Details

analyze78.0ms (0.9%)

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)

sample136.0ms (1.6%)

Algorithm

1×

intervals

Symmetry

(sort a b)

Results

35.0ms	68×	body	1024	valid
10.0ms	2×	body	2048	valid
9.0ms	33×	body	512	valid
8.0ms	143×	body	128	valid
1.0ms	10×	body	256	valid
0.0ms	1×	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

29.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.1b	(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))
✓	3.3b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series578.0ms (6.9%)

Counts

2 → 48

Calls

2 calls:

573.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
5.0ms	(+.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)))

simplify91.0ms (1.1%)

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 → 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

prune48.0ms (0.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	81	3	84

Error

0.4b

Counts

84 → 3

Alt Table

Status	Error	Program
	30.3b	(log1p.f64 (exp.f64 b))
✓	29.1b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
▶	1.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))

Compiler

Compiled 1339 to 606 computations (54.7% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series253.0ms (3%)

Counts

1 → 24

Calls

1 calls:

253.0ms

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

rewrite10.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64`
3×	`fma-def_binary64`
2×	`sum-log_binary64`
2×	`add-sqr-sqrt_binary64`

Counts

1 → 18

Calls

1 calls:

9.0ms

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

simplify57.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

738×	`fma-neg_binary64`
607×	`cancel-sign-sub-inv_binary64`
480×	`associate-+l+_binary64`
358×	`associate-+r+_binary64`
345×	`times-frac_binary64`

Counts

42 → 33

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	60	776
1	173	733
2	444	723
3	1289	715
4	3017	714
5	4985	714

prune25.0ms (0.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	32	1	33
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	32	4	36

Error

0.4b

Counts

36 → 4

Alt Table

Status	Error	Program
▶	2.2b	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
	30.3b	(log1p.f64 (exp.f64 b))
✓	29.1b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
✓	1.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))

Compiler

Compiled 629 to 344 computations (45.3% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series1.0s (11.9%)

Counts

2 → 48

Calls

2 calls:

740.0ms	(log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))
260.0ms	(expm1.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

rewrite2.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 22

Calls

2 calls:

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

simplify111.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

427×	`associate-+r+_binary64`
269×	`associate-+l+_binary64`
268×	`+-commutative_binary64`
226×	`cancel-sign-sub-inv_binary64`
216×	`times-frac_binary64`

Counts

70 → 76

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	281	3342
1	879	3194
2	3748	3133
3	4963	3133
4	4976	3133

prune109.0ms (1.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	107	2	109
Fresh	0	1	1
Picked	1	0	1
Done	0	2	2
Total	108	5	113

Error

0.4b

Counts

113 → 5

Alt Table

Status	Error	Program
✓	1.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
▶	2.2b	(expm1.f64 (expm1.f64 (log1p.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))))
	63.8b	(expm1.f64 (-.f64 (+.f64 (/.f64 (exp.f64 a) b) (+.f64 (log.f64 (/.f64 1 (+.f64 1 (exp.f64 a)))) (+.f64 (/.f64 1 b) (+.f64 (/.f64 (log.f64 (+.f64 1 (exp.f64 a))) b) (/.f64 (*.f64 (log.f64 (+.f64 1 (exp.f64 a))) (exp.f64 a)) b))))) (log.f64 (/.f64 1 b))))
	30.3b	(log1p.f64 (exp.f64 b))
✓	29.1b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 4677 to 2889 computations (38.2% saved)

localize12.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series2.9s (34.1%)

Counts

3 → 72

Calls

3 calls:

1.9s

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

644.0ms

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

294.0ms

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

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`log1p-expm1-u_binary64`
4×	`expm1-log1p-u_binary64`
3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`

Counts

3 → 33

Calls

3 calls:

1.0ms

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

1.0ms

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

0.0ms

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

simplify198.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

841×	`associate-/l*_binary64`
811×	`fma-def_binary64`
337×	`+-commutative_binary64`
295×	`associate-+r+_binary64`
198×	`*-commutative_binary64`

Counts

105 → 128

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	869	13780
1	3111	12776
2	5826	12776

prune372.0ms (4.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	173	5	178

Error

0.4b

Counts

178 → 5

Alt Table

Status	Error	Program
	3.9b	(expm1.f64 (expm1.f64 (.f64 (.f64 (cbrt.f64 (log1p.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))) (cbrt.f64 (log1p.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))) (cbrt.f64 (log1p.f64 (log1p.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))))))
	30.3b	(log1p.f64 (exp.f64 b))
✓	29.1b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
✓	1.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	63.9b	(expm1.f64 (expm1.f64 (+.f64 (/.f64 (log1p.f64 (exp.f64 a)) (.f64 b (+.f64 (-.f64 1 (log1p.f64 (exp.f64 a))) (log.f64 b)))) (+.f64 (fma.f64 (/.f64 (log1p.f64 (exp.f64 a)) b) (/.f64 (exp.f64 a) (+.f64 (-.f64 1 (log1p.f64 (exp.f64 a))) (log.f64 b))) (/.f64 1 (.f64 b (+.f64 (-.f64 1 (log1p.f64 (exp.f64 a))) (log.f64 b))))) (+.f64 (log.f64 (+.f64 (-.f64 1 (log1p.f64 (exp.f64 a))) (log.f64 b))) (/.f64 (exp.f64 a) (*.f64 b (+.f64 (-.f64 1 (log1p.f64 (exp.f64 a))) (log.f64 b)))))))))

Compiler

Compiled 21156 to 14451 computations (31.7% saved)

regimes174.0ms (2.1%)

Accuracy

Total 0.6b remaining (49.3%)

Threshold costs 0.6b (49.3%)

Counts

34 → 1

Compiler

Compiled 3913 to 2807 computations (28.3% 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	9	16
1	13	16
2	12	16

end6.0ms (0.1%)

Compiler: Compiled 36 to 24 computations (33.3% saved)

sample2.2s (26.6%)

Algorithm

1×

intervals

Results

1.0s	1930×	body	1024	valid
254.0ms	947×	body	512	valid
243.0ms	4420×	body	128	valid
135.0ms	193×	body	2048	valid
76.0ms	510×	body	256	valid
7.0ms	145×	body	128	overflowed

Compiler

Compiled 165 to 100 computations (39.4% saved)

Details

analyze78.0ms (0.9%)

sample136.0ms (1.6%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series578.0ms (6.9%)

rewrite7.0ms (0.1%)

simplify91.0ms (1.1%)

prune48.0ms (0.6%)

localize8.0ms (0.1%)

series253.0ms (3%)

rewrite10.0ms (0.1%)

simplify57.0ms (0.7%)

prune25.0ms (0.3%)

localize10.0ms (0.1%)

series1.0s (11.9%)

rewrite2.0ms (0%)

simplify111.0ms (1.3%)

prune109.0ms (1.3%)

localize12.0ms (0.1%)

series2.9s (34.1%)

rewrite3.0ms (0%)

simplify198.0ms (2.4%)

prune372.0ms (4.4%)

regimes174.0ms (2.1%)

simplify2.0ms (0%)

end6.0ms (0.1%)

sample2.2s (26.6%)

Profiling