Details

analyze879.0ms (5.3%)

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)

sample12.2s (73.9%)

Results

9.5s	7820×	body	8192	exit
1.4s	1998×	body	1024	valid
601.0ms	4586×	body	128	valid
400.0ms	954×	body	512	valid
174.0ms	195×	body	2048	valid
132.0ms	523×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

preprocess17.0ms (0.1%)

Algorithm

2×	egg-herbie

Rules

1×	`swap-a-b`
1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	9	20
0	2	2
1	2	2

Stop Event

1×	unsound
1×	saturated

Symmetry

(sort a b)

Compiler

Compiled 8 to 6 computations (25% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	8	10

Stop Event

1×

saturated

Counts

1 → 1

prune1.0ms (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

30.2b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	30.2b	(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))
✓	5.0b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series353.0ms (2.1%)

Counts

2 → 48

Calls

12 calls:

118.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))	b	-inf
79.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))	a	inf
73.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))	b	inf
72.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))	a	-inf
4.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))	b	0

rewrite44.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

666×	`log1p-expm1-u_binary64`
666×	`expm1-log1p-u_binary64`
455×	`prod-diff_binary64`
71×	`add-sqr-sqrt_binary64`
68×	`add-log-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	138	18
2	1802	18

Stop Event

1×	node limit

Counts

2 → 58

simplify41.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

562×	`fma-neg_binary64`
396×	`associate-+l+_binary64`
328×	`fma-def_binary64`
238×	`times-frac_binary64`
220×	`associate-+r+_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	746
1	248	742
2	902	714
3	4283	710

Stop Event

1×	node limit

Counts

106 → 90

prune94.0ms (0.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	3	91

Error

1.0b

Counts

91 → 3

Alt Table

Status	Error	Program
▶	2.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))
	30.3b	(log.f64 (cbrt.f64 (pow.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 3)))
	32.4b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))

Compiler

Compiled 1448 to 711 computations (50.9% saved)

localize7.0ms (0%)

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

series337.0ms (2%)

Counts

4 → 44

Calls

18 calls:

71.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))	a	-inf
70.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))	a	inf
68.0ms	(log1p.f64 (exp.f64 a))	a	inf
68.0ms	(log1p.f64 (exp.f64 a))	a	-inf
15.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (+.f64 1 (exp.f64 a))))	b	0

rewrite61.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

816×	`prod-diff_binary64`
317×	`fma-def_binary64`
170×	`expm1-udef_binary64`
170×	`log1p-udef_binary64`
153×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	36
1	189	36
2	2632	36

Stop Event

1×	node limit

Counts

4 → 144

simplify31.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

468×	`associate-l_binary64`
437×	`cancel-sign-sub-inv_binary64`
377×	`associate-r_binary64`
367×	`associate-+r+_binary64`
318×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	58	588
1	171	569
2	515	551
3	1865	547

Stop Event

1×	node limit

Counts

188 → 177

prune149.0ms (0.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	173	4	177
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	174	6	180

Error

1.0b

Counts

180 → 6

Alt Table

Status	Error	Program
	2.0b	(expm1.f64 (log1p.f64 (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a)))))
	22.6b	(cbrt.f64 (pow.f64 (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a))) 3))
	30.3b	(log.f64 (cbrt.f64 (pow.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 3)))
	32.4b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
▶	2.0b	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
	2.8b	(+.f64 (log1p.f64 (exp.f64 a)) (.f64 (pow.f64 (cbrt.f64 b) 2) (.f64 (cbrt.f64 b) (/.f64 1 (+.f64 1 (exp.f64 a))))))

Compiler

Compiled 3068 to 1665 computations (45.7% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
	0.0b	(log1p.f64 (exp.f64 a))
	0.0b	(/.f64 b (+.f64 1 (exp.f64 a)))
✓	0.1b	(expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

series199.0ms (1.2%)

Counts

2 → 48

Calls

12 calls:

71.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))	a	-inf
69.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))	a	inf
15.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))	b	0
13.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))	b	inf
12.0ms	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))	b	-inf

rewrite57.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

492×	`log-prod_binary64`
348×	`fma-def_binary64`
185×	`expm1-udef_binary64`
185×	`log1p-udef_binary64`
175×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	210	25
2	2844	25

Stop Event

1×	node limit

Counts

2 → 113

simplify40.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

404×	`associate-+l+_binary64`
357×	`cancel-sign-sub-inv_binary64`
290×	`associate-+r+_binary64`
289×	`associate-l_binary64`
286×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	647
1	127	628
2	387	612
3	1430	608
4	4264	608

Stop Event

1×	node limit

Counts

161 → 133

prune168.0ms (1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	201	0	201
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	201	6	207

Error

1.0b

Counts

207 → 6

Alt Table

Status	Error	Program
▶	2.0b	(expm1.f64 (log1p.f64 (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a)))))
	22.6b	(cbrt.f64 (pow.f64 (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a))) 3))
	30.3b	(log.f64 (cbrt.f64 (pow.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 3)))
	32.4b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
✓	2.0b	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
	2.8b	(+.f64 (log1p.f64 (exp.f64 a)) (.f64 (pow.f64 (cbrt.f64 b) 2) (.f64 (cbrt.f64 b) (/.f64 1 (+.f64 1 (exp.f64 a))))))

Compiler

Compiled 3691 to 2102 computations (43.1% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a)))
	0.0b	(/.f64 b (+.f64 1 (exp.f64 a)))
✓	0.0b	(log1p.f64 (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a))))
✓	0.1b	(expm1.f64 (log1p.f64 (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a)))))

series811.0ms (4.9%)

Counts

3 → 72

Calls

18 calls:

201.0ms	(log1p.f64 (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a))))	a	inf
198.0ms	(log1p.f64 (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a))))	a	-inf
72.0ms	(+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a)))	a	-inf
71.0ms	(+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a)))	a	inf
71.0ms	(expm1.f64 (log1p.f64 (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a)))))	a	-inf

rewrite59.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

877×	`prod-diff_binary64`
185×	`expm1-udef_binary64`
185×	`log1p-udef_binary64`
102×	`add-sqr-sqrt_binary64`
100×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	50
1	210	50
2	2833	50

Stop Event

1×	node limit

Counts

3 → 94

simplify71.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	259	3244
1	867	3162
2	3916	3099

Stop Event

1×	node limit

Counts

166 → 103

prune129.0ms (0.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	144	6	150

Error

1.0b

Counts

150 → 6

Alt Table

Status	Error	Program
	63.3b	(expm1.f64 (+.f64 (-.f64 (/.f64 (exp.f64 a) b) (log1p.f64 (exp.f64 a))) (+.f64 (+.f64 (/.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (exp.f64 a))) (+.f64 (/.f64 1 b) (/.f64 (log1p.f64 (exp.f64 a)) b))) (log.f64 b))))
	22.6b	(cbrt.f64 (pow.f64 (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a))) 3))
	30.3b	(log.f64 (cbrt.f64 (pow.f64 (+.f64 (exp.f64 a) (exp.f64 b)) 3)))
	32.4b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
✓	2.0b	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
	21.0b	(expm1.f64 (exp.f64 (log.f64 (log1p.f64 (+.f64 (/.f64 b (+.f64 1 (exp.f64 a))) (log1p.f64 (exp.f64 a)))))))

Compiler

Compiled 5303 to 3200 computations (39.7% saved)

regimes479.0ms (2.9%)

Accuracy

Total 0.6b remaining (56.7%)

Threshold costs 0.6b (56.7%)

Counts

108 → 1

Compiler

Compiled 8904 to 6555 computations (26.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`
1×	`unpow1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	16
1	14	16

Stop Event

1×

saturated

end243.0ms (1.5%)

Stop Event

1×

fuel

Compiler

Compiled 149 to 99 computations (33.6% saved)

Details

analyze879.0ms (5.3%)

sample12.2s (73.9%)

preprocess17.0ms (0.1%)

simplify9.0ms (0.1%)

prune1.0ms (0%)

localize5.0ms (0%)

series353.0ms (2.1%)

rewrite44.0ms (0.3%)

simplify41.0ms (0.2%)

prune94.0ms (0.6%)

localize7.0ms (0%)

series337.0ms (2%)

rewrite61.0ms (0.4%)

simplify31.0ms (0.2%)

prune149.0ms (0.9%)

localize9.0ms (0.1%)

series199.0ms (1.2%)

rewrite57.0ms (0.3%)

simplify40.0ms (0.2%)

prune168.0ms (1%)

localize9.0ms (0.1%)

series811.0ms (4.9%)

rewrite59.0ms (0.4%)

simplify71.0ms (0.4%)

prune129.0ms (0.8%)

regimes479.0ms (2.9%)

simplify2.0ms (0%)

end243.0ms (1.5%)

Profiling