Details

analyze76.0ms (1.3%)

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%	37.5%	12.6%	6
50%	25%	25.1%	7
50%	18.7%	31.3%	8
50%	12.5%	37.6%	9
50%	9.4%	40.7%	10
50%	6.2%	43.8%	11
50%	4.7%	45.4%	12
50%	3.1%	46.9%	13
50%	2.3%	47.7%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample98.0ms (1.7%)

Algorithm

1×

intervals

Symmetry

(sort a b)

Results

29.0ms	60×	body	1024	valid
8.0ms	30×	body	512	valid
8.0ms	147×	body	128	valid
3.0ms	5×	body	2048	valid
2.0ms	14×	body	256	valid
0.0ms	5×	body	128	overflowed

Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify6.0ms (0.1%)

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

prune48.0ms (0.8%)

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

28.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.0b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	4.3b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series587.0ms (9.9%)

Counts

2 → 48

Calls

2 calls:

582.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite7.0ms (0.1%)

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)))

simplify88.0ms (1.5%)

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

prune102.0ms (1.7%)

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

0.6b

Counts

84 → 3

Alt Table

Status	Error	Program
▶	0.8b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	28.0b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	30.4b	(+.f64 (log1p.f64 (exp.f64 b)) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (.f64 (.f64 (/.f64 a (+.f64 1 (exp.f64 b))) a) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 b)))))))

Compiler

Compiled 1401 to 648 computations (53.7% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series492.0ms (8.3%)

Counts

4 → 44

Calls

4 calls:

265.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
205.0ms	(log1p.f64 (exp.f64 a))
20.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
2.0ms	(+.f64 1 (exp.f64 a))

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
9×	`add-log-exp_binary64`

Counts

4 → 81

Calls

4 calls:

7.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
4.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
3.0ms	(+.f64 1 (exp.f64 a))
0.0ms	(log1p.f64 (exp.f64 a))

simplify107.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

571×	`fma-neg_binary64`
461×	`cancel-sign-sub-inv_binary64`
403×	`fma-def_binary64`
224×	`distribute-rgt-in_binary64`
201×	`associate-+l+_binary64`

Counts

125 → 120

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	152	1715
1	382	1640
2	927	1622
3	2571	1611
4	4779	1610
5	4994	1610
6	4923	1610

prune188.0ms (3.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	117	3	120
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	118	5	123

Error

0.6b

Counts

123 → 5

Alt Table

Status	Error	Program
▶	0.8b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 (neg.f64 b) (-.f64 -1 (exp.f64 a))))
	28.0b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	30.4b	(+.f64 (log1p.f64 (exp.f64 b)) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (.f64 (.f64 (/.f64 a (+.f64 1 (exp.f64 b))) a) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 b)))))))
	25.0b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
	0.8b	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))

Compiler

Compiled 2161 to 1145 computations (47% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series281.0ms (4.7%)

Counts

3 → 60

Calls

3 calls:

260.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 (neg.f64 b) (-.f64 -1 (exp.f64 a))))
19.0ms	(/.f64 (neg.f64 b) (-.f64 -1 (exp.f64 a)))
2.0ms	(-.f64 -1 (exp.f64 a))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64`
65×	`add-sqr-sqrt_binary64`
50×	`times-frac_binary64`
41×	`add-cube-cbrt_binary64`
18×	`distribute-lft-neg-in_binary64`

Counts

3 → 133

Calls

3 calls:

14.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 (neg.f64 b) (-.f64 -1 (exp.f64 a))))
6.0ms	(/.f64 (neg.f64 b) (-.f64 -1 (exp.f64 a)))
3.0ms	(-.f64 -1 (exp.f64 a))

simplify114.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

580×	`fma-def_binary64`
403×	`fma-neg_binary64`
350×	`div-sub_binary64`
278×	`cancel-sign-sub-inv_binary64`
209×	`distribute-rgt-in_binary64`

Counts

193 → 192

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	240	3222
1	559	3074
2	1911	2956
3	4276	2946
4	4901	2946

prune160.0ms (2.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	211	0	211
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	211	5	216

Error

0.6b

Counts

216 → 5

Alt Table

Status	Error	Program
✓	0.8b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 (neg.f64 b) (-.f64 -1 (exp.f64 a))))
	28.0b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	30.4b	(+.f64 (log1p.f64 (exp.f64 b)) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (.f64 (.f64 (/.f64 a (+.f64 1 (exp.f64 b))) a) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 b)))))))
	25.0b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
▶	0.8b	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))

Compiler

Compiled 4190 to 1953 computations (53.4% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series320.0ms (5.4%)

Counts

2 → 48

Calls

2 calls:

301.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
19.0ms	(expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

2.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
0.0ms	(expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

simplify88.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

486×	`distribute-rgt-neg-in_binary64`
438×	`associate-+r+_binary64`
366×	`cancel-sign-sub-inv_binary64`
347×	`associate-l_binary64`
332×	`sub-neg_binary64`

Counts

78 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	1175
1	204	1119
2	532	1103
3	1544	1099
4	3675	1099
5	4727	1099
6	5033	1099

prune102.0ms (1.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	112	4	116

Error

0.6b

Counts

116 → 4

Alt Table

Status	Error	Program
	0.9b	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))))
✓	0.8b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 (neg.f64 b) (-.f64 -1 (exp.f64 a))))
	30.4b	(+.f64 (log1p.f64 (exp.f64 b)) (+.f64 (/.f64 a (+.f64 1 (exp.f64 b))) (.f64 (.f64 (/.f64 a (+.f64 1 (exp.f64 b))) a) (-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 b)))))))
	25.0b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))

Compiler

Compiled 2010 to 1150 computations (42.8% saved)

regimes705.0ms (11.9%)

Accuracy

Total 0.5b remaining (50%)

Threshold costs 0.5b (50%)

Counts

139 → 1

Compiler

Compiled 14161 to 9867 computations (30.3% 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	11	20
1	15	20
2	14	20

end6.0ms (0.1%)

Compiler: Compiled 42 to 30 computations (28.6% saved)

sample2.3s (38.4%)

Algorithm

1×

intervals

Results

1.0s	1893×	body	1024	valid
271.0ms	962×	body	512	valid
243.0ms	4408×	body	128	valid
161.0ms	225×	body	2048	valid
75.0ms	512×	body	256	valid
7.0ms	135×	body	128	overflowed

Compiler

Compiled 97 to 68 computations (29.9% saved)

Details

analyze76.0ms (1.3%)

sample98.0ms (1.7%)

simplify6.0ms (0.1%)

prune48.0ms (0.8%)

localize5.0ms (0.1%)

series587.0ms (9.9%)

rewrite7.0ms (0.1%)

simplify88.0ms (1.5%)

prune102.0ms (1.7%)

localize6.0ms (0.1%)

series492.0ms (8.3%)

rewrite18.0ms (0.3%)

simplify107.0ms (1.8%)

prune188.0ms (3.2%)

localize7.0ms (0.1%)

series281.0ms (4.7%)

rewrite34.0ms (0.6%)

simplify114.0ms (1.9%)

prune160.0ms (2.7%)

localize8.0ms (0.1%)

series320.0ms (5.4%)

rewrite4.0ms (0.1%)

simplify88.0ms (1.5%)

prune102.0ms (1.7%)

regimes705.0ms (11.9%)

simplify2.0ms (0%)

end6.0ms (0.1%)

sample2.3s (38.4%)

Profiling