Details

analyze2.0ms (0.1%)

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)

sample57.0ms (2.7%)

Algorithm

1×

intervals

Results

12.0ms	48×	body	1024	valid
10.0ms	155×	body	128	valid
5.0ms	30×	body	512	valid
4.0ms	9×	body	2048	valid
1.0ms	14×	body	256	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify13.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	31	8
5	48	8
6	73	8
7	93	8
8	110	8
9	120	8
10	124	8
11	126	8
12	112	8

prune3.0ms (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

25.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	25.8b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 25 to 16 computations (36% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.4b	(-.f64 (log1p.f64 N) (log.f64 N))

series4.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

4.0ms

(-.f64 (log1p.f64 N) (log.f64 N))

rewrite6.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`prod-diff_binary64`
11×	`add-cube-cbrt_binary64`
6×	`pow1_binary64`

Counts

1 → 39

Calls

1 calls:

4.0ms

(-.f64 (log1p.f64 N) (log.f64 N))

simplify114.0ms (5.4%)

Algorithm

1×	egg-herbie

Rules

435×	`fma-neg_binary64`
299×	`fma-def_binary64`
276×	`associate-l_binary64`
252×	`associate-/r*_binary64`
244×	`cancel-sign-sub-inv_binary64`

Counts

51 → 56

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	102	928
1	214	635
2	600	575
3	2045	572
4	4184	572
5	4526	572
6	4942	572
7	4836	572

prune33.0ms (1.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	55	2	57

Error

0.0b

Counts

57 → 2

Alt Table

Status	Error	Program
▶	25.7b	(log.f64 (/.f64 (+.f64 1 N) N))
	36.1b	(-.f64 (+.f64 (/.f64 1 N) (/.f64 1/3 (pow.f64 N 3))) (+.f64 (/.f64 1/2 (*.f64 N N)) (/.f64 1/4 (pow.f64 N 4))))

Compiler

Compiled 888 to 313 computations (64.8% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (+.f64 1 N) N)
✓	2.2b	(log.f64 (/.f64 (+.f64 1 N) N))

series5.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(log.f64 (/.f64 (+.f64 1 N) N))
2.0ms	(/.f64 (+.f64 1 N) N)

rewrite11.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
24×	`times-frac_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
16×	`log-prod_binary64`

Counts

2 → 64

Calls

2 calls:

4.0ms	(/.f64 (+.f64 1 N) N)
3.0ms	(log.f64 (/.f64 (+.f64 1 N) N))

simplify83.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

809×	`fma-def_binary64`
443×	`distribute-rgt-in_binary64`
395×	`associate-/l/_binary64`
394×	`fma-neg_binary64`
377×	`distribute-lft-in_binary64`

Counts

88 → 116

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	119	1207
1	263	1146
2	664	1124
3	1868	1117
4	4464	1079
5	4932	1079

prune60.0ms (2.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	113	3	116
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	114	4	118

Error

0.0b

Counts

118 → 4

Alt Table

Status	Error	Program
✓	25.7b	(log.f64 (/.f64 (+.f64 1 N) N))
▶	0.5b	(*.f64 (sqrt.f64 (log1p.f64 (/.f64 1 N))) (sqrt.f64 (log1p.f64 (/.f64 1 N))))
	15.9b	(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))
	0.6b	(expm1.f64 (log1p.f64 (log1p.f64 (/.f64 1 N))))

Compiler

Compiled 1526 to 1058 computations (30.7% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (/.f64 1 N))
✓	0.1b	(sqrt.f64 (log1p.f64 (/.f64 1 N)))
✓	0.5b	(*.f64 (sqrt.f64 (log1p.f64 (/.f64 1 N))) (sqrt.f64 (log1p.f64 (/.f64 1 N))))

series20.0ms (0.9%)

Counts

3 → 28

Calls

3 calls:

13.0ms	(sqrt.f64 (log1p.f64 (/.f64 1 N)))
3.0ms	(*.f64 (sqrt.f64 (log1p.f64 (/.f64 1 N))) (sqrt.f64 (log1p.f64 (/.f64 1 N))))
3.0ms	(log1p.f64 (/.f64 1 N))

rewrite11.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
21×	`sqrt-prod_binary64`
19×	`pow1_binary64`
12×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`

Counts

3 → 79

Calls

3 calls:

5.0ms	(*.f64 (sqrt.f64 (log1p.f64 (/.f64 1 N))) (sqrt.f64 (log1p.f64 (/.f64 1 N))))
1.0ms	(sqrt.f64 (log1p.f64 (/.f64 1 N)))
0.0ms	(log1p.f64 (/.f64 1 N))

simplify119.0ms (5.6%)

Algorithm

1×	egg-herbie

Rules

639×	`cancel-sign-sub-inv_binary64`
588×	`fma-neg_binary64`
234×	`associate-/l/_binary64`
183×	`neg-mul-1_binary64`
168×	`associate-l_binary64`

Counts

107 → 100

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	113	1403
1	239	1323
2	713	1267
3	2435	1210
4	4421	1210
5	4932	1210
6	4991	1210
7	4915	1210

prune92.0ms (4.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	126	2	128
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	127	5	132

Error

Counts

132 → 5

Alt Table

Status	Error	Program
▶	0.0b	(log1p.f64 (/.f64 1 N))
✓	25.7b	(log.f64 (/.f64 (+.f64 1 N) N))
✓	0.5b	(*.f64 (sqrt.f64 (log1p.f64 (/.f64 1 N))) (sqrt.f64 (log1p.f64 (/.f64 1 N))))
	15.9b	(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))
	25.0b	(*.f64 (sqrt.f64 (log1p.f64 (/.f64 1 N))) (log.f64 (exp.f64 (sqrt.f64 (log1p.f64 (/.f64 1 N))))))

Compiler

Compiled 2348 to 1769 computations (24.7% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
	0.0b	(log1p.f64 (/.f64 1 N))

prune5.0ms (0.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	4	0	4
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	4	5	9

Error

Counts

9 → 5

Alt Table

Status	Error	Program
✓	0.0b	(log1p.f64 (/.f64 1 N))
✓	25.7b	(log.f64 (/.f64 (+.f64 1 N) N))
✓	0.5b	(*.f64 (sqrt.f64 (log1p.f64 (/.f64 1 N))) (sqrt.f64 (log1p.f64 (/.f64 1 N))))
	15.9b	(cbrt.f64 (pow.f64 (log1p.f64 (/.f64 1 N)) 3))
	25.0b	(*.f64 (sqrt.f64 (log1p.f64 (/.f64 1 N))) (log.f64 (exp.f64 (sqrt.f64 (log1p.f64 (/.f64 1 N))))))

Compiler

Compiled 91 to 75 computations (17.6% saved)

regimes44.0ms (2.1%)

Accuracy

Total 0.0b remaining (18%)

Threshold costs 0.0b (18%)

Counts

25 → 1

Compiler

Compiled 542 to 434 computations (19.9% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	6
1	7	6
2	6	6

end0.0ms (0%)

Compiler: Compiled 5 to 4 computations (20% saved)

sample1.4s (67.1%)

Algorithm

1×

intervals

Results

544.0ms	2013×	body	1024	valid
328.0ms	4325×	body	128	valid
160.0ms	938×	body	512	valid
99.0ms	251×	body	2048	valid
51.0ms	473×	body	256	valid

Compiler

Compiled 61 to 50 computations (18% saved)

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	31	8
5	48	8
6	73	8
7	93	8
8	110	8
9	120	8
10	124	8
11	126	8
12	112	8

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	31	8
5	48	8
6	73	8
7	93	8
8	110	8
9	120	8
10	124	8
11	126	8
12	112	8

Details

analyze2.0ms (0.1%)

sample57.0ms (2.7%)

simplify13.0ms (0.6%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series4.0ms (0.2%)

rewrite6.0ms (0.3%)

simplify114.0ms (5.4%)

prune33.0ms (1.5%)

localize4.0ms (0.2%)

series5.0ms (0.2%)

rewrite11.0ms (0.5%)

simplify83.0ms (3.9%)

prune60.0ms (2.8%)

localize5.0ms (0.2%)

series20.0ms (0.9%)

rewrite11.0ms (0.5%)

simplify119.0ms (5.6%)

prune92.0ms (4.3%)

localize3.0ms (0.1%)

prune5.0ms (0.2%)

regimes44.0ms (2.1%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.4s (67.1%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	8
2	17	8
3	24	8
4	31	8
5	48	8
6	73	8
7	93	8
8	110	8
9	120	8
10	124	8
11	126	8
12	112	8