Details

analyze478.0ms (18.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 9 to 6 computations (33.3% saved)

sample1.7s (64.1%)

Results

877.0ms	2690×	body	1024	valid
288.0ms	1324×	body	512	valid
257.0ms	3259×	body	128	valid
112.0ms	291×	body	2048	valid
110.0ms	692×	body	256	valid

Compiler

Compiled 26 to 17 computations (34.6% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

1×	`+-commutative_binary64`
1×	`sub-neg_binary64`
1×	`1-exp_binary64`
1×	`expm1-def_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8

Stop Event

1×

saturated

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

1.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 25 to 15 computations (40% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))

series12.0ms (0.5%)

Counts

1 → 12

Calls

1 calls:

12.0ms

(/.f64 (exp.f64 x) (expm1.f64 x))

rewrite33.0ms (1.3%)

Algorithm

1×	batch-egg-rewrite

Rules

477×	`log1p-expm1-u_binary64`
477×	`expm1-log1p-u_binary64`
332×	`unpow-prod-down_binary64`
258×	`log-prod_binary64`
131×	`pow2_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	99	8
2	1299	8

Stop Event

1×	node limit

Counts

1 → 66

Calls

1 calls:

31.0ms

(/.f64 (exp.f64 x) (expm1.f64 x))

simplify33.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

1089×	`fma-neg_binary64`
754×	`fma-def_binary64`
260×	`cancel-sign-sub-inv_binary64`
211×	`associate-l_binary64`
208×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	18	110
1	46	106
2	101	104
3	306	104
4	830	104
5	1782	104
6	3144	104
7	4892	104

Stop Event

1×	node limit

Counts

78 → 75

prune37.0ms (1.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	73	3	76

Error

0.8b

Counts

76 → 3

Alt Table

Status	Error	Program
	23.1b	(-.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 1/720 (pow.f64 x 3) -1/2))
▶	22.5b	(+.f64 1/2 (/.f64 1 x))
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 1010 to 452 computations (55.2% saved)

localize3.0ms (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

0.8b

Counts

3 → 3

Alt Table

Status	Error	Program
▶	23.1b	(-.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 1/720 (pow.f64 x 3) -1/2))
✓	22.5b	(+.f64 1/2 (/.f64 1 x))
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 40 to 31 computations (22.5% saved)

localize8.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 1/720 (pow.f64 x 3) -1/2))
✓	0.0b	(fma.f64 1/720 (pow.f64 x 3) -1/2)
✓	0.1b	(fma.f64 x 1/12 (/.f64 1 x))

series7.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

3.0ms	(fma.f64 1/720 (pow.f64 x 3) -1/2)
2.0ms	(-.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 1/720 (pow.f64 x 3) -1/2))
2.0ms	(fma.f64 x 1/12 (/.f64 1 x))

rewrite55.0ms (2.1%)

Algorithm

1×	batch-egg-rewrite

Rules

509×	`prod-diff_binary64`
236×	`fma-def_binary64`
209×	`expm1-udef_binary64`
209×	`log1p-udef_binary64`
136×	`fma-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	34
1	259	34
2	2991	34

Stop Event

1×	node limit

Counts

3 → 132

Calls

3 calls:

52.0ms	(-.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 1/720 (pow.f64 x 3) -1/2))
52.0ms	(fma.f64 1/720 (pow.f64 x 3) -1/2)
52.0ms	(fma.f64 x 1/12 (/.f64 1 x))

simplify42.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1114×	`fma-neg_binary64`
449×	`fma-def_binary64`
329×	`cancel-sign-sub-inv_binary64`
235×	`associate-l_binary64`
208×	`unswap-sqr_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	22	351
1	55	317
2	123	307
3	378	307
4	948	307
5	2015	307
6	3228	307
7	4915	307

Stop Event

1×	node limit

Counts

168 → 153

prune119.0ms (4.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	153	3	156

Error

0.8b

Counts

156 → 3

Alt Table

Status	Error	Program
✓	23.1b	(-.f64 (fma.f64 x 1/12 (/.f64 1 x)) (fma.f64 1/720 (pow.f64 x 3) -1/2))
✓	22.5b	(+.f64 1/2 (/.f64 1 x))
✓	1.0b	(/.f64 (exp.f64 x) (expm1.f64 x))

Compiler

Compiled 3668 to 2977 computations (18.8% saved)

regimes43.0ms (1.7%)

Accuracy

Total 0.1b remaining (20.5%)

Threshold costs 0.1b (20.5%)

Counts

15 → 1

Compiler

Compiled 440 to 337 computations (23.4% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	12	11

Stop Event

1×

saturated

end52.0ms (2%)

Compiler: Compiled 42 to 32 computations (23.8% saved)

Details

analyze478.0ms (18.3%)

sample1.7s (64.1%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series12.0ms (0.5%)

rewrite33.0ms (1.3%)

simplify33.0ms (1.2%)

prune37.0ms (1.4%)

localize3.0ms (0.1%)

prune2.0ms (0.1%)

localize8.0ms (0.3%)

series7.0ms (0.3%)

rewrite55.0ms (2.1%)

simplify42.0ms (1.6%)

prune119.0ms (4.6%)

regimes43.0ms (1.7%)

simplify2.0ms (0.1%)

end52.0ms (2%)

Profiling