Details

analyze70.0ms (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)

sample217.0ms (3.8%)

Algorithm

1×

intervals

Symmetry

(sort a b)

Results

99.0ms	66×	body	1024	valid
9.0ms	32×	body	512	valid
7.0ms	141×	body	128	valid
2.0ms	14×	body	256	valid
2.0ms	3×	body	2048	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

29.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.2b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	3.0b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series498.0ms (8.7%)

Counts

2 → 48

Calls

2 calls:

488.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
10.0ms	(+.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)))

simplify80.0ms (1.4%)

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 (1%)

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
	29.2b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 (exp.f64 b) (exp.f64 a))) 3))
▶	1.3b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	31.9b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 1367 to 626 computations (54.2% 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	(log1p.f64 (exp.f64 a))
✓	0.0b	(+.f64 1 (exp.f64 a))

series483.0ms (8.4%)

Counts

4 → 44

Calls

4 calls:

259.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
202.0ms	(log1p.f64 (exp.f64 a))
19.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
3.0ms	(+.f64 1 (exp.f64 a))

rewrite17.0ms (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:

8.0ms	(+.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))

simplify106.0ms (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

prune86.0ms (1.5%)

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
	31.9b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
▶	1.3b	(+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a)))
	29.2b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 (exp.f64 b) (exp.f64 a))) 3))
	25.9b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
	18.6b	(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

Compiler

Compiled 2125 to 1121 computations (47.2% 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 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a)))
	0.0b	(log1p.f64 (exp.f64 a))
	0.0b	(+.f64 1 (exp.f64 a))

series347.0ms (6%)

Counts

1 → 24

Calls

1 calls:

347.0ms

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

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`fma-def_binary64`
17×	`*-un-lft-identity_binary64`
12×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`

Counts

1 → 33

Calls

1 calls:

9.0ms

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

simplify70.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

941×	`fma-neg_binary64`
586×	`cancel-sign-sub-inv_binary64`
480×	`associate-+l+_binary64`
358×	`associate-+r+_binary64`
305×	`times-frac_binary64`

Counts

57 → 51

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	60	780
1	180	737
2	442	723
3	1275	715
4	2933	714
5	4893	714
6	5063	714

prune98.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	140	0	140
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	140	5	145

Error

0.6b

Counts

145 → 5

Alt Table

Status	Error	Program
	31.9b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
✓	1.3b	(+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a)))
	29.2b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 (exp.f64 b) (exp.f64 a))) 3))
	25.9b	(+.f64 (log1p.f64 (exp.f64 a)) (exp.f64 (-.f64 (log.f64 b) (log1p.f64 (exp.f64 a)))))
▶	18.6b	(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

Compiler

Compiled 2482 to 1300 computations (47.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(log1p.f64 (exp.f64 a))
	0.0b	(+.f64 1 (exp.f64 a))
✓	0.0b	(log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))
✓	1.3b	(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

series855.0ms (14.9%)

Counts

2 → 48

Calls

2 calls:

571.0ms	(log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))
283.0ms	(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
8×	`log-prod_binary64`
5×	`add-sqr-sqrt_binary64`
5×	`add-cube-cbrt_binary64`
4×	`exp-sum_binary64`

Counts

2 → 37

Calls

2 calls:

10.0ms	(exp.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))
7.0ms	(log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))

simplify74.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

821×	`fma-def_binary64`
271×	`cancel-sign-sub-inv_binary64`
205×	`sub-neg_binary64`
198×	`associate-/l/_binary64`
156×	`distribute-rgt-in_binary64`

Counts

85 → 94

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	222	2938
1	628	2741
2	2529	2615
3	4984	2615

prune116.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	139	5	144

Error

0.6b

Counts

144 → 5

Alt Table

Status	Error	Program
	19.2b	(pow.f64 (exp.f64 (*.f64 (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))) (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))) (cbrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))
	29.2b	(cbrt.f64 (pow.f64 (log.f64 (+.f64 (exp.f64 b) (exp.f64 a))) 3))
	31.9b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
✓	1.3b	(+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a)))
	63.1b	(pow.f64 (exp.f64 (sqrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))))) (sqrt.f64 (log.f64 (+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a)))))))

Compiler

Compiled 3981 to 2425 computations (39.1% saved)

regimes341.0ms (5.9%)

Accuracy

Total 0.6b remaining (49.6%)

Threshold costs 0.6b (49.6%)

Counts

76 → 1

Compiler

Compiled 6139 to 4471 computations (27.2% saved)

simplify3.0ms (0.1%)

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

end5.0ms (0.1%)

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

sample2.2s (37.4%)

Algorithm

1×

intervals

Results

981.0ms	1948×	body	1024	valid
251.0ms	942×	body	512	valid
231.0ms	4417×	body	128	valid
132.0ms	193×	body	2048	valid
69.0ms	500×	body	256	valid
8.0ms	146×	body	128	overflowed

Compiler

Compiled 127 to 85 computations (33.1% saved)

Details

analyze70.0ms (1.2%)

sample217.0ms (3.8%)

simplify6.0ms (0.1%)

prune2.0ms (0%)

localize5.0ms (0.1%)

series498.0ms (8.7%)

rewrite7.0ms (0.1%)

simplify80.0ms (1.4%)

prune59.0ms (1%)

localize6.0ms (0.1%)

series483.0ms (8.4%)

rewrite17.0ms (0.3%)

simplify106.0ms (1.8%)

prune86.0ms (1.5%)

localize6.0ms (0.1%)

series347.0ms (6%)

rewrite11.0ms (0.2%)

simplify70.0ms (1.2%)

prune98.0ms (1.7%)

localize9.0ms (0.2%)

series855.0ms (14.9%)

rewrite19.0ms (0.3%)

simplify74.0ms (1.3%)

prune116.0ms (2%)

regimes341.0ms (5.9%)

simplify3.0ms (0.1%)

end5.0ms (0.1%)

sample2.2s (37.4%)

Profiling