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 (73%)

Results

898.0ms	2101×	body	1024	valid
515.0ms	4323×	body	128	valid
298.0ms	1057×	body	512	valid
150.0ms	255×	body	2048	valid
108.0ms	520×	body	256	valid

Compiler

Compiled 26 to 20 computations (23.1% saved)

simplify9.0ms (0.3%)

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

31.1b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.1b	(-.f64 (log1p.f64 N) (log.f64 N))

Compiler

Compiled 25 to 16 computations (36% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 N)
✓	2.7b	(-.f64 (log1p.f64 N) (log.f64 N))

series5.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

3.0ms	(-.f64 (log1p.f64 N) (log.f64 N))
2.0ms	(log1p.f64 N)

rewrite40.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

541×	`expm1-log1p-u_binary64`
540×	`log1p-expm1-u_binary64`
394×	`prod-diff_binary64`
252×	`log-prod_binary64`
168×	`fma-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	11
1	106	11
2	1431	11

Stop Event

1×	node limit

Counts

2 → 106

Calls

2 calls:

38.0ms	(log1p.f64 N)
38.0ms	(-.f64 (log1p.f64 N) (log.f64 N))

simplify24.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

565×	`fma-def_binary64`
324×	`fma-neg_binary64`
270×	`associate--l+_binary64`
260×	`cancel-sign-sub-inv_binary64`
249×	`associate-+l-_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	56	376
1	164	350
2	474	346
3	1508	335

Stop Event

1×	node limit

Counts

130 → 139

prune62.0ms (2.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	138	2	140

Error

0.0b

Counts

140 → 2

Alt Table

Status	Error	Program
▶	30.7b	(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
	31.0b	(log.f64 (/.f64 (+.f64 N 1) N))

Compiler

Compiled 1962 to 840 computations (57.2% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
✓	0.4b	(/.f64 -1/2 (*.f64 N N))

series5.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

2.0ms	(/.f64 -1/2 (*.f64 N N))
2.0ms	(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))

rewrite43.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

801×	`prod-diff_binary64`
304×	`fma-def_binary64`
164×	`fma-neg_binary64`
151×	`expm1-udef_binary64`
151×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	8	20
1	184	18
2	2616	18

Stop Event

1×	node limit

Counts

2 → 88

Calls

2 calls:

42.0ms	(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
41.0ms	(/.f64 -1/2 (*.f64 N N))

simplify19.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

732×	`times-frac_binary64`
530×	`associate-/r*_binary64`
492×	`associate-/l/_binary64`
303×	`associate-/l*_binary64`
284×	`associate-*l/_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	216
1	26	216
2	46	216
3	100	216
4	264	216
5	937	216

Stop Event

1×	node limit

Counts

112 → 93

prune45.0ms (1.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	92	1	93
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	92	3	95

Error

0.0b

Counts

95 → 3

Alt Table

Status	Error	Program
✓	30.7b	(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
▶	31.0b	(log.f64 (/.f64 (+.f64 N 1) N))
	51.4b	(.f64 (.f64 N (+.f64 N -1/2)) (pow.f64 N -3))

Compiler

Compiled 1296 to 928 computations (28.4% saved)

localize4.0ms (0.1%)

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

2 calls:

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

rewrite42.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

635×	`log1p-expm1-u_binary64`
635×	`expm1-log1p-u_binary64`
115×	`fma-def_binary64`
108×	`log1p-udef_binary64`
107×	`expm1-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	6	16
1	127	15
2	1684	15

Stop Event

1×	node limit

Counts

2 → 88

Calls

2 calls:

40.0ms	(/.f64 (+.f64 N 1) N)
40.0ms	(log.f64 (/.f64 (+.f64 N 1) N))

simplify25.0ms (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	35	255
1	96	253
2	237	253
3	689	250
4	2177	250

Stop Event

1×	node limit

Counts

112 → 104

prune70.0ms (2.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	104	3	107

Error

0.0b

Counts

107 → 3

Alt Table

Status	Error	Program
✓	30.7b	(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
▶	31.0b	(neg.f64 (log.f64 (/.f64 (/.f64 N (+.f64 N 1)) 1)))
	51.4b	(.f64 (.f64 N (+.f64 N -1/2)) (pow.f64 N -3))

Compiler

Compiled 1295 to 705 computations (45.6% saved)

localize6.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

series5.0ms (0.2%)

Counts

2 → 24

Calls

2 calls:

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

rewrite39.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

668×	`log1p-expm1-u_binary64`
668×	`expm1-log1p-u_binary64`
118×	`fma-neg_binary64`
117×	`fma-def_binary64`
111×	`log1p-udef_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	7	16
1	157	15
2	1877	15

Stop Event

1×	node limit

Counts

2 → 87

Calls

2 calls:

38.0ms	(/.f64 N (+.f64 N 1))
38.0ms	(log.f64 (/.f64 (/.f64 N (+.f64 N 1)) 1))

simplify34.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

464×	`fma-def_binary64`
416×	`times-frac_binary64`
391×	`sub-neg_binary64`
293×	`cancel-sign-sub-inv_binary64`
238×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	44	322
1	119	318
2	335	313
3	1047	309
4	4121	309

Stop Event

1×	node limit

Counts

111 → 114

prune51.0ms (1.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	114	0	114
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	114	3	117

Error

0.0b

Counts

117 → 3

Alt Table

Status	Error	Program
✓	30.7b	(+.f64 (/.f64 1 N) (/.f64 -1/2 (*.f64 N N)))
✓	31.0b	(neg.f64 (log.f64 (/.f64 (/.f64 N (+.f64 N 1)) 1)))
	51.4b	(.f64 (.f64 N (+.f64 N -1/2)) (pow.f64 N -3))

Compiler

Compiled 1628 to 970 computations (40.4% saved)

regimes130.0ms (4.8%)

Accuracy

Total 0.1b remaining (37.9%)

Threshold costs 0.1b (37.9%)

Counts

61 → 2

Compiler

Compiled 1152 to 862 computations (25.2% saved)

bsearch1.0ms (0%)

Compiler: Compiled 8 to 6 computations (25% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	38
1	29	38
2	34	38
3	37	38
4	38	38

Stop Event

1×

saturated

end61.0ms (2.2%)

Compiler: Compiled 82 to 62 computations (24.4% saved)

Details

analyze1.0ms (0%)

sample2.0s (73%)

simplify9.0ms (0.3%)

prune2.0ms (0.1%)

localize4.0ms (0.2%)

series5.0ms (0.2%)

rewrite40.0ms (1.4%)

simplify24.0ms (0.9%)

prune62.0ms (2.3%)

localize5.0ms (0.2%)

series5.0ms (0.2%)

rewrite43.0ms (1.6%)

simplify19.0ms (0.7%)

prune45.0ms (1.7%)

localize4.0ms (0.1%)

series4.0ms (0.2%)

rewrite42.0ms (1.5%)

simplify25.0ms (0.9%)

prune70.0ms (2.5%)

localize6.0ms (0.2%)

series5.0ms (0.2%)

rewrite39.0ms (1.4%)

simplify34.0ms (1.3%)

prune51.0ms (1.9%)

regimes130.0ms (4.8%)

bsearch1.0ms (0%)

simplify2.0ms (0.1%)

end61.0ms (2.2%)

Profiling