Details

analyze2.4s (17.7%)

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%	49.9%	50.1%	9
0%	49.7%	50.3%	10
0%	49.5%	50.5%	11
0.1%	49%	50.9%	12
0.2%	48.5%	51.2%	13
0.3%	48.3%	51.5%	14

Compiler

Compiled 34 to 24 computations (29.4% saved)

sample8.2s (62%)

Symmetry

(sort a b)

Results

4.9s	4227×	body	2048	valid
1.8s	2467×	body	1024	valid
370.0ms	620×	body	1024	invalid
360.0ms	721×	body	512	valid
336.0ms	374×	body	2048	invalid
119.0ms	269×	body	512	invalid
105.0ms	583×	body	128	valid
78.0ms	245×	body	256	valid
56.0ms	298×	body	128	invalid
50.0ms	148×	body	256	invalid
24.0ms	13×	body	4096	valid
2.0ms	1×	body	8192	exit

Compiler

Compiled 61 to 43 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

40.7b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	40.7b	(/.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)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 eps (+.f64 a b)))
✓	0.1b	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
✓	0.1b	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
✓	38.9b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series470.0ms (3.5%)

Counts

4 → 144

Calls

4 calls:

383.0ms	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))
34.0ms	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
34.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
18.0ms	(expm1.f64 (*.f64 eps (+.f64 a b)))

rewrite18.0ms (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 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
3.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
0.0ms	(expm1.f64 (*.f64 eps (+.f64 a b)))

simplify135.0ms (1%)

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 → 229

Iterations

Useful iterations: 1 (0.0ms)

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

prune168.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	225	4	229
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	226	4	230

Error

0.0b

Counts

230 → 4

Alt Table

Status	Error	Program
	28.0b	(/.f64 eps (/.f64 (expm1.f64 (.f64 a eps)) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))
	18.1b	(/.f64 (+.f64 a b) (*.f64 a b))
▶	6.9b	(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))))
	40.6b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))

Compiler

Compiled 11450 to 3855 computations (66.3% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.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))
✓	6.0b	(.f64 a (.f64 eps eps))
✓	6.4b	(.f64 b (.f64 eps eps))

series65.0ms (0.5%)

Counts

4 → 120

Calls

4 calls:

24.0ms	(+.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 b (.f64 eps eps))
9.0ms	(.f64 a (.f64 eps eps))

rewrite20.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
14×	`pow1_binary64`

Counts

4 → 81

Calls

4 calls:

6.0ms	(+.f64 (/.f64 1 b) (fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a)))
5.0ms	(.f64 a (.f64 eps eps))
4.0ms	(.f64 b (.f64 eps eps))
0.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))

simplify124.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

562×	`associate-+l+_binary64`
523×	`associate-l_binary64`
384×	`associate-r_binary64`
262×	`cancel-sign-sub-inv_binary64`
220×	`unswap-sqr_binary64`

Counts

201 → 131

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	105	2505
1	236	2362
2	656	2362
3	2257	2360
4	4524	2360
5	5001	2360

prune104.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	131	4	135

Error

0.0b

Counts

135 → 4

Alt Table

Status	Error	Program
	28.0b	(/.f64 eps (/.f64 (expm1.f64 (.f64 a eps)) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))
▶	18.1b	(/.f64 (+.f64 a b) (*.f64 a b))
✓	6.9b	(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))))
	40.6b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))

Compiler

Compiled 3651 to 1728 computations (52.7% saved)

localize4.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	18.3b	(/.f64 (+.f64 a b) (*.f64 a b))

series9.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

9.0ms

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

rewrite7.0ms (0.1%)

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))

simplify79.0ms (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

prune25.0ms (0.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

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

Error

0.0b

Counts

37 → 3

Alt Table

Status	Error	Program
✓	6.9b	(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))))
▶	9.6b	(/.f64 1 (/.f64 a (/.f64 (+.f64 a b) b)))
	40.6b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))

Compiler

Compiled 520 to 184 computations (64.6% saved)

localize6.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 a b) b)
✓	0.0b	(/.f64 1 (/.f64 a (/.f64 (+.f64 a b) b)))
✓	6.1b	(/.f64 a (/.f64 (+.f64 a b) b))

series26.0ms (0.2%)

Counts

3 → 72

Calls

3 calls:

11.0ms	(/.f64 a (/.f64 (+.f64 a b) b))
9.0ms	(/.f64 1 (/.f64 a (/.f64 (+.f64 a b) b)))
5.0ms	(/.f64 (+.f64 a b) b)

rewrite75.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

603×	`times-frac_binary64`
383×	`*-un-lft-identity_binary64`
279×	`add-sqr-sqrt_binary64`
279×	`add-cube-cbrt_binary64`
72×	`associate-/r*_binary64`

Counts

3 → 361

Calls

3 calls:

12.0ms	(/.f64 1 (/.f64 a (/.f64 (+.f64 a b) b)))
7.0ms	(/.f64 a (/.f64 (+.f64 a b) b))
4.0ms	(/.f64 (+.f64 a b) b)

simplify242.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

645×	`fma-def_binary64`
426×	`*-commutative_binary64`
390×	`distribute-rgt-in_binary64`
326×	`distribute-lft-in_binary64`
292×	`associate-/r/_binary64`

Counts

433 → 453

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	293	9263
1	614	8556
2	1998	8382
3	2951	8356
4	4989	8356

prune236.0ms (1.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	453	0	453
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	453	3	456

Error

0.0b

Counts

456 → 3

Alt Table

Status	Error	Program
✓	6.9b	(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))))
✓	9.6b	(/.f64 1 (/.f64 a (/.f64 (+.f64 a b) b)))
	40.6b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))

Compiler

Compiled 9408 to 2732 computations (71% saved)

regimes719.0ms (5.4%)

Accuracy

Total 1.2b remaining (96.4%)

Threshold costs 0b (0%)

Counts

140 → 3

Compiler

Compiled 11018 to 6808 computations (38.2% saved)

bsearch6.0ms (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	43	145
1	56	145
2	59	145
3	57	145

end101.0ms (0.8%)

Compiler: Compiled 451 to 262 computations (41.9% saved)

Details

analyze2.4s (17.7%)

sample8.2s (62%)

simplify23.0ms (0.2%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series470.0ms (3.5%)

rewrite18.0ms (0.1%)

simplify135.0ms (1%)

prune168.0ms (1.3%)

localize12.0ms (0.1%)

series65.0ms (0.5%)

rewrite20.0ms (0.2%)

simplify124.0ms (0.9%)

prune104.0ms (0.8%)

localize4.0ms (0%)

series9.0ms (0.1%)

rewrite7.0ms (0.1%)

simplify79.0ms (0.6%)

prune25.0ms (0.2%)

localize6.0ms (0%)

series26.0ms (0.2%)

rewrite75.0ms (0.6%)

simplify242.0ms (1.8%)

prune236.0ms (1.8%)

regimes719.0ms (5.4%)

bsearch6.0ms (0%)

simplify4.0ms (0%)

end101.0ms (0.8%)

Profiling