Details

analyze2.6s (21.8%)

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)

sample232.0ms (2%)

Algorithm

1×

intervals

Results

142.0ms	156×	body	2048	valid
30.0ms	66×	body	1024	valid
8.0ms	19×	body	1024	overflowed
7.0ms	305×	pre	128	true
5.0ms	10×	body	2048	overflowed
4.0ms	14×	body	512	valid
1.0ms	7×	body	256	valid
1.0ms	5×	body	512	overflowed
1.0ms	13×	body	128	valid
1.0ms	11×	body	128	overflowed
1.0ms	4×	body	256	overflowed

Compiler

Compiled 64 to 46 computations (28.1% saved)

simplify31.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	28
1	47	28
2	108	28
3	254	28
4	897	28
5	5292	28

prune4.0ms (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

45.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	45.6b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

Compiler

Compiled 87 to 54 computations (37.9% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 eps (+.f64 a b)))
✓	0.0b	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
✓	0.1b	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
✓	43.4b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-cbrt-cube_binary64`
20×	`add-exp-log_binary64`
12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`

Counts

4 → 74

Calls

4 calls:

4.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
3.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
3.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
0.0ms	(expm1.f64 (*.f64 eps (+.f64 a b)))

series495.0ms (4.2%)

Counts

4 → 144

Calls

4 calls:

386.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
50.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
41.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
16.0ms	(expm1.f64 (*.f64 eps (+.f64 a b)))

simplify156.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

828×	`fma-def_binary64`
622×	`times-frac_binary64`
470×	`associate-/l*_binary64`
249×	`*-commutative_binary64`
191×	`+-commutative_binary64`

Counts

218 → 424

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	646	8872
1	2166	8105
2	5325	8105

prune157.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	421	3	424
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	421	4	425

Error

0.0b

Counts

425 → 4

Alt Table

Status	Error	Program
▶	4.8b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
	45.5b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))
	14.7b	(/.f64 (+.f64 a b) (*.f64 a b))
✓	45.6b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

Compiler

Compiled 11305 to 3830 computations (66.1% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
✓	0.0b	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
✓	5.0b	(.f64 b (.f64 eps eps))
✓	6.5b	(.f64 a (.f64 eps eps))

rewrite12.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`
8×	`add-sqr-sqrt_binary64`
6×	`associate-l_binary64`

Counts

4 → 62

Calls

4 calls:

5.0ms	(.f64 a (.f64 eps eps))
4.0ms	(.f64 b (.f64 eps eps))
0.0ms	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
0.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))

series174.0ms (1.5%)

Counts

4 → 120

Calls

4 calls:

71.0ms	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))))
50.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
28.0ms	(.f64 a (.f64 eps eps))
25.0ms	(.f64 b (.f64 eps eps))

simplify115.0ms (1%)

Algorithm

1×	egg-herbie

Rules

766×	`unswap-sqr_binary64`
610×	`fma-def_binary64`
470×	`associate-l_binary64`
333×	`associate-r_binary64`
295×	`associate-+r+_binary64`

Counts

182 → 349

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	103	2698
1	202	2339
2	549	2269
3	1651	2269
4	3788	2269
5	5058	2269

prune86.0ms (0.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	347	2	349
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	349	4	353

Error

0.0b

Counts

353 → 4

Alt Table

Status	Error	Program
	45.5b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))
✓	45.6b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
	34.5b	(.f64 (sqrt.f64 (fma.f64 eps (.f64 (+.f64 a b) (.f64 eps 1/12)) (+.f64 (/.f64 1 a) (/.f64 1 b)))) (sqrt.f64 (fma.f64 eps (.f64 (+.f64 a b) (*.f64 eps 1/12)) (+.f64 (/.f64 1 a) (/.f64 1 b)))))
▶	2.7b	(+.f64 (/.f64 1 b) (/.f64 1 a))

Compiler

Compiled 3170 to 1552 computations (51% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 b) (/.f64 1 a))

rewrite13.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
15×	`times-frac_binary64`
13×	`fma-def_binary64`
10×	`add-sqr-sqrt_binary64`
10×	`add-cube-cbrt_binary64`

Counts

1 → 34

Calls

1 calls:

11.0ms

(+.f64 (/.f64 1 b) (/.f64 1 a))

series12.0ms (0.1%)

Counts

1 → 6

Calls

1 calls:

12.0ms

(+.f64 (/.f64 1 b) (/.f64 1 a))

simplify128.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

450×	`fma-neg_binary64`
421×	`div-sub_binary64`
357×	`fma-def_binary64`
329×	`sub-neg_binary64`
281×	`distribute-rgt-in_binary64`

Counts

40 → 47

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	36	332
1	106	302
2	241	301
3	565	301
4	1313	301
5	2794	301
6	4202	301
7	4546	301
8	4845	301
9	4973	301
10	4870	301

prune24.0ms (0.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	46	1	47
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	47	4	51

Error

0.0b

Counts

51 → 4

Alt Table

Status	Error	Program
	45.5b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))
▶	33.5b	(*.f64 (sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
✓	45.6b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
✓	2.7b	(+.f64 (/.f64 1 b) (/.f64 1 a))

Compiler

Compiled 634 to 467 computations (26.3% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 (/.f64 1 b) (/.f64 1 a))
	0.1b	(sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
✓	0.1b	(sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
✓	0.2b	(*.f64 (sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))

rewrite59.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

117×	`*-un-lft-identity_binary64`
96×	`sqrt-prod_binary64`
67×	`distribute-lft-out_binary64`
62×	`add-sqr-sqrt_binary64`
52×	`div-inv_binary64`

Counts

2 → 143

Calls

2 calls:

30.0ms	(*.f64 (sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
18.0ms	(sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

series27.0ms (0.2%)

Counts

2 → 40

Calls

2 calls:

14.0ms	(sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
13.0ms	(*.f64 (sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))

simplify152.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

404×	`fma-neg_binary64`
367×	`distribute-rgt-in_binary64`
348×	`distribute-lft-in_binary64`
339×	`associate-l_binary64`
287×	`associate-r_binary64`

Counts

183 → 312

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	143	3141
1	313	2824
2	856	2724
3	2714	2674
4	4927	2674
5	4998	2674

prune155.0ms (1.3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	434	1	435
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	434	5	439

Error

Counts

439 → 5

Alt Table

Status	Error	Program
	33.9b	(*.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))) 4) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
	45.5b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))
✓	33.5b	(*.f64 (sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (sqrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
✓	45.6b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
✓	2.7b	(+.f64 (/.f64 1 b) (/.f64 1 a))

Compiler

Compiled 5966 to 4526 computations (24.1% saved)

regimes219.0ms (1.8%)

Accuracy

Total 0.0b remaining (61.6%)

Threshold costs 0.0b (61.6%)

Compiler

Compiled 4782 to 3024 computations (36.8% saved)

bsearch2.0ms (0%)

Compiler: Compiled 27 to 19 computations (29.6% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

8×	`*-commutative_binary64`
6×	`+-commutative_binary64`
3×	`sub-neg_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	152
1	59	152
2	62	152
3	60	152

end10.0ms (0.1%)

Compiler: Compiled 309 to 171 computations (44.7% saved)

sample7.0s (58.7%)

Algorithm

1×

intervals

Results

3.7s	4122×	body	2048	valid
1.2s	2396×	body	1024	valid
283.0ms	402×	body	2048	overflowed
239.0ms	595×	body	1024	overflowed
224.0ms	680×	body	512	valid
216.0ms	9728×	pre	128	true
75.0ms	287×	body	512	overflowed
54.0ms	275×	body	256	valid
50.0ms	516×	body	128	valid
29.0ms	143×	body	256	overflowed
29.0ms	298×	body	128	overflowed
18.0ms	11×	body	4096	valid
3.0ms	3×	body	2048	invalid

Compiler

Compiled 237 to 155 computations (34.6% saved)

Details

analyze2.6s (21.8%)

sample232.0ms (2%)

simplify31.0ms (0.3%)

prune4.0ms (0%)

localize13.0ms (0.1%)

rewrite14.0ms (0.1%)

series495.0ms (4.2%)

simplify156.0ms (1.3%)

prune157.0ms (1.3%)

localize12.0ms (0.1%)

rewrite12.0ms (0.1%)

series174.0ms (1.5%)

simplify115.0ms (1%)

prune86.0ms (0.7%)

localize6.0ms (0.1%)

rewrite13.0ms (0.1%)

series12.0ms (0.1%)

simplify128.0ms (1.1%)

prune24.0ms (0.2%)

localize9.0ms (0.1%)

rewrite59.0ms (0.5%)

series27.0ms (0.2%)

simplify152.0ms (1.3%)

prune155.0ms (1.3%)

regimes219.0ms (1.8%)

bsearch2.0ms (0%)

simplify5.0ms (0%)

end10.0ms (0.1%)

sample7.0s (58.7%)

Profiling