Details

analyze789.0ms (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)

sample12.7s (70.2%)

Symmetry

(sort a b)

Results

9.7s	7717×	body	8192	exit
1.6s	2047×	body	1024	valid
626.0ms	4543×	body	128	valid
427.0ms	976×	body	512	valid
172.0ms	184×	body	2048	valid
133.0ms	506×	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

28.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	28.8b	(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))
✓	4.1b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series319.0ms (1.8%)

Counts

2 → 48

Calls

2 calls:

315.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.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)))

simplify83.0ms (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

prune59.0ms (0.3%)

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
	32.0b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
	29.3b	(+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
▶	1.2b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))

Compiler

Compiled 1379 to 624 computations (54.7% saved)

localize6.0ms (0%)

Local error

Found 3 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 b (+.f64 1 (exp.f64 a))))

series213.0ms (1.2%)

Counts

3 → 32

Calls

3 calls:

194.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
17.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
1.0ms	(+.f64 1 (exp.f64 a))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`

Counts

3 → 70

Calls

3 calls:

9.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
4.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
2.0ms	(+.f64 1 (exp.f64 a))

simplify84.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

534×	`fma-neg_binary64`
435×	`associate-/l*_binary64`
384×	`fma-def_binary64`
381×	`cancel-sign-sub-inv_binary64`
224×	`distribute-rgt-in_binary64`

Counts

102 → 103

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	138	1554
1	354	1479
2	867	1463
3	2390	1452
4	4939	1451
5	5066	1451

prune79.0ms (0.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	101	2	103
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	102	4	106

Error

0.6b

Counts

106 → 4

Alt Table

Status	Error	Program
	32.0b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
	29.3b	(+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
▶	1.6b	(+.f64 (log1p.f64 (exp.f64 a)) (*.f64 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a)))) (-.f64 1 (exp.f64 a))))
	19.5b	(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

Compiler

Compiled 1851 to 966 computations (47.8% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))
✓	0.0b	(*.f64 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a)))) (-.f64 1 (exp.f64 a)))
✓	2.4b	(-.f64 1 (exp.f64 a))

series57.0ms (0.3%)

Counts

3 → 52

Calls

3 calls:

31.0ms	(*.f64 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a)))) (-.f64 1 (exp.f64 a)))
25.0ms	(/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))
2.0ms	(-.f64 1 (exp.f64 a))

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`add-sqr-sqrt_binary64`
75×	`*-un-lft-identity_binary64`
69×	`add-cube-cbrt_binary64`
61×	`times-frac_binary64`
34×	`associate-l_binary64`

Counts

3 → 176

Calls

3 calls:

12.0ms	(*.f64 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a)))) (-.f64 1 (exp.f64 a)))
3.0ms	(-.f64 1 (exp.f64 a))
3.0ms	(/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))

simplify151.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

645×	`fma-def_binary64`
465×	`distribute-rgt-in_binary64`
404×	`fma-neg_binary64`
192×	`cancel-sign-sub-inv_binary64`
168×	`associate-l_binary64`

Counts

228 → 271

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	276	4853
1	640	4540
2	2168	4167
3	4772	4166
4	4946	4166

prune254.0ms (1.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	270	1	271
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	271	4	275

Error

0.6b

Counts

275 → 4

Alt Table

Status	Error	Program
▶	1.6b	(+.f64 (log1p.f64 (exp.f64 a)) (+.f64 (.f64 1 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))) (cbrt.f64 (exp.f64 a))) (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a)))))))
	32.0b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
	29.3b	(+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	19.5b	(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

Compiler

Compiled 7545 to 2233 computations (70.4% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(.f64 (.f64 (neg.f64 (*.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))) (cbrt.f64 (exp.f64 a))) (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a)))))
✓	0.0b	(cbrt.f64 (exp.f64 a))
✓	0.0b	(*.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))
✓	2.4b	(+.f64 (.f64 1 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))) (cbrt.f64 (exp.f64 a))) (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))))

series392.0ms (2.2%)

Counts

4 → 72

Calls

4 calls:

191.0ms	(*.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))
127.0ms	(cbrt.f64 (exp.f64 a))
48.0ms	(+.f64 (.f64 1 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))) (cbrt.f64 (exp.f64 a))) (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))))
27.0ms	(.f64 (.f64 (neg.f64 (*.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))) (cbrt.f64 (exp.f64 a))) (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a)))))

rewrite36.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

41×	`add-sqr-sqrt_binary64`
40×	`associate-r_binary64`
33×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
30×	`times-frac_binary64`

Counts

4 → 129

Calls

4 calls:

10.0ms	(.f64 (.f64 (neg.f64 (*.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))) (cbrt.f64 (exp.f64 a))) (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a)))))
7.0ms	(+.f64 (.f64 1 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))) (cbrt.f64 (exp.f64 a))) (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))))
5.0ms	(*.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))
1.0ms	(cbrt.f64 (exp.f64 a))

simplify125.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

759×	`fma-def_binary64`
505×	`associate-l_binary64`
333×	`associate-r_binary64`
238×	`fma-neg_binary64`
170×	`*-commutative_binary64`

Counts

201 → 230

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	261	3513
1	717	3304
2	3307	3218
3	4991	3218
4	4957	3218

prune293.0ms (1.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	275	1	276
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	276	4	280

Error

0.6b

Counts

280 → 4

Alt Table

Status	Error	Program
	32.0b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
	29.3b	(+.f64 (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) (log.f64 (sqrt.f64 (+.f64 (exp.f64 a) (exp.f64 b)))))
	1.6b	(+.f64 (log1p.f64 (exp.f64 a)) (+.f64 (.f64 1 (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a))))) (.f64 (.f64 (neg.f64 (.f64 (cbrt.f64 (*.f64 (cbrt.f64 (exp.f64 a)) (cbrt.f64 (exp.f64 a)))) (pow.f64 (cbrt.f64 (cbrt.f64 (exp.f64 a))) 4))) (cbrt.f64 (exp.f64 a))) (/.f64 b (neg.f64 (expm1.f64 (+.f64 a a)))))))
	19.5b	(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

Compiler

Compiled 10795 to 2589 computations (76% saved)

regimes2.1s (11.7%)

Accuracy

Total 0.5b remaining (47.9%)

Threshold costs 0.5b (47.9%)

Counts

373 → 1

Compiler

Compiled 61857 to 35641 computations (42.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`*-commutative_binary64`
9×	`+-commutative_binary64`
7×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	36
1	27	36
2	41	34
3	59	32
4	70	32
5	75	32
6	76	32
7	74	32

end228.0ms (1.3%)

Compiler: Compiled 175 to 96 computations (45.1% saved)

Details

analyze789.0ms (4.4%)

sample12.7s (70.2%)

simplify6.0ms (0%)

prune2.0ms (0%)

localize5.0ms (0%)

series319.0ms (1.8%)

rewrite7.0ms (0%)

simplify83.0ms (0.5%)

prune59.0ms (0.3%)

localize6.0ms (0%)

series213.0ms (1.2%)

rewrite18.0ms (0.1%)

simplify84.0ms (0.5%)

prune79.0ms (0.4%)

localize10.0ms (0.1%)

series57.0ms (0.3%)

rewrite33.0ms (0.2%)

simplify151.0ms (0.8%)

prune254.0ms (1.4%)

localize16.0ms (0.1%)

series392.0ms (2.2%)

rewrite36.0ms (0.2%)

simplify125.0ms (0.7%)

prune293.0ms (1.6%)

regimes2.1s (11.7%)

simplify3.0ms (0%)

end228.0ms (1.3%)

Profiling