Details

analyze69.0ms (1.5%)

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)

sample138.0ms (2.9%)

Algorithm

1×

intervals

Symmetry

(sort a b)

Results

35.0ms	65×	body	1024	valid
7.0ms	134×	body	128	valid
7.0ms	26×	body	512	valid
7.0ms	10×	body	2048	valid
3.0ms	21×	body	256	valid
0.0ms	4×	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

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

31.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	31.2b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	4.7b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series588.0ms (12.4%)

Counts

1 → 24

Calls

1 calls:

588.0ms

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

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`*-un-lft-identity_binary64`
4×	`log-prod_binary64`
2×	`add-exp-log_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`

Counts

1 → 17

Calls

1 calls:

3.0ms

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

simplify55.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

534×	`fma-neg_binary64`
260×	`associate-+l+_binary64`
228×	`times-frac_binary64`
214×	`fma-def_binary64`
196×	`associate-/l*_binary64`

Counts

41 → 44

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	96	805
1	260	771
2	794	743
3	3305	729
4	4972	729

prune38.0ms (0.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	41	3	44
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	42	3	45

Error

0.2b

Counts

45 → 3

Alt Table

Status	Error	Program
	0.7b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	32.9b	(log1p.f64 (exp.f64 b))
▶	0.4b	(+.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)))))))

Compiler

Compiled 915 to 456 computations (50.2% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.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))))
✓	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)))))))

series446.0ms (9.4%)

Counts

3 → 60

Calls

3 calls:

331.0ms

(+.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)))))))

105.0ms

(+.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))))))

10.0ms

(+.f64 1/2 (/.f64 -1/2 (+.f64 1 (exp.f64 a))))

rewrite33.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`fma-def_binary64`
23×	`*-un-lft-identity_binary64`
15×	`add-log-exp_binary64`
13×	`add-sqr-sqrt_binary64`
13×	`add-cube-cbrt_binary64`

Counts

3 → 76

Calls

3 calls:

10.0ms

(+.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)))))))

9.0ms

(+.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))))))

8.0ms

(+.f64 1/2 (/.f64 -1/2 (+.f64 1 (exp.f64 a))))

simplify175.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

525×	`fma-neg_binary64`
394×	`cancel-sign-sub-inv_binary64`
357×	`associate-*l/_binary64`
350×	`times-frac_binary64`
172×	`associate-/r*_binary64`

Counts

136 → 144

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	183	4587
1	605	4358
2	2147	3568
3	4812	3554
4	5130	3554

prune249.0ms (5.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	144	0	144
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	144	3	147

Error

0.2b

Counts

147 → 3

Alt Table

Status	Error	Program
▶	0.7b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	32.9b	(log1p.f64 (exp.f64 b))
✓	0.4b	(+.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)))))))

Compiler

Compiled 5534 to 3443 computations (37.8% saved)

localize6.0ms (0.1%)

prune2.0ms (0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	1	1
Total	3	3

Error

0.2b

Counts

3 → 3

Alt Table

Status	Error	Program
✓	0.7b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
▶	32.9b	(log1p.f64 (exp.f64 b))
✓	0.4b	(+.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)))))))

Compiler

Compiled 52 to 36 computations (30.8% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.2b	(log1p.f64 (exp.f64 b))

series262.0ms (5.5%)

Counts

1 → 12

Calls

1 calls:

262.0ms

(log1p.f64 (exp.f64 b))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

2×	`expm1-log1p-u_binary64`
1×	`*-un-lft-identity_binary64`
1×	`add-sqr-sqrt_binary64`
1×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 11

Calls

1 calls:

0.0ms

(log1p.f64 (exp.f64 b))

simplify96.0ms (2%)

Algorithm

1×	egg-herbie

Rules

749×	`fma-def_binary64`
668×	`fma-neg_binary64`
607×	`distribute-rgt-neg-in_binary64`
528×	`cancel-sign-sub-inv_binary64`
420×	`sub-neg_binary64`

Counts

23 → 19

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	31	178
1	57	165
2	108	159
3	279	153
4	830	153
5	1786	153
6	2983	153
7	4155	153
8	4520	153
9	4899	153
10	4840	153

prune16.0ms (0.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	19	0	19
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	19	3	22

Error

0.2b

Counts

22 → 3

Alt Table

Status	Error	Program
✓	0.7b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
✓	32.9b	(log1p.f64 (exp.f64 b))
✓	0.4b	(+.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)))))))

Compiler

Compiled 192 to 114 computations (40.6% saved)

regimes316.0ms (6.7%)

Accuracy

Total 0.3b remaining (42.1%)

Threshold costs 0.3b (42.1%)

Counts

59 → 1

Compiler

Compiled 6493 to 4638 computations (28.6% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`distribute-neg-frac_binary64`
1×	`*-lft-identity_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	36
1	26	36
2	33	36
3	35	36
4	36	36
5	34	36

end6.0ms (0.1%)

Compiler: Compiled 75 to 54 computations (28% saved)

sample2.2s (46.4%)

Algorithm

1×

intervals

Results

1.0s	2038×	body	1024	valid
241.0ms	887×	body	512	valid
230.0ms	4382×	body	128	valid
147.0ms	198×	body	2048	valid
75.0ms	495×	body	256	valid
7.0ms	139×	body	128	overflowed

Compiler

Compiled 83 to 59 computations (28.9% saved)

Details

analyze69.0ms (1.5%)

sample138.0ms (2.9%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series588.0ms (12.4%)

rewrite4.0ms (0.1%)

simplify55.0ms (1.2%)

prune38.0ms (0.8%)

localize12.0ms (0.3%)

series446.0ms (9.4%)

rewrite33.0ms (0.7%)

simplify175.0ms (3.7%)

prune249.0ms (5.3%)

localize6.0ms (0.1%)

prune2.0ms (0%)

localize3.0ms (0.1%)

series262.0ms (5.5%)

rewrite1.0ms (0%)

simplify96.0ms (2%)

prune16.0ms (0.3%)

regimes316.0ms (6.7%)

simplify3.0ms (0.1%)

end6.0ms (0.1%)

sample2.2s (46.4%)

Profiling