	(.f64 (.f64 x (-.f64 1/2 y)) (*.f64 x (-.f64 1/2 y)))
✓	1.0b	(pow.f64 (log.f64 2) 2)
✓	13.2b	(/.f64 (-.f64 (.f64 (.f64 x (-.f64 1/2 y)) (.f64 x (-.f64 1/2 y))) (pow.f64 (log.f64 2) 2)) (-.f64 (.f64 x (-.f64 1/2 y)) (log.f64 2)))

series79.0ms (1.4%)

Counts

4 → 72

Calls

18 calls:

11.0ms	(/.f64 (-.f64 (.f64 (.f64 x (-.f64 1/2 y)) (.f64 x (-.f64 1/2 y))) (pow.f64 (log.f64 2) 2)) (-.f64 (.f64 x (-.f64 1/2 y)) (log.f64 2)))	y	0
9.0ms	(/.f64 (-.f64 (.f64 (.f64 x (-.f64 1/2 y)) (.f64 x (-.f64 1/2 y))) (pow.f64 (log.f64 2) 2)) (-.f64 (.f64 x (-.f64 1/2 y)) (log.f64 2)))	x	inf
8.0ms	(/.f64 (-.f64 (.f64 (.f64 x (-.f64 1/2 y)) (.f64 x (-.f64 1/2 y))) (pow.f64 (log.f64 2) 2)) (-.f64 (.f64 x (-.f64 1/2 y)) (log.f64 2)))	x	-inf
6.0ms	(/.f64 (-.f64 (.f64 (.f64 x (-.f64 1/2 y)) (.f64 x (-.f64 1/2 y))) (pow.f64 (log.f64 2) 2)) (-.f64 (.f64 x (-.f64 1/2 y)) (log.f64 2)))	y	inf
6.0ms	(/.f64 (-.f64 (.f64 (.f64 x (-.f64 1/2 y)) (.f64 x (-.f64 1/2 y))) (pow.f64 (log.f64 2) 2)) (-.f64 (.f64 x (-.f64 1/2 y)) (log.f64 2)))	y	-inf

rewrite74.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

265×	`expm1-udef_binary64`
264×	`log1p-udef_binary64`
149×	`add-sqr-sqrt_binary64`
149×	`log1p-expm1-u_binary64`
149×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	66
1	307	44
2	4445	44

Stop Event

1×	node limit

Counts

4 → 121

simplify59.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

256×	`cancel-sign-sub-inv_binary64`
238×	`sub-neg_binary64`
225×	`associate-+r+_binary64`
216×	`times-frac_binary64`
212×	`distribute-neg-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	208	2885
1	721	2627
2	3215	2494

Stop Event

1×	node limit

Counts

193 → 170

prune156.0ms (2.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	170	3	173

Error

0.2b

Counts

173 → 3

Alt Table

Status	Error	Program
	57.9b	(/.f64 (.f64 (-.f64 (+.f64 1/4 (pow.f64 y 2)) y) (pow.f64 x 2)) (-.f64 (.f64 x (-.f64 1/2 y)) (log.f64 2)))
✓	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	11.3b	(fma.f64 x (-.f64 (fma.f64 x 1/8 1/2) y) (log.f64 2))

Compiler

Compiled 5896 to 4674 computations (20.7% saved)

regimes98.0ms (1.7%)

Accuracy

Total 0.2b remaining (46.7%)

Threshold costs 0.2b (46.7%)

Counts

33 → 1

Compiler

Compiled 1415 to 1111 computations (21.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	13	11
2	25	11
3	31	11
4	35	11
5	36	11

Stop Event

1×

saturated

end60.0ms (1.1%)

Stop Event

1×

fuel

Compiler

Compiled 61 to 44 computations (27.9% saved)

Details

analyze476.0ms (8.4%)

sample3.9s (69.1%)

preprocess38.0ms (0.7%)

simplify35.0ms (0.6%)

prune3.0ms (0%)

localize5.0ms (0.1%)

series230.0ms (4.1%)

rewrite66.0ms (1.2%)

simplify44.0ms (0.8%)

prune71.0ms (1.3%)

localize5.0ms (0.1%)

series12.0ms (0.2%)

rewrite37.0ms (0.6%)

simplify30.0ms (0.5%)

prune31.0ms (0.5%)

localize11.0ms (0.2%)

series10.0ms (0.2%)

rewrite44.0ms (0.8%)

simplify29.0ms (0.5%)

prune27.0ms (0.5%)

localize10.0ms (0.2%)

series79.0ms (1.4%)

rewrite74.0ms (1.3%)

simplify59.0ms (1.1%)

prune156.0ms (2.8%)

regimes98.0ms (1.7%)

simplify3.0ms (0.1%)

end60.0ms (1.1%)

Profiling