Details

analyze1.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	0%	50%	4

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample2.0s (77%)

Results

821.0ms	1989×	body	1024	valid
540.0ms	4418×	body	128	valid
312.0ms	1057×	body	512	valid
176.0ms	271×	body	2048	valid
104.0ms	521×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

preprocess16.0ms (0.6%)

Algorithm

2×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	33	8
5	50	8
6	87	8
7	123	8
8	164	8
9	200	8
10	226	8
11	228	8
0	1	1

Stop Event

1×	saturated
1×	saturated

Compiler

Compiled 8 to 6 computations (25% saved)

simplify12.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

39×	`fma-def_binary64`
32×	`fma-neg_binary64`
15×	`cancel-sign-sub-inv_binary64`
12×	`sub-neg_binary64`
10×	`distribute-rgt-in_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	33	8
5	50	8
6	87	8
7	123	8
8	164	8
9	200	8
10	226	8
11	228	8

Stop Event

1×

saturated

Counts

1 → 2

prune2.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	2	1	3

Error

29.5b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	29.5b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 25 to 16 computations (36% saved)

localize4.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.9b	(-.f64 (log1p.f64 N) (log.f64 N))

series3.0ms (0.1%)

Counts

1 → 12

Calls

3 calls:

1.0ms	(-.f64 (log1p.f64 N) (log.f64 N))	N	-inf
1.0ms	(-.f64 (log1p.f64 N) (log.f64 N))	N	inf
1.0ms	(-.f64 (log1p.f64 N) (log.f64 N))	N	0

rewrite35.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

581×	`pow1_binary64`
541×	`add-log-exp_binary64`
541×	`expm1-log1p-u_binary64`
540×	`log1p-expm1-u_binary64`
529×	`add-exp-log_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	106	8
2	1449	8

Stop Event

1×	node limit

Counts

1 → 35

simplify23.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-neg_binary64`
511×	`cancel-sign-sub-inv_binary64`
415×	`times-frac_binary64`
223×	`fma-def_binary64`
191×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	34	186
1	94	184
2	235	184
3	685	181
4	2172	181

Stop Event

1×	node limit

Counts

47 → 49

prune43.0ms (1.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	46	3	49
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	3	50

Error

0.0b

Counts

50 → 3

Alt Table

Status	Error	Program
	32.0b	(-.f64 (+.f64 (/.f64 1 N) (.f64 1/3 (/.f64 1 (pow.f64 N 3)))) (+.f64 (.f64 1/4 (/.f64 1 (pow.f64 N 4))) (*.f64 1/2 (/.f64 1 (pow.f64 N 2)))))
	30.8b	(/.f64 1 N)
▶	29.4b	(log.f64 (/.f64 (+.f64 N 1) N))

Compiler

Compiled 699 to 344 computations (50.8% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 N 1) N)
✓	2.8b	(log.f64 (/.f64 (+.f64 N 1) N))

series4.0ms (0.2%)

Counts

2 → 24

Calls

6 calls:

1.0ms	(log.f64 (/.f64 (+.f64 N 1) N))	N	-inf
1.0ms	(log.f64 (/.f64 (+.f64 N 1) N))	N	inf
1.0ms	(log.f64 (/.f64 (+.f64 N 1) N))	N	0
1.0ms	(/.f64 (+.f64 N 1) N)	N	-inf
1.0ms	(/.f64 (+.f64 N 1) N)	N	inf

rewrite44.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

680×	`pow1_binary64`
635×	`log1p-expm1-u_binary64`
635×	`expm1-log1p-u_binary64`
634×	`add-log-exp_binary64`
64×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	127	15
2	1703	15

Stop Event

1×	node limit

Counts

2 → 60

simplify26.0ms (1%)

Algorithm

1×	egg-herbie

Rules

736×	`fma-neg_binary64`
511×	`cancel-sign-sub-inv_binary64`
415×	`times-frac_binary64`
223×	`fma-def_binary64`
191×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	35	255
1	96	253
2	237	253
3	689	250
4	2177	250

Stop Event

1×	node limit

Counts

84 → 76

prune30.0ms (1.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	76	3	79

Error

0.0b

Counts

79 → 3

Alt Table

Status	Error	Program
	31.9b	(+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (*.f64 N N)) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/4 (pow.f64 N 4)))))
▶	30.8b	(/.f64 1 N)
✓	29.4b	(log.f64 (/.f64 (+.f64 N 1) N))

Compiler

Compiled 884 to 538 computations (39.1% saved)

localize2.0ms (0.1%)

prune2.0ms (0.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	1	1
Picked	1	1
Done	1	1
Total	3	3

Error

0.0b

Counts

3 → 3

Alt Table

Status	Error	Program
▶	31.9b	(+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (*.f64 N N)) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/4 (pow.f64 N 4)))))
✓	30.8b	(/.f64 1 N)
✓	29.4b	(log.f64 (/.f64 (+.f64 N 1) N))

Compiler

Compiled 55 to 42 computations (23.6% saved)

localize11.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 -1/4 (pow.f64 N 4))
✓	0.5b	(/.f64 1/3 (pow.f64 N 3))
✓	0.8b	(/.f64 -1/2 (*.f64 N N))
✓	21.5b	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/4 (pow.f64 N 4)))

series13.0ms (0.5%)

Counts

4 → 24

Calls

12 calls:

2.0ms	(/.f64 -1/4 (pow.f64 N 4))	N	0
1.0ms	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/4 (pow.f64 N 4)))	N	0
1.0ms	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/4 (pow.f64 N 4)))	N	-inf
1.0ms	(+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/4 (pow.f64 N 4)))	N	inf
1.0ms	(/.f64 1/3 (pow.f64 N 3))	N	0

rewrite65.0ms (2.5%)

Algorithm

1×	batch-egg-rewrite

Rules

938×	`prod-diff_binary64`
154×	`add-sqr-sqrt_binary64`
150×	`add-log-exp_binary64`
150×	`log1p-expm1-u_binary64`
150×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	37
1	331	35
2	4153	35

Stop Event

1×	node limit

Counts

4 → 125

simplify31.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

388×	`distribute-neg-frac_binary64`
375×	`times-frac_binary64`
340×	`fma-def_binary64`
315×	`associate-l_binary64`
242×	`associate-/l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	249
1	47	249
2	95	249
3	216	249
4	772	249
5	3566	249

Stop Event

1×	node limit

Counts

149 → 131

prune93.0ms (3.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	131	3	134

Error

0.0b

Counts

134 → 3

Alt Table

Status	Error	Program
✓	31.9b	(+.f64 (/.f64 1 N) (+.f64 (/.f64 -1/2 (*.f64 N N)) (+.f64 (/.f64 1/3 (pow.f64 N 3)) (/.f64 -1/4 (pow.f64 N 4)))))
✓	30.8b	(/.f64 1 N)
✓	29.4b	(log.f64 (/.f64 (+.f64 N 1) N))

Compiler

Compiled 3482 to 2633 computations (24.4% saved)

regimes58.0ms (2.3%)

Accuracy

Total 0.0b remaining (1.5%)

Threshold costs 0.0b (1.5%)

Counts

21 → 2

Compiler

Compiled 594 to 452 computations (23.9% saved)

bsearch1.0ms (0%)

Algorithm

1×	left-value

Calls

1 calls:

0.0ms

(-.f64 (log.f64 (+.f64 N 1)) (log.f64 N))

Steps

Iters	Point		Range
0.00037743709491433464	∈ [	0.00037743709491433464	,	1.1257989073736718	]

Compiler

Compiled 8 to 6 computations (25% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
2×	`*-commutative_binary64`
2×	`sub-neg_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	27	54
1	35	54
2	39	54
3	41	54
4	42	54

Stop Event

1×

saturated

end64.0ms (2.5%)

Stop Event

1×

done

Compiler

Compiled 107 to 81 computations (24.3% saved)

Details

analyze1.0ms (0%)

sample2.0s (77%)

preprocess16.0ms (0.6%)

simplify12.0ms (0.5%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series3.0ms (0.1%)

rewrite35.0ms (1.4%)

simplify23.0ms (0.9%)

prune43.0ms (1.7%)

localize4.0ms (0.2%)

series4.0ms (0.2%)

rewrite44.0ms (1.7%)

simplify26.0ms (1%)

prune30.0ms (1.2%)

localize2.0ms (0.1%)

prune2.0ms (0.1%)

localize11.0ms (0.4%)

series13.0ms (0.5%)

rewrite65.0ms (2.5%)

simplify31.0ms (1.2%)

prune93.0ms (3.6%)

regimes58.0ms (2.3%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end64.0ms (2.5%)

Profiling