Details

analyze766.0ms (4.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
50%	50%	0.1%	5
50%	50%	0.1%	6
50%	50%	0.1%	7
50%	50%	0.1%	8
50%	50%	0.1%	9
50%	50%	0.1%	10
50%	50%	0.1%	11
50%	50%	0.1%	12
50%	50%	0.1%	13
50%	50%	0.1%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample12.2s (70.1%)

Symmetry

(sort a b)

Results

9.4s	7519×	body	8192	exit
1.4s	1997×	body	1024	valid
580.0ms	4547×	body	128	valid
420.0ms	1002×	body	512	valid
186.0ms	205×	body	2048	valid
130.0ms	505×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	8	10
2	8	10

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

30.4b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.4b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	4.6b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series429.0ms (2.5%)

Counts

2 → 48

Calls

2 calls:

425.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64`
4×	`add-log-exp_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`log-prod_binary64`
4×	`add-cube-cbrt_binary64`

Counts

2 → 34

Calls

2 calls:

3.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
3.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

simplify79.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

618×	`fma-neg_binary64`
418×	`associate-+l+_binary64`
392×	`fma-def_binary64`
238×	`times-frac_binary64`
229×	`associate-+r+_binary64`

Counts

82 → 83

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	123	1238
1	334	1183
2	1034	1155
3	4062	1151
4	4828	1151
5	4973	1151

prune60.0ms (0.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	3	84

Error

0.8b

Counts

84 → 3

Alt Table

Status	Error	Program
	30.4b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
▶	1.1b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	33.4b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 1365 to 624 computations (54.3% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (exp.f64 a))
✓	0.0b	(/.f64 b (+.f64 1 (exp.f64 a)))
✓	0.0b	(+.f64 1 (exp.f64 a))

series202.0ms (1.2%)

Counts

3 → 20

Calls

3 calls:

184.0ms	(log1p.f64 (exp.f64 a))
17.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
2.0ms	(+.f64 1 (exp.f64 a))

rewrite11.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
5×	`distribute-lft-out_binary64`

Counts

3 → 63

Calls

3 calls:

4.0ms	(+.f64 1 (exp.f64 a))
4.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
0.0ms	(log1p.f64 (exp.f64 a))

simplify83.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

811×	`fma-neg_binary64`
515×	`associate-l_binary64`
419×	`associate-r_binary64`
353×	`cancel-sign-sub-inv_binary64`
305×	`associate-/l*_binary64`

Counts

83 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	122	988
1	280	911
2	654	899
3	1629	896
4	4281	896
5	4969	896
6	4918	896

prune69.0ms (0.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	88	5	93

Error

0.8b

Counts

93 → 5

Alt Table

Status	Error	Program
	1.9b	(+.f64 (log1p.f64 (exp.f64 a)) (.f64 (.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
	30.4b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	25.0b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
	33.4b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
▶	1.1b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 (neg.f64 b) (-.f64 -1 (exp.f64 a))))

Compiler

Compiled 1604 to 854 computations (46.8% saved)

localize7.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(log1p.f64 (exp.f64 a))
✓	0.0b	(/.f64 (neg.f64 b) (-.f64 -1 (exp.f64 a)))
✓	0.0b	(-.f64 -1 (exp.f64 a))

series21.0ms (0.1%)

Counts

2 → 36

Calls

2 calls:

19.0ms	(/.f64 (neg.f64 b) (-.f64 -1 (exp.f64 a)))
2.0ms	(-.f64 -1 (exp.f64 a))

rewrite16.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`*-un-lft-identity_binary64`
63×	`add-sqr-sqrt_binary64`
50×	`times-frac_binary64`
39×	`add-cube-cbrt_binary64`
18×	`distribute-lft-neg-in_binary64`

Counts

2 → 113

Calls

2 calls:

5.0ms	(/.f64 (neg.f64 b) (-.f64 -1 (exp.f64 a)))
3.0ms	(-.f64 -1 (exp.f64 a))

simplify97.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

965×	`times-frac_binary64`
459×	`div-sub_binary64`
364×	`fma-def_binary64`
344×	`fma-neg_binary64`
190×	`cancel-sign-sub-inv_binary64`

Counts

149 → 151

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	201	2447
1	438	2334
2	1581	2230
3	4110	2220
4	4898	2220

prune135.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	170	0	170
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	170	5	175

Error

0.8b

Counts

175 → 5

Alt Table

Status	Error	Program
▶	1.9b	(+.f64 (log1p.f64 (exp.f64 a)) (.f64 (.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
	30.4b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	25.0b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
	33.4b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
✓	1.1b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 (neg.f64 b) (-.f64 -1 (exp.f64 a))))

Compiler

Compiled 3442 to 1589 computations (53.8% saved)

localize60.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(+.f64 1 (exp.f64 a))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))
✓	0.6b	(*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))
✓	0.6b	(cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))

series1.6s (9%)

Counts

3 → 72

Calls

3 calls:

985.0ms

(*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

548.0ms

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

28.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

rewrite63.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

134×	`cbrt-prod_binary64`
114×	`*-un-lft-identity_binary64`
91×	`times-frac_binary64`
88×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`

Counts

3 → 191

Calls

3 calls:

20.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

19.0ms

(*.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

3.0ms

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

simplify181.0ms (1%)

Algorithm

1×	egg-herbie

Rules

608×	`fma-def_binary64`
345×	`times-frac_binary64`
321×	`fma-neg_binary64`
296×	`associate-l_binary64`
279×	`associate-r_binary64`

Counts

263 → 278

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	282	6834
1	584	5969
2	1970	5544
3	3998	5367
4	5083	5367

prune502.0ms (2.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	453	3	456
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	454	7	461

Error

0.8b

Counts

461 → 7

Alt Table

Status	Error	Program
✓	1.1b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 (neg.f64 b) (-.f64 -1 (exp.f64 a))))
	25.0b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (log.f64 (.f64 (.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))))
	30.4b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	25.0b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
	2.3b	(+.f64 (log1p.f64 (exp.f64 a)) (.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))) (.f64 (cbrt.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))) (.f64 (cbrt.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) (cbrt.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))) (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
	33.4b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
	2.3b	(+.f64 (log1p.f64 (exp.f64 a)) (.f64 (.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) (pow.f64 (cbrt.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a))))) 5)) (cbrt.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))))

Compiler

Compiled 15904 to 9394 computations (40.9% saved)

regimes519.0ms (3%)

Accuracy

Total 0.6b remaining (52.8%)

Threshold costs 0.6b (52.8%)

Counts

100 → 1

Compiler

Compiled 13427 to 9322 computations (30.6% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	16
1	13	16
2	12	16

end285.0ms (1.6%)

Compiler: Compiled 227 to 154 computations (32.2% saved)

Details

analyze766.0ms (4.4%)

sample12.2s (70.1%)

simplify5.0ms (0%)

prune2.0ms (0%)

localize9.0ms (0.1%)

series429.0ms (2.5%)

rewrite7.0ms (0%)

simplify79.0ms (0.5%)

prune60.0ms (0.3%)

localize7.0ms (0%)

series202.0ms (1.2%)

rewrite11.0ms (0.1%)

simplify83.0ms (0.5%)

prune69.0ms (0.4%)

localize7.0ms (0%)

series21.0ms (0.1%)

rewrite16.0ms (0.1%)

simplify97.0ms (0.6%)

prune135.0ms (0.8%)

localize60.0ms (0.3%)

series1.6s (9%)

rewrite63.0ms (0.4%)

simplify181.0ms (1%)

prune502.0ms (2.9%)

regimes519.0ms (3%)

simplify2.0ms (0%)

end285.0ms (1.6%)

Profiling