Details

analyze885.0ms (5.8%)

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)

sample12.4s (81.2%)

Symmetry

(sort a b)

Results

9.7s	7891×	body	8192	exit
1.4s	1957×	body	1024	valid
604.0ms	4612×	body	128	valid
400.0ms	984×	body	512	valid
182.0ms	197×	body	2048	valid
132.0ms	506×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	8	10

Stop Event

1×

saturated

Counts

1 → 1

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

26.6b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	26.6b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 24 to 18 computations (25% saved)

localize49.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (exp.f64 a) (exp.f64 b))
✓	2.5b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

series359.0ms (2.3%)

Counts

2 → 48

Calls

2 calls:

355.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))
4.0ms	(+.f64 (exp.f64 a) (exp.f64 b))

rewrite42.0ms (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

Calls

2 calls:

41.0ms	(+.f64 (exp.f64 a) (exp.f64 b))
41.0ms	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

simplify40.0ms (0.3%)

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

prune57.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	87	3	90
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	87	4	91

Error

0.4b

Counts

91 → 4

Alt Table

Status	Error	Program
	29.6b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
	27.8b	(pow.f64 (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) 3)
✓	26.6b	(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 1456 to 717 computations (50.8% saved)

localize6.0ms (0%)

Local error

Found 2 expressions with local error:

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

series20.0ms (0.1%)

Counts

2 → 8

Calls

2 calls:

18.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
1.0ms	(+.f64 1 (exp.f64 a))

rewrite38.0ms (0.2%)

Algorithm

1×	batch-egg-rewrite

Rules

709×	`log1p-expm1-u_binary64`
709×	`expm1-log1p-u_binary64`
127×	`expm1-udef_binary64`
127×	`log1p-udef_binary64`
96×	`prod-diff_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
1	144	15
2	1880	15

Stop Event

1×	node limit

Counts

2 → 67

Calls

2 calls:

37.0ms	(/.f64 b (+.f64 1 (exp.f64 a)))
37.0ms	(+.f64 1 (exp.f64 a))

simplify25.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

602×	`fma-def_binary64`
435×	`distribute-rgt-neg-in_binary64`
383×	`distribute-lft-neg-in_binary64`
330×	`associate-l_binary64`
268×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	107
1	95	99
2	293	89
3	973	80
4	3275	80

Stop Event

1×	node limit

Counts

75 → 80

prune78.0ms (0.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	77	3	80
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	78	6	84

Error

0.4b

Counts

84 → 6

Alt Table

Status	Error	Program
	29.6b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
▶	1.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))
	1.7b	(+.f64 (log1p.f64 (exp.f64 a)) (pow.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) 3))
	27.8b	(pow.f64 (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) 3)
	1.0b	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
✓	26.6b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 1386 to 765 computations (44.8% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))))
	0.0b	(+.f64 1 (exp.f64 a))
✓	0.0b	(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))
✓	0.5b	(log1p.f64 (+.f64 1 (exp.f64 a)))

series165.0ms (1.1%)

Counts

3 → 48

Calls

3 calls:

145.0ms	(log1p.f64 (+.f64 1 (exp.f64 a)))
19.0ms	(/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))))
2.0ms	(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))

rewrite43.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

785×	`expm1-log1p-u_binary64`
784×	`log1p-expm1-u_binary64`
145×	`prod-diff_binary64`
87×	`egg-rr`
79×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	23
1	165	23
2	2089	23

Stop Event

1×	node limit

Counts

3 → 87

Calls

3 calls:

42.0ms	(/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a)))))
42.0ms	(expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))
42.0ms	(log1p.f64 (+.f64 1 (exp.f64 a)))

simplify37.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

808×	`fma-def_binary64`
434×	`distribute-rgt-neg-in_binary64`
400×	`associate-l_binary64`
383×	`distribute-lft-neg-in_binary64`
308×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	49	444
1	132	436
2	380	426
3	1251	411
4	3936	411

Stop Event

1×	node limit

Counts

135 → 110

prune119.0ms (0.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	148	0	148
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	148	6	154

Error

0.4b

Counts

154 → 6

Alt Table

Status	Error	Program
	29.6b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
✓	1.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))
	1.7b	(+.f64 (log1p.f64 (exp.f64 a)) (pow.f64 (cbrt.f64 (/.f64 b (+.f64 1 (exp.f64 a)))) 3))
	27.8b	(pow.f64 (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) 3)
▶	1.0b	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))))
✓	26.6b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 2504 to 1402 computations (44% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

series235.0ms (1.5%)

Counts

2 → 48

Calls

2 calls:

216.0ms	(log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))
19.0ms	(expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

rewrite43.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

784×	`expm1-log1p-u_binary64`
783×	`log1p-expm1-u_binary64`
286×	`prod-diff_binary64`
79×	`add-sqr-sqrt_binary64`
73×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	20
1	165	20
2	2086	20

Stop Event

1×	node limit

Counts

2 → 64

Calls

2 calls:

42.0ms	(log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a))))
42.0ms	(expm1.f64 (log1p.f64 (/.f64 b (+.f64 1 (exp.f64 a)))))

simplify34.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

595×	`times-frac_binary64`
408×	`associate-/l*_binary64`
354×	`fma-def_binary64`
270×	`associate-/r*_binary64`
200×	`cancel-sign-sub-inv_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1129
1	418	1077
2	1621	1044

Stop Event

1×	node limit

Counts

112 → 103

prune130.0ms (0.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	184	5	189

Error

0.4b

Counts

189 → 5

Alt Table

Status	Error	Program
	29.6b	(+.f64 (log1p.f64 (exp.f64 b)) (/.f64 a (+.f64 1 (exp.f64 b))))
✓	1.0b	(+.f64 (log1p.f64 (exp.f64 a)) (/.f64 b (expm1.f64 (log1p.f64 (+.f64 1 (exp.f64 a))))))
	63.4b	(+.f64 (log1p.f64 (exp.f64 a)) (expm1.f64 (+.f64 (/.f64 (exp.f64 a) b) (+.f64 (-.f64 (/.f64 1 b) (log1p.f64 (exp.f64 a))) (log.f64 b)))))
	27.8b	(pow.f64 (cbrt.f64 (log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))) 3)
✓	26.6b	(log.f64 (+.f64 (exp.f64 a) (exp.f64 b)))

Compiler

Compiled 3820 to 2228 computations (41.7% saved)

regimes232.0ms (1.5%)

Accuracy

Total 0.6b remaining (49.8%)

Threshold costs 0.6b (49.8%)

Counts

50 → 1

Compiler

Compiled 4168 to 3042 computations (27% 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

Stop Event

1×

saturated

end215.0ms (1.4%)

Compiler: Compiled 115 to 78 computations (32.2% saved)

Details

analyze885.0ms (5.8%)

sample12.4s (81.2%)

simplify6.0ms (0%)

prune2.0ms (0%)

localize49.0ms (0.3%)

series359.0ms (2.3%)

rewrite42.0ms (0.3%)

simplify40.0ms (0.3%)

prune57.0ms (0.4%)

localize6.0ms (0%)

series20.0ms (0.1%)

rewrite38.0ms (0.2%)

simplify25.0ms (0.2%)

prune78.0ms (0.5%)

localize9.0ms (0.1%)

series165.0ms (1.1%)

rewrite43.0ms (0.3%)

simplify37.0ms (0.2%)

prune119.0ms (0.8%)

localize8.0ms (0.1%)

series235.0ms (1.5%)

rewrite43.0ms (0.3%)

simplify34.0ms (0.2%)

prune130.0ms (0.8%)

regimes232.0ms (1.5%)

simplify2.0ms (0%)

end215.0ms (1.4%)

Profiling