Details

analyze782.0ms (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)

sample13.1s (73.6%)

Symmetry

(sort a b)

Results

10.2s	7868×	body	8192	exit
1.5s	1996×	body	1024	valid
655.0ms	4581×	body	128	valid
447.0ms	1011×	body	512	valid
189.0ms	189×	body	2048	valid
134.0ms	479×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify6.0ms (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

28.7b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.7b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	2.7b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series548.0ms (3.1%)

Counts

2 → 48

Calls

2 calls:

543.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
5.0ms	(+.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	(+.f64 (exp.f64 a) (exp.f64 b))
3.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

simplify90.0ms (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

prune66.0ms (0.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	79	4	83
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	80	4	84

Error

0.6b

Counts

84 → 4

Alt Table

Status	Error	Program
▶	0.9b	(+.f64 (log1p.f64 (exp.f64 a)) (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))))))
	1.1b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	28.7b	(log.f64 (fma.f64 (*.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a))) (cbrt.f64 (exp.f64 a)) (exp.f64 b)))
	28.7b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 (exp.f64 b) (exp.f64 a))) 3))

Compiler

Compiled 1435 to 666 computations (53.6% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 a))
✓	0.0b	(/.f64 b (+.f64 1 (exp.f64 a)))
✓	0.0b	(+.f64 (log1p.f64 (exp.f64 a)) (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))))))
✓	0.0b	(-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a))))

series314.0ms (1.8%)

Counts

4 → 44

Calls

4 calls:

283.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))))))
19.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
9.0ms	(-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a))))
2.0ms	(+.f64 1 (exp.f64 a))

rewrite39.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

104×	`*-un-lft-identity_binary64`
71×	`add-sqr-sqrt_binary64`
66×	`add-cube-cbrt_binary64`
61×	`times-frac_binary64`
54×	`prod-diff_binary64`

Counts

4 → 164

Calls

4 calls:

9.0ms	(-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a))))
9.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))))))
5.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
3.0ms	(+.f64 1 (exp.f64 a))

simplify204.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

466×	`fma-neg_binary64`
400×	`cancel-sign-sub-inv_binary64`
359×	`times-frac_binary64`
201×	`distribute-rgt-neg-in_binary64`
188×	`exp-prod_binary64`

Counts

208 → 221

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	360	5516
1	932	4772
2	2528	3771
3	4249	3767
4	4954	3767
5	4741	3767

prune413.0ms (2.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	320	0	320
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	320	4	324

Error

0.6b

Counts

324 → 4

Alt Table

Status	Error	Program
✓	0.9b	(+.f64 (log1p.f64 (exp.f64 a)) (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))))))
▶	1.1b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	28.7b	(log.f64 (fma.f64 (*.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a))) (cbrt.f64 (exp.f64 a)) (exp.f64 b)))
	28.7b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 (exp.f64 b) (exp.f64 a))) 3))

Compiler

Compiled 13240 to 8366 computations (36.8% saved)

localize7.0ms (0%)

Local error

Found 4 expressions with local error:

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

series462.0ms (2.6%)

Counts

2 → 36

Calls

2 calls:

263.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
199.0ms	(log1p.f64 (exp.f64 a))

rewrite8.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-log-exp_binary64`
5×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`fma-def_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 29

Calls

2 calls:

7.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
0.0ms	(log1p.f64 (exp.f64 a))

simplify87.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

816×	`times-frac_binary64`
500×	`associate-+l+_binary64`
381×	`associate-l_binary64`
366×	`associate-+r+_binary64`
304×	`associate-r_binary64`

Counts

65 → 50

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	74	937
1	201	894
2	504	882
3	1471	874
4	3583	874
5	4820	874
6	5359	874

prune160.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	120	6	126

Error

0.6b

Counts

126 → 6

Alt Table

Status	Error	Program
✓	0.9b	(+.f64 (log1p.f64 (exp.f64 a)) (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))))))
	1.4b	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
	28.7b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 (exp.f64 b) (exp.f64 a))) 3))
▶	1.4b	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
	19.4b	(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
	28.7b	(log.f64 (fma.f64 (*.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a))) (cbrt.f64 (exp.f64 a)) (exp.f64 b)))

Compiler

Compiled 2180 to 1159 computations (46.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f64 (exp.f64 a))
	0.0b	(+.f64 1 (exp.f64 a))
	0.0b	(/.f64 b (+.f64 1 (exp.f64 a)))
✓	0.0b	(expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

series20.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

20.0ms

(expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`
1×	`add-exp-log_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

simplify74.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

829×	`fma-neg_binary64`
819×	`times-frac_binary64`
657×	`distribute-rgt-neg-in_binary64`
506×	`distribute-lft-neg-in_binary64`
422×	`fma-def_binary64`

Counts

35 → 26

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	39	398
1	86	371
2	226	360
3	575	356
4	1671	356
5	3095	356
6	4703	356
7	5508	356

prune133.0ms (0.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	116	5	121

Error

0.6b

Counts

121 → 5

Alt Table

Status	Error	Program
	1.4b	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))))
✓	0.9b	(+.f64 (log1p.f64 (exp.f64 a)) (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (.f64 (.f64 (/.f64 b (+.f64 1 (exp.f64 a))) b) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a)))))))
	28.7b	(log.f64 (fma.f64 (*.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a))) (cbrt.f64 (exp.f64 a)) (exp.f64 b)))
	2.2b	(+.f64 (log1p.f64 (exp.f64 a)) (.f64 (.f64 (cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))) (cbrt.f64 (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))))
	28.7b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 (exp.f64 b) (exp.f64 a))) 3))

Compiler

Compiled 2152 to 1239 computations (42.4% saved)

regimes967.0ms (5.4%)

Accuracy

Total 0.5b remaining (41.4%)

Threshold costs 0.5b (41.4%)

Counts

195 → 1

Compiler

Compiled 20982 to 14893 computations (29% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
3×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	36
1	24	36
2	31	36
3	33	36
4	34	36
5	32	36

end279.0ms (1.6%)

Compiler: Compiled 208 to 146 computations (29.8% saved)

Details

analyze782.0ms (4.4%)

sample13.1s (73.6%)

simplify6.0ms (0%)

prune2.0ms (0%)

localize5.0ms (0%)

series548.0ms (3.1%)

rewrite7.0ms (0%)

simplify90.0ms (0.5%)

prune66.0ms (0.4%)

localize14.0ms (0.1%)

series314.0ms (1.8%)

rewrite39.0ms (0.2%)

simplify204.0ms (1.1%)

prune413.0ms (2.3%)

localize7.0ms (0%)

series462.0ms (2.6%)

rewrite8.0ms (0%)

simplify87.0ms (0.5%)

prune160.0ms (0.9%)

localize9.0ms (0.1%)

series20.0ms (0.1%)

rewrite1.0ms (0%)

simplify74.0ms (0.4%)

prune133.0ms (0.7%)

regimes967.0ms (5.4%)

simplify3.0ms (0%)

end279.0ms (1.6%)

Profiling