Details

analyze379.0ms (13.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
12.5%	62.5%	25%	4
18.7%	43.7%	37.5%	5
21.9%	34.4%	43.8%	6
23.4%	29.7%	46.9%	7
24.2%	27.3%	48.5%	8
24.6%	26.2%	49.2%	9
24.8%	25.6%	49.6%	10
24.9%	25.3%	49.8%	11
24.9%	25.1%	49.9%	12
25%	25.1%	50%	13
25%	25%	50%	14

Compiler

Compiled 11 to 8 computations (27.3% saved)

sample1.6s (57.4%)

Results

814.0ms	8256×	body	128	valid
745.0ms	8237×	body	128	invalid

Compiler

Compiled 22 to 16 computations (27.3% saved)

preprocess36.0ms (1.3%)

Algorithm

2×	egg-herbie

Rules

868×	`fma-neg_binary64`
396×	`unsub-neg_binary64`
348×	`distribute-neg-in_binary64`
330×	`fma-def_binary64`
262×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	18	12
2	22	12
3	37	12
4	78	12
5	154	12
6	360	12
7	751	12
8	2365	12
9	4284	12
0	1	1

Stop Event

1×	saturated
1×	node limit

Compiler

Compiled 10 to 7 computations (30% saved)

simplify27.0ms (1%)

Algorithm

1×	egg-herbie

Rules

868×	`fma-neg_binary64`
396×	`unsub-neg_binary64`
348×	`distribute-neg-in_binary64`
330×	`fma-def_binary64`
262×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	12
1	18	12
2	22	12
3	37	12
4	78	12
5	154	12
6	360	12
7	751	12
8	2365	12
9	4284	12

Stop Event

1×	node limit

Counts

1 → 2

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

34.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	34.3b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))

Compiler

Compiled 36 to 24 computations (33.3% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
✓	0.0b	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
✓	31.9b	(sqrt.f64 (fma.f64 x x -1))

series13.0ms (0.5%)

Counts

3 → 36

Calls

9 calls:

3.0ms	(sqrt.f64 (fma.f64 x x -1))	x	-inf
2.0ms	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))	x	0
1.0ms	(sqrt.f64 (fma.f64 x x -1))	x	0
1.0ms	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))	x	-inf
1.0ms	(log.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))	x	inf

rewrite48.0ms (1.8%)

Algorithm

1×	batch-egg-rewrite

Rules

671×	`log1p-expm1-u_binary64`
671×	`expm1-log1p-u_binary64`
615×	`prod-diff_binary64`
81×	`egg-rr`
69×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	29
1	142	29
2	1814	29

Stop Event

1×	node limit

Counts

3 → 81

simplify39.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

442×	`fma-neg_binary64`
301×	`sub-neg_binary64`
257×	`distribute-neg-frac_binary64`
230×	`fma-def_binary64`
183×	`associate-+l+_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	104	681
1	307	648
2	920	646
3	3390	646

Stop Event

1×	node limit

Counts

117 → 144

prune78.0ms (2.8%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	143	2	145

Error

Counts

145 → 2

Alt Table

Status	Error	Program
	34.3b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))) (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))))
▶	0.2b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 2242 to 1662 computations (25.9% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x 2 (/.f64 -1/2 x))
✓	0.0b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

series10.0ms (0.3%)

Counts

2 → 24

Calls

6 calls:

5.0ms	(fma.f64 x 2 (/.f64 -1/2 x))	x	0
1.0ms	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))	x	0
1.0ms	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))	x	inf
1.0ms	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))	x	-inf
1.0ms	(fma.f64 x 2 (/.f64 -1/2 x))	x	inf

rewrite45.0ms (1.6%)

Algorithm

1×	batch-egg-rewrite

Rules

606×	`log1p-expm1-u_binary64`
606×	`expm1-log1p-u_binary64`
283×	`log-prod_binary64`
126×	`expm1-udef_binary64`
126×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	18
1	146	18
2	1652	18

Stop Event

1×	node limit

Counts

2 → 57

simplify30.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

741×	`fma-def_binary64`
415×	`cancel-sign-sub-inv_binary64`
356×	`sub-neg_binary64`
315×	`fma-neg_binary64`
245×	`associate-l_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	64	374
1	177	342
2	537	342
3	2039	342

Stop Event

1×	node limit

Counts

81 → 84

prune49.0ms (1.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	84	2	86

Error

Counts

86 → 2

Alt Table

Status	Error	Program
▶	34.3b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))) (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))))
✓	0.2b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 1202 to 932 computations (22.5% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1)))))
✓	0.0b	(sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))
	0.0b	(+.f64 x (sqrt.f64 (fma.f64 x x -1)))
	31.9b	(sqrt.f64 (fma.f64 x x -1))

series16.0ms (0.6%)

Counts

2 → 8

Calls

6 calls:

4.0ms	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1)))))	x	inf
4.0ms	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1)))))	x	0
3.0ms	(log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1)))))	x	-inf
2.0ms	(sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))	x	-inf
2.0ms	(sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))	x	inf

rewrite47.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

732×	`log1p-expm1-u_binary64`
732×	`expm1-log1p-u_binary64`
615×	`prod-diff_binary64`
76×	`add-sqr-sqrt_binary64`
73×	`add-cbrt-cube_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	26
1	161	26
2	2006	26

Stop Event

1×	node limit

Counts

2 → 49

simplify22.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

792×	`fma-def_binary64`
576×	`times-frac_binary64`
511×	`associate-/l*_binary64`
471×	`cancel-sign-sub-inv_binary64`
235×	`fma-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	45	240
1	119	216
2	356	214
3	1428	202

Stop Event

1×	node limit

Counts

57 → 63

prune212.0ms (7.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	330	0	330
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	330	2	332

Error

Counts

332 → 2

Alt Table

Status	Error	Program
✓	34.3b	(+.f64 (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))) (log.f64 (sqrt.f64 (+.f64 x (sqrt.f64 (fma.f64 x x -1))))))
✓	0.2b	(log.f64 (fma.f64 x 2 (/.f64 -1/2 x)))

Compiler

Compiled 8555 to 6279 computations (26.6% saved)

regimes55.0ms (2%)

Accuracy

Total 0.3b remaining (88.4%)

Threshold costs 0.3b (88.4%)

Counts

20 → 1

Compiler

Compiled 633 to 466 computations (26.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10

Stop Event

1×

saturated

end47.0ms (1.7%)

Stop Event

1×

done

Compiler

Compiled 44 to 32 computations (27.3% saved)

Details

analyze379.0ms (13.7%)

sample1.6s (57.4%)

preprocess36.0ms (1.3%)

simplify27.0ms (1%)

prune3.0ms (0.1%)

localize6.0ms (0.2%)

series13.0ms (0.5%)

rewrite48.0ms (1.8%)

simplify39.0ms (1.4%)

prune78.0ms (2.8%)

localize5.0ms (0.2%)

series10.0ms (0.3%)

rewrite45.0ms (1.6%)

simplify30.0ms (1.1%)

prune49.0ms (1.8%)

localize8.0ms (0.3%)

series16.0ms (0.6%)

rewrite47.0ms (1.7%)

simplify22.0ms (0.8%)

prune212.0ms (7.7%)

regimes55.0ms (2%)

simplify2.0ms (0.1%)

end47.0ms (1.7%)

Profiling