Details

analyze2.6s (21.1%)

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)

sample8.5s (68.5%)

Symmetry

(sort a b)

Results

5.1s	4179×	body	2048	valid
1.7s	2453×	body	1024	valid
361.0ms	782×	body	512	valid
354.0ms	576×	body	1024	invalid
314.0ms	379×	body	2048	invalid
301.0ms	305×	body	512	invalid
95.0ms	557×	body	128	valid
84.0ms	267×	body	256	valid
47.0ms	278×	body	128	invalid
38.0ms	137×	body	256	invalid
30.0ms	18×	body	4096	valid

Compiler

Compiled 95 to 67 computations (29.5% saved)

simplify23.0ms (0.2%)

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

42.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	42.9b	(/.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)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 eps (+.f64 a b))
✓	0.1b	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
✓	0.3b	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
✓	41.2b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series230.0ms (1.9%)

Counts

4 → 132

Calls

4 calls:

179.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
24.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
21.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
7.0ms	(*.f64 eps (+.f64 a b))

rewrite19.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-cbrt-cube_binary64`
22×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
10×	`associate-r_binary64`

Counts

4 → 88

Calls

4 calls:

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

simplify124.0ms (1%)

Algorithm

1×	egg-herbie

Rules

712×	`fma-def_binary64`
622×	`times-frac_binary64`
470×	`associate-/l*_binary64`
257×	`*-commutative_binary64`
166×	`+-commutative_binary64`

Counts

220 → 226

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	638	8331
1	2107	7574
2	5317	7574

prune166.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	224	2	226
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	224	3	227

Error

Counts

227 → 3

Alt Table

Status	Error	Program
▶	4.7b	(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))))
	13.7b	(/.f64 (+.f64 a b) (*.f64 a b))
✓	42.9b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

Compiler

Compiled 10714 to 3505 computations (67.3% saved)

localize14.0ms (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))
✓	6.5b	(.f64 a (.f64 eps eps))
✓	6.5b	(.f64 b (.f64 eps eps))

series60.0ms (0.5%)

Counts

4 → 120

Calls

4 calls:

26.0ms	(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))))
19.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
7.0ms	(.f64 b (.f64 eps eps))
7.0ms	(.f64 a (.f64 eps eps))

rewrite11.0ms (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:

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

simplify94.0ms (0.8%)

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 → 122

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

prune91.0ms (0.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	122	3	125

Error

Counts

125 → 3

Alt Table

Status	Error	Program
✓	4.7b	(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))))
▶	13.7b	(/.f64 (+.f64 a b) (*.f64 a b))
✓	42.9b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

Compiler

Compiled 3055 to 1474 computations (51.8% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	12.7b	(/.f64 (+.f64 a b) (*.f64 a b))

series7.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

7.0ms

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

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`*-un-lft-identity_binary64`
6×	`add-cbrt-cube_binary64`
6×	`add-exp-log_binary64`
4×	`associate-/l*_binary64`
4×	`times-frac_binary64`

Counts

1 → 27

Calls

1 calls:

5.0ms

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

simplify83.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

581×	`associate-/r*_binary64`
450×	`sub-neg_binary64`
441×	`associate-/r/_binary64`
370×	`fma-def_binary64`
349×	`distribute-rgt-in_binary64`

Counts

51 → 33

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	57	613
1	152	550
2	469	550
3	1544	550
4	3494	550
5	3895	550
6	4902	550
7	5491	550

prune21.0ms (0.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	33	0	33
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	33	3	36

Error

Counts

36 → 3

Alt Table

Status	Error	Program
✓	4.7b	(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))))
✓	13.7b	(/.f64 (+.f64 a b) (*.f64 a b))
✓	42.9b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

Compiler

Compiled 481 to 157 computations (67.4% saved)

regimes221.0ms (1.8%)

Accuracy

Total 0.5b remaining (92.8%)

Threshold costs 0.5b (92.8%)

Counts

62 → 3

Compiler

Compiled 4594 to 2904 computations (36.8% saved)

bsearch2.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	132
1	49	132
2	52	132
3	50	132

end88.0ms (0.7%)

Remove: (sort a b)
Compiler: Compiled 411 to 234 computations (43.1% saved)

Details

analyze2.6s (21.1%)

sample8.5s (68.5%)

simplify23.0ms (0.2%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series230.0ms (1.9%)

rewrite19.0ms (0.2%)

simplify124.0ms (1%)

prune166.0ms (1.3%)

localize14.0ms (0.1%)

series60.0ms (0.5%)

rewrite11.0ms (0.1%)

simplify94.0ms (0.8%)

prune91.0ms (0.7%)

localize4.0ms (0%)

series7.0ms (0.1%)

rewrite6.0ms (0%)

simplify83.0ms (0.7%)

prune21.0ms (0.2%)

regimes221.0ms (1.8%)

bsearch2.0ms (0%)

simplify4.0ms (0%)

end88.0ms (0.7%)

Profiling