Details

analyze2.2s (16.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	49.3%	50.3%	10
0.6%	48.9%	50.5%	11
1.1%	48.1%	50.9%	12
1.5%	47.3%	51.2%	13
1.7%	46.9%	51.5%	14

Compiler

Compiled 34 to 24 computations (29.4% saved)

sample8.1s (62.6%)

Results

4.9s	4211×	body	2048	valid
1.8s	2477×	body	1024	valid
361.0ms	575×	body	1024	invalid
333.0ms	724×	body	512	valid
331.0ms	375×	body	2048	invalid
166.0ms	293×	body	512	invalid
101.0ms	551×	body	128	valid
89.0ms	282×	body	256	valid
44.0ms	280×	body	128	invalid
43.0ms	140×	body	256	invalid
18.0ms	11×	body	4096	valid

Compiler

Compiled 68 to 48 computations (29.4% saved)

preprocess50.0ms (0.4%)

Algorithm

2×	egg-herbie

Rules

333×	`div-sub_binary64`
265×	`fma-neg_binary64`
234×	`unswap-sqr_binary64`
205×	`associate-/l*_binary64`
191×	`associate-l_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	112
1	146	112
2	314	112
3	789	112
4	3415	112
0	3	3
1	3	3

Stop Event

1×	unsound
1×	node limit

Symmetry

(sort a b)

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify17.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

986×	`times-frac_binary64`
580×	`associate-/l*_binary64`
372×	`fma-def_binary64`
125×	`distribute-rgt-in_binary64`
122×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	47	28
2	108	28
3	271	28
4	989	28

Stop Event

1×	node limit

Counts

1 → 2

prune6.0ms (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

30.4b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	30.4b	(.f64 eps (/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (.f64 eps b))))

Compiler

Compiled 87 to 54 computations (37.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 eps (+.f64 a b))
✓	0.8b	(/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (*.f64 eps b)))
✓	12.3b	(/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a)))
✓	28.1b	(.f64 eps (/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (.f64 eps b))))

series387.0ms (3%)

Counts

4 → 132

Calls

36 calls:

44.0ms	(.f64 eps (/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (.f64 eps b))))	eps
31.0ms	(.f64 eps (/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (.f64 eps b))))	a
31.0ms	(.f64 eps (/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (.f64 eps b))))	b
30.0ms	(/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (*.f64 eps b)))	a
30.0ms	(/.f64 (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))) (expm1.f64 (*.f64 eps b)))	b

rewrite85.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

898×	`prod-diff_binary64`
151×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`
143×	`expm1-log1p-u_binary64`
139×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	77
1	300	77
2	4272	77

Stop Event

1×	node limit

Counts

4 → 129

simplify112.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

684×	`times-frac_binary64`
671×	`fma-def_binary64`
610×	`associate-/l*_binary64`
233×	`*-commutative_binary64`
213×	`+-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	655	9041
1	2314	8400

Stop Event

1×	node limit

Counts

261 → 212

prune186.0ms (1.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	208	4	212
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	209	4	213

Error

Counts

213 → 4

Alt Table

Status	Error	Program
▶	7.1b	(+.f64 (fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b)) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
	29.5b	(/.f64 1 (/.f64 (expm1.f64 (.f64 eps b)) (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))))))
	29.6b	(.f64 (/.f64 eps (expm1.f64 (.f64 a eps))) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (.f64 b eps))))
	40.7b	(.f64 eps (/.f64 (+.f64 a b) (.f64 eps (*.f64 a b))))

Compiler

Compiled 12874 to 4672 computations (63.7% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
✓	0.1b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b))
✓	6.7b	(.f64 a (.f64 eps eps))
✓	8.8b	(.f64 b (.f64 eps eps))

series50.0ms (0.4%)

Counts

4 → 120

Calls

30 calls:

3.0ms	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b))	eps	-inf
3.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))	b	-inf
3.0ms	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b))	a	-inf
2.0ms	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b))	a	0
2.0ms	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b))	a	inf

rewrite54.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

625×	`log-prod_binary64`
227×	`expm1-udef_binary64`
227×	`log1p-udef_binary64`
209×	`log-pow_binary64`
188×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	42
1	267	42
2	3209	42

Stop Event

1×	node limit

Counts

4 → 94

simplify139.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

603×	`sqr-pow_binary64`
417×	`associate-l_binary64`
364×	`*-commutative_binary64`
330×	`fabs-mul_binary64`
312×	`cube-prod_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	16	1290
1	32	1236
2	65	1236
3	147	1236
4	384	1236
5	1224	1236
6	1654	1236
7	2076	1236
8	2176	1236
9	2324	1236
10	2498	1236
11	2749	1236
12	3070	1236
13	3440	1236
14	3894	1236
15	4475	1236

Stop Event

1×	node limit

Counts

214 → 108

prune78.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	109	3	112

Error

Counts

112 → 3

Alt Table

Status	Error	Program
	29.6b	(.f64 (/.f64 eps (expm1.f64 (.f64 a eps))) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (.f64 b eps))))
	29.5b	(/.f64 1 (/.f64 (expm1.f64 (.f64 eps b)) (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))))))
▶	5.6b	(+.f64 (fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b)) (/.f64 1 a))

Compiler

Compiled 2953 to 1507 computations (49% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b)) (/.f64 1 a))
	0.1b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b))
	6.7b	(.f64 a (.f64 eps eps))

series19.0ms (0.1%)

Counts

1 → 36

Calls

9 calls:

3.0ms	(+.f64 (fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b)) (/.f64 1 a))	b	-inf
2.0ms	(+.f64 (fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b)) (/.f64 1 a))	b	inf
2.0ms	(+.f64 (fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b)) (/.f64 1 a))	b	0
2.0ms	(+.f64 (fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b)) (/.f64 1 a))	a	-inf
2.0ms	(+.f64 (fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b)) (/.f64 1 a))	eps	0

rewrite47.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

641×	`prod-diff_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
126×	`add-sqr-sqrt_binary64`
119×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	20
1	255	20
2	3236	20

Stop Event

1×	node limit

Counts

1 → 35

simplify90.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

599×	`sqr-pow_binary64`
404×	`fabs-mul_binary64`
386×	`cube-prod_binary64`
274×	`pow-sqr_binary64`
259×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	604
1	34	604
2	61	604
3	118	604
4	276	604
5	829	604
6	1229	604
7	1655	604
8	1755	604
9	1890	604
10	2062	604
11	2305	604
12	2618	604
13	2988	604
14	3445	604
15	4026	604
16	4738	604

Stop Event

1×	node limit

Counts

71 → 47

prune75.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	101	0	101
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	101	3	104

Error

Counts

104 → 3

Alt Table

Status	Error	Program
	29.6b	(.f64 (/.f64 eps (expm1.f64 (.f64 a eps))) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (.f64 b eps))))
▶	29.5b	(/.f64 1 (/.f64 (expm1.f64 (.f64 eps b)) (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))))))
✓	5.6b	(+.f64 (fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b)) (/.f64 1 a))

Compiler

Compiled 2161 to 1251 computations (42.1% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(*.f64 eps (+.f64 a b))
✓	6.4b	(.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (*.f64 eps a))))
	12.3b	(/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a)))
✓	14.6b	(/.f64 (expm1.f64 (.f64 eps b)) (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a)))))

series212.0ms (1.6%)

Counts

2 → 72

Calls

18 calls:

50.0ms	(/.f64 (expm1.f64 (.f64 eps b)) (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a)))))	eps	0
21.0ms	(/.f64 (expm1.f64 (.f64 eps b)) (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a)))))	a	0
20.0ms	(/.f64 (expm1.f64 (.f64 eps b)) (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a)))))	b	0
15.0ms	(.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (*.f64 eps a))))	eps	0
12.0ms	(/.f64 (expm1.f64 (.f64 eps b)) (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a)))))	eps	-inf

rewrite71.0ms (0.5%)

Algorithm

1×	batch-egg-rewrite

Rules

907×	`prod-diff_binary64`
151×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`
143×	`expm1-log1p-u_binary64`
139×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	48
1	300	48
2	4284	48

Stop Event

1×	node limit

Counts

2 → 69

simplify71.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

567×	`associate-/l*_binary64`
533×	`times-frac_binary64`
417×	`fma-def_binary64`
320×	`associate-/r*_binary64`
210×	`*-commutative_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	541	5528
1	1856	5499

Stop Event

1×	node limit

Counts

141 → 122

prune165.0ms (1.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	213	0	213
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	213	3	216

Error

Counts

216 → 3

Alt Table

Status	Error	Program
	29.6b	(.f64 (/.f64 eps (expm1.f64 (.f64 a eps))) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (.f64 b eps))))
✓	29.5b	(/.f64 1 (/.f64 (expm1.f64 (.f64 eps b)) (.f64 eps (/.f64 (expm1.f64 (.f64 eps (+.f64 a b))) (expm1.f64 (.f64 eps a))))))
✓	5.6b	(+.f64 (fma.f64 1/12 (.f64 a (.f64 eps eps)) (/.f64 1 b)) (/.f64 1 a))

Compiler

Compiled 10885 to 4623 computations (57.5% saved)

regimes464.0ms (3.6%)

Accuracy

Total 0.4b remaining (94.3%)

Threshold costs 0.4b (94.3%)

Counts

89 → 3

Compiler

Compiled 6874 to 4520 computations (34.2% saved)

bsearch3.0ms (0%)

Algorithm

2×	left-value

Calls

2 calls:

0.0ms

(/.f64 (*.f64 eps (-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)) (*.f64 (-.f64 (exp.f64 (*.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1)))

0.0ms

(/.f64 (*.f64 eps (-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)) (*.f64 (-.f64 (exp.f64 (*.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1)))

Steps

Iters	Point		Range
8.379449481345716e-23	∈ [	8.379449481345716e-23	,	#hash((type . real) (value . +inf))	]
#hash((type . real) (value . -inf))	∈ [	#hash((type . real) (value . -inf))	,	-1.3010421935607938e-16	]

Compiler

Compiled 27 to 19 computations (29.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

7×	`*-commutative_binary64`
5×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	138
1	57	138
2	60	138

Stop Event

1×

saturated

end222.0ms (1.7%)

Stop Event

1×

fuel

Compiler

Compiled 433 to 244 computations (43.6% saved)

Details

analyze2.2s (16.9%)

sample8.1s (62.6%)

preprocess50.0ms (0.4%)

simplify17.0ms (0.1%)

prune6.0ms (0%)

localize11.0ms (0.1%)

series387.0ms (3%)

rewrite85.0ms (0.7%)

simplify112.0ms (0.9%)

prune186.0ms (1.4%)

localize11.0ms (0.1%)

series50.0ms (0.4%)

rewrite54.0ms (0.4%)

simplify139.0ms (1.1%)

prune78.0ms (0.6%)

localize8.0ms (0.1%)

series19.0ms (0.1%)

rewrite47.0ms (0.4%)

simplify90.0ms (0.7%)

prune75.0ms (0.6%)

localize20.0ms (0.2%)

series212.0ms (1.6%)

rewrite71.0ms (0.5%)

simplify71.0ms (0.5%)

prune165.0ms (1.3%)

regimes464.0ms (3.6%)

bsearch3.0ms (0%)

simplify3.0ms (0%)

end222.0ms (1.7%)

Profiling