Details

analyze2.8s (20.9%)

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)

sample8.5s (64.4%)

Symmetry

(sort a b)

Results

5.0s	4177×	body	2048	valid
1.9s	2472×	body	1024	valid
375.0ms	576×	body	1024	invalid
361.0ms	720×	body	512	valid
310.0ms	353×	body	2048	invalid
153.0ms	317×	body	512	invalid
121.0ms	602×	body	128	valid
86.0ms	268×	body	256	valid
54.0ms	314×	body	128	invalid
48.0ms	163×	body	256	invalid
30.0ms	17×	body	4096	valid

Compiler

Compiled 95 to 67 computations (29.5% saved)

simplify24.0ms (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

prune5.0ms (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

41.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	41.7b	(/.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 a))
✓	0.0b	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
✓	0.1b	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
✓	39.8b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series445.0ms (3.4%)

Counts

4 → 132

Calls

4 calls:

378.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
31.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
29.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
6.0ms	(expm1.f64 (*.f64 eps a))

rewrite17.0ms (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:

5.0ms	(.f64 eps (expm1.f64 (.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)))
0.0ms	(expm1.f64 (*.f64 eps a))

simplify127.0ms (1%)

Algorithm

1×	egg-herbie

Rules

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

Counts

206 → 213

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	613	8300
1	2021	7554
2	5057	7554

prune151.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	210	3	213
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	210	4	214

Error

0.0b

Counts

214 → 4

Alt Table

Status	Error	Program
	41.6b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))
	16.6b	(/.f64 (+.f64 a b) (*.f64 a b))
✓	41.7b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
▶	7.6b	(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))))

Compiler

Compiled 10528 to 3502 computations (66.7% 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))))
✓	0.1b	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
✓	5.6b	(.f64 b (.f64 eps eps))
✓	7.5b	(.f64 a (.f64 eps eps))

series72.0ms (0.5%)

Counts

4 → 120

Calls

4 calls:

31.0ms	(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))))
22.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
10.0ms	(.f64 a (.f64 eps eps))
9.0ms	(.f64 b (.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 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 (0.7%)

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

prune83.0ms (0.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	1	1	2
Picked	1	0	1
Done	0	1	1
Total	122	4	126

Error

0.0b

Counts

126 → 4

Alt Table

Status	Error	Program
	50.7b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (.f64 (sqrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))) (sqrt.f64 (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))))
✓	41.7b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
▶	4.7b	(+.f64 (/.f64 1 b) (/.f64 1 a))
	16.6b	(/.f64 (+.f64 a b) (*.f64 a b))

Compiler

Compiled 3125 to 1519 computations (51.4% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0%)

Counts

1 → 6

Calls

1 calls:

6.0ms

(+.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))

simplify118.0ms (0.9%)

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 → 37

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	37	0	37
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	37	4	41

Error

0.0b

Counts

41 → 4

Alt Table

Status	Error	Program
	50.7b	(fma.f64 1/12 (.f64 a (.f64 eps eps)) (+.f64 (/.f64 1 b) (.f64 (sqrt.f64 (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))) (sqrt.f64 (fma.f64 1/12 (.f64 b (*.f64 eps eps)) (/.f64 1 a))))))
✓	41.7b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
✓	4.7b	(+.f64 (/.f64 1 b) (/.f64 1 a))
▶	16.6b	(/.f64 (+.f64 a b) (*.f64 a b))

Compiler

Compiled 642 to 461 computations (28.2% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	16.2b	(/.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))

simplify84.0ms (0.6%)

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

prune23.0ms (0.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	34	3	37

Error

Counts

37 → 3

Alt Table

Status	Error	Program
✓	41.7b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
✓	4.7b	(+.f64 (/.f64 1 b) (/.f64 1 a))
	11.0b	(/.f64 (/.f64 (+.f64 a b) a) b)

Compiler

Compiled 467 to 150 computations (67.9% saved)

regimes356.0ms (2.7%)

Accuracy

Total 0.3b remaining (92.2%)

Threshold costs 0.3b (92.2%)

Counts

48 → 3

Compiler

Compiled 3490 to 2228 computations (36.2% saved)

bsearch2.0ms (0%)

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

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	135
1	53	135
2	56	135
3	54	135

end241.0ms (1.8%)

Compiler: Compiled 405 to 223 computations (44.9% saved)

Details

analyze2.8s (20.9%)

sample8.5s (64.4%)

simplify24.0ms (0.2%)

prune5.0ms (0%)

localize13.0ms (0.1%)

series445.0ms (3.4%)

rewrite17.0ms (0.1%)

simplify127.0ms (1%)

prune151.0ms (1.1%)

localize12.0ms (0.1%)

series72.0ms (0.5%)

rewrite12.0ms (0.1%)

simplify94.0ms (0.7%)

prune83.0ms (0.6%)

localize4.0ms (0%)

series6.0ms (0%)

rewrite13.0ms (0.1%)

simplify118.0ms (0.9%)

prune24.0ms (0.2%)

localize4.0ms (0%)

series7.0ms (0.1%)

rewrite6.0ms (0%)

simplify84.0ms (0.6%)

prune23.0ms (0.2%)

regimes356.0ms (2.7%)

bsearch2.0ms (0%)

simplify4.0ms (0%)

end241.0ms (1.8%)

Profiling