Details

analyze3.3s (20.8%)

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%	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)

sample8.7s (54.8%)

Symmetry

(sort a b)

Results

5.1s	4199×	body	2048	valid
1.9s	2445×	body	1024	valid
406.0ms	623×	body	1024	invalid
384.0ms	431×	body	2048	invalid
383.0ms	777×	body	512	valid
128.0ms	276×	body	512	invalid
108.0ms	565×	body	128	valid
94.0ms	260×	body	256	valid
62.0ms	331×	body	128	invalid
48.0ms	154×	body	256	invalid
27.0ms	10×	body	4096	valid
4.0ms	1×	body	8192	exit

Compiler

Compiled 95 to 67 computations (29.5% saved)

simplify24.0ms (0.1%)

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

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)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
✓	0.0b	(expm1.f64 (*.f64 eps (+.f64 a b)))
✓	0.1b	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
✓	39.9b	(/.f64 (.f64 eps (expm1.f64 (.f64 eps (+.f64 a b)))) (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b))))

series382.0ms (2.4%)

Counts

4 → 144

Calls

4 calls:

301.0ms	(/.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)))
31.0ms	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
16.0ms	(expm1.f64 (*.f64 eps (+.f64 a b)))

rewrite16.0ms (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)))

simplify148.0ms (0.9%)

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

prune156.0ms (1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	226	3	229
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	227	3	230

Error

Counts

230 → 3

Alt Table

Status	Error	Program
	41.7b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))
	29.3b	(/.f64 eps (/.f64 (expm1.f64 (.f64 a eps)) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))
▶	7.9b	(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))))

Compiler

Compiled 11430 to 3843 computations (66.4% 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))
✓	6.8b	(.f64 a (.f64 eps eps))
✓	7.0b	(.f64 b (.f64 eps eps))

series70.0ms (0.4%)

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))))
21.0ms	(fma.f64 1/12 (.f64 b (.f64 eps eps)) (/.f64 1 a))
10.0ms	(.f64 b (.f64 eps eps))
8.0ms	(.f64 a (.f64 eps eps))

rewrite14.0ms (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:

6.0ms	(.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))))

simplify98.0ms (0.6%)

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

prune116.0ms (0.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	122	3	125

Error

Counts

125 → 3

Alt Table

Status	Error	Program
	41.7b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))
▶	29.3b	(/.f64 eps (/.f64 (expm1.f64 (.f64 a eps)) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))
✓	7.9b	(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))))

Compiler

Compiled 3102 to 1505 computations (51.5% saved)

localize70.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(expm1.f64 (*.f64 (+.f64 a b) eps))
✓	0.4b	(/.f64 (expm1.f64 (.f64 a eps)) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps))))
✓	13.5b	(/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (.f64 b eps)))
✓	26.8b	(/.f64 eps (/.f64 (expm1.f64 (.f64 a eps)) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))

series710.0ms (4.5%)

Counts

4 → 144

Calls

4 calls:

381.0ms	(/.f64 eps (/.f64 (expm1.f64 (.f64 a eps)) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))
260.0ms	(/.f64 (expm1.f64 (.f64 a eps)) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps))))
51.0ms	(/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (.f64 b eps)))
17.0ms	(expm1.f64 (*.f64 (+.f64 a b) eps))

rewrite79.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

480×	`times-frac_binary64`
239×	`*-un-lft-identity_binary64`
239×	`add-sqr-sqrt_binary64`
239×	`add-cube-cbrt_binary64`
60×	`associate-/r*_binary64`

Counts

4 → 312

Calls

4 calls:

10.0ms	(/.f64 eps (/.f64 (expm1.f64 (.f64 a eps)) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))
6.0ms	(/.f64 (expm1.f64 (.f64 a eps)) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps))))
2.0ms	(/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (.f64 b eps)))
0.0ms	(expm1.f64 (*.f64 (+.f64 a b) eps))

simplify395.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

868×	`fma-def_binary64`
331×	`*-commutative_binary64`
317×	`associate-/r/_binary64`
279×	`+-commutative_binary64`
231×	`associate-+r+_binary64`

Counts

456 → 560

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1337	25506
1	4026	25113
2	5054	25113

prune332.0ms (2.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	560	0	560
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	560	3	563

Error

Counts

563 → 3

Alt Table

Status	Error	Program
▶	41.7b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))
✓	29.3b	(/.f64 eps (/.f64 (expm1.f64 (.f64 a eps)) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))
✓	7.9b	(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))))

Compiler

Compiled 28919 to 7344 computations (74.6% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (*.f64 eps b)))
	0.0b	(expm1.f64 (*.f64 eps (+.f64 a b)))
	0.1b	(.f64 eps (expm1.f64 (.f64 eps (+.f64 a b))))
✓	40.4b	(/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b)))))

series242.0ms (1.5%)

Counts

1 → 36

Calls

1 calls:

242.0ms

(/.f64 (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))) (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b)))))

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-cbrt-cube_binary64`
13×	`add-exp-log_binary64`
4×	`cbrt-unprod_binary64`
4×	`cbrt-undiv_binary64`
4×	`div-exp_binary64`

Counts

1 → 23

Calls

1 calls:

4.0ms

(/.f64 (*.f64 (expm1.f64 (*.f64 eps a)) (expm1.f64 (*.f64 eps b))) (*.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b)))))

simplify91.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
619×	`associate-/l*_binary64`
390×	`associate-/r*_binary64`
307×	`fma-def_binary64`
193×	`*-commutative_binary64`

Counts

59 → 66

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	514	5337
1	1690	5119
2	5171	5119

prune193.0ms (1.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	229	3	232

Error

Counts

232 → 3

Alt Table

Status	Error	Program
✓	41.7b	(/.f64 1 (/.f64 (.f64 (expm1.f64 (.f64 eps a)) (expm1.f64 (.f64 eps b))) (.f64 eps (expm1.f64 (*.f64 eps (+.f64 a b))))))
✓	29.3b	(/.f64 eps (/.f64 (expm1.f64 (.f64 a eps)) (/.f64 (expm1.f64 (.f64 (+.f64 a b) eps)) (expm1.f64 (*.f64 b eps)))))
✓	7.9b	(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))))

Compiler

Compiled 12698 to 5140 computations (59.5% saved)

regimes453.0ms (2.8%)

Accuracy

Total 0.1b remaining (72.2%)

Threshold costs 0.1b (72.2%)

Counts

102 → 3

Compiler

Compiled 8178 to 5228 computations (36.1% saved)

bsearch3.0ms (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`
1×	`if-if-or-not_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	124
1	52	124
2	55	124
3	53	124

end249.0ms (1.6%)

Compiler: Compiled 400 to 227 computations (43.3% saved)

Details

analyze3.3s (20.8%)

sample8.7s (54.8%)

simplify24.0ms (0.1%)

prune4.0ms (0%)

localize12.0ms (0.1%)

series382.0ms (2.4%)

rewrite16.0ms (0.1%)

simplify148.0ms (0.9%)

prune156.0ms (1%)

localize12.0ms (0.1%)

series70.0ms (0.4%)

rewrite14.0ms (0.1%)

simplify98.0ms (0.6%)

prune116.0ms (0.7%)

localize70.0ms (0.4%)

series710.0ms (4.5%)

rewrite79.0ms (0.5%)

simplify395.0ms (2.5%)

prune332.0ms (2.1%)

localize13.0ms (0.1%)

series242.0ms (1.5%)

rewrite6.0ms (0%)

simplify91.0ms (0.6%)

prune193.0ms (1.2%)

regimes453.0ms (2.8%)

bsearch3.0ms (0%)

simplify4.0ms (0%)

end249.0ms (1.6%)

Profiling