Details

analyze197.0ms (1.2%)

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)

sample120.0ms (0.7%)

Algorithm

1×

intervals

Results

56.0ms	60×	body	1024	valid
15.0ms	31×	body	512	valid
13.0ms	145×	body	128	valid
6.0ms	5×	body	2048	valid
4.0ms	15×	body	256	valid
0.0ms	3×	body	128	overflowed

Compiler

Compiled 19 to 15 computations (21.1% saved)

simplify16.0ms (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

prune3.0ms (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

28.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.2b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize11.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	3.3b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

rewrite15.0ms (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:

8.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
5.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

series1.1s (6.5%)

Counts

2 → 48

Calls

2 calls:

1.0s	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
7.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

simplify155.0ms (1%)

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 → 120

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

prune128.0ms (0.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	116	4	120
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	4	121

Error

0.4b

Counts

121 → 4

Alt Table

Status	Error	Program
▶	1.1b	(+.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)))))))
	1.2b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	28.5b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	32.1b	(log.f64 (fma.f64 1/2 (*.f64 a a) (fma.f64 1/6 (pow.f64 a 3) (+.f64 1 (+.f64 (exp.f64 b) a)))))

Compiler

Compiled 1415 to 670 computations (52.7% saved)

localize24.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite59.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`*-un-lft-identity_binary64`
77×	`add-sqr-sqrt_binary64`
73×	`times-frac_binary64`
72×	`add-cube-cbrt_binary64`
54×	`prod-diff_binary64`

Counts

3 → 161

Calls

3 calls:

19.0ms	(-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a))))
11.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
7.0ms	(/.f64 1/2 (+.f64 1 (exp.f64 a)))

series122.0ms (0.8%)

Counts

3 → 20

Calls

3 calls:

61.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
37.0ms	(-.f64 1/2 (/.f64 1/2 (+.f64 1 (exp.f64 a))))
24.0ms	(/.f64 1/2 (+.f64 1 (exp.f64 a)))

simplify346.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

607×	`fma-def_binary64`
357×	`associate-/l*_binary64`
247×	`cancel-sign-sub-inv_binary64`
242×	`fma-neg_binary64`
164×	`times-frac_binary64`

Counts

181 → 311

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	291	3788
1	709	3192
2	1751	2553
3	4288	2553
4	4904	2553
5	4719	2553

prune555.0ms (3.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	368	0	368
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	368	4	372

Error

0.4b

Counts

372 → 4

Alt Table

Status	Error	Program
✓	1.1b	(+.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)))))))
▶	1.2b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	28.5b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	32.1b	(log.f64 (fma.f64 1/2 (*.f64 a a) (fma.f64 1/6 (pow.f64 a 3) (+.f64 1 (+.f64 (exp.f64 b) a)))))

Compiler

Compiled 10369 to 6660 computations (35.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite23.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

3 → 46

Calls

3 calls:

15.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
5.0ms	(+.f64 1 (exp.f64 a))
1.0ms	(log1p.f64 (exp.f64 a))

series1.1s (6.5%)

Counts

3 → 40

Calls

3 calls:

622.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
435.0ms	(log1p.f64 (exp.f64 a))
2.0ms	(+.f64 1 (exp.f64 a))

simplify112.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

540×	`fma-neg_binary64`
473×	`associate-l_binary64`
402×	`times-frac_binary64`
380×	`associate-r_binary64`
336×	`fma-def_binary64`

Counts

86 → 135

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	102	1116
1	284	1055
2	686	1043
3	1962	1033
4	4275	1032
5	5013	1032

prune228.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	248	1	249
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	249	4	253

Error

0.4b

Counts

253 → 4

Alt Table

Status	Error	Program
✓	1.1b	(+.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)))))))
▶	26.4b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
	28.5b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	32.1b	(log.f64 (fma.f64 1/2 (*.f64 a a) (fma.f64 1/6 (pow.f64 a 3) (+.f64 1 (+.f64 (exp.f64 b) a)))))

Compiler

Compiled 2102 to 1113 computations (47.1% saved)

localize14.0ms (0.1%)

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)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
✓	0.1b	(-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))
✓	3.5b	(exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a))))

rewrite36.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
24×	`prod-diff_binary64`
24×	`add-cube-cbrt_binary64`
19×	`exp-sum_binary64`

Counts

3 → 95

Calls

3 calls:

15.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
8.0ms	(exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a))))
6.0ms	(-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))

series6.0s (36.9%)

Counts

3 → 72

Calls

3 calls:

2.5s	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
1.9s	(exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a))))
1.6s	(-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))

simplify172.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

890×	`fma-neg_binary64`
769×	`fma-def_binary64`
539×	`times-frac_binary64`
258×	`cancel-sign-sub-inv_binary64`
197×	`associate-+l+_binary64`

Counts

167 → 301

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	193	2783
1	412	2395
2	1191	2155
3	3673	2153
4	5368	2153

prune220.0ms (1.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	337	1	338
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	338	4	342

Error

0.4b

Counts

342 → 4

Alt Table

Status	Error	Program
✓	1.1b	(+.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)))))))
	26.9b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (fma.f64 (*.f64 (cbrt.f64 (log.f64 b)) (cbrt.f64 (log.f64 b))) (cbrt.f64 (log.f64 b)) (neg.f64 (log1p.f64 (exp.f64 a))))))
	28.5b	(expm1.f64 (log1p.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	32.1b	(log.f64 (fma.f64 1/2 (*.f64 a a) (fma.f64 1/6 (pow.f64 a 3) (+.f64 1 (+.f64 (exp.f64 b) a)))))

Compiler

Compiled 3371 to 1125 computations (66.6% saved)

regimes1.9s (11.8%)

Accuracy

Total 0.4b remaining (46.9%)

Threshold costs 0.4b (46.9%)

Compiler

Compiled 23337 to 15558 computations (33.3% saved)

simplify7.0ms (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	44
1	24	44
2	31	44
3	33	44
4	34	44
5	32	44

end12.0ms (0.1%)

Compiler: Compiled 90 to 60 computations (33.3% saved)

sample3.6s (22.4%)

Algorithm

1×

intervals

Results

1.6s	1919×	body	1024	valid
428.0ms	992×	body	512	valid
359.0ms	4399×	body	128	valid
231.0ms	205×	body	2048	valid
112.0ms	485×	body	256	valid
9.0ms	126×	body	128	overflowed

Compiler

Compiled 122 to 82 computations (32.8% saved)

Details

analyze197.0ms (1.2%)

sample120.0ms (0.7%)

simplify16.0ms (0.1%)

prune3.0ms (0%)

localize11.0ms (0.1%)

rewrite15.0ms (0.1%)

series1.1s (6.5%)

simplify155.0ms (1%)

prune128.0ms (0.8%)

localize24.0ms (0.1%)

rewrite59.0ms (0.4%)

series122.0ms (0.8%)

simplify346.0ms (2.1%)

prune555.0ms (3.4%)

localize13.0ms (0.1%)

rewrite23.0ms (0.1%)

series1.1s (6.5%)

simplify112.0ms (0.7%)

prune228.0ms (1.4%)

localize14.0ms (0.1%)

rewrite36.0ms (0.2%)

series6.0s (36.9%)

simplify172.0ms (1.1%)

prune220.0ms (1.4%)

regimes1.9s (11.8%)

simplify7.0ms (0%)

end12.0ms (0.1%)

sample3.6s (22.4%)

Profiling