Details

analyze455.0ms (18.9%)

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)

sample1.6s (65%)

Results

810.0ms	2684×	body	1024	valid
276.0ms	1342×	body	512	valid
248.0ms	3256×	body	128	valid
106.0ms	312×	body	2048	valid
94.0ms	662×	body	256	valid
0.0ms	1×	body	128	invalid

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

0.8b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.8b	(/.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
✓	0.7b	(/.f64 (exp.f64 x) (expm1.f64 x))

series7.0ms (0.3%)

Counts

1 → 12

Calls

1 calls:

7.0ms

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

rewrite34.0ms (1.4%)

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:

33.0ms

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

simplify32.0ms (1.3%)

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

prune41.0ms (1.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	2	76

Error

0.6b

Counts

76 → 2

Alt Table

Status	Error	Program
▶	0.8b	(.f64 (sqrt.f64 (exp.f64 x)) (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))
	20.5b	(+.f64 1/2 (/.f64 1 x))

Compiler

Compiled 1002 to 442 computations (55.9% saved)

localize6.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (expm1.f64 x))
✓	0.7b	(.f64 (sqrt.f64 (exp.f64 x)) (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))
✓	0.7b	(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))

series24.0ms (1%)

Counts

3 → 36

Calls

3 calls:

11.0ms	(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))
7.0ms	(.f64 (sqrt.f64 (exp.f64 x)) (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))
6.0ms	(/.f64 1 (expm1.f64 x))

rewrite42.0ms (1.7%)

Algorithm

1×	batch-egg-rewrite

Rules

713×	`log1p-expm1-u_binary64`
713×	`expm1-log1p-u_binary64`
141×	`expm1-udef_binary64`
141×	`log1p-udef_binary64`
82×	`add-sqr-sqrt_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	9	27
1	176	24
2	2094	24

Stop Event

1×	node limit

Counts

3 → 67

Calls

3 calls:

40.0ms	(/.f64 1 (expm1.f64 x))
40.0ms	(.f64 (sqrt.f64 (exp.f64 x)) (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))
40.0ms	(*.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x)))

simplify34.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

636×	`fma-neg_binary64`
458×	`cancel-sign-sub-inv_binary64`
436×	`fma-def_binary64`
371×	`distribute-rgt-neg-in_binary64`
279×	`sub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	38	367
1	107	329
2	273	323
3	834	321
4	2106	321
5	3968	321

Stop Event

1×	node limit

Counts

103 → 90

prune39.0ms (1.6%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	90	2	92

Error

0.6b

Counts

92 → 2

Alt Table

Status	Error	Program
✓	0.8b	(.f64 (sqrt.f64 (exp.f64 x)) (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))
▶	20.5b	(+.f64 1/2 (/.f64 1 x))

Compiler

Compiled 1191 to 532 computations (55.3% saved)

localize3.0ms (0.1%)

prune1.0ms (0.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

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

Error

0.6b

Counts

2 → 2

Alt Table

Status	Error	Program
✓	0.8b	(.f64 (sqrt.f64 (exp.f64 x)) (.f64 (sqrt.f64 (exp.f64 x)) (/.f64 1 (expm1.f64 x))))
✓	20.5b	(+.f64 1/2 (/.f64 1 x))

Compiler

Compiled 19 to 13 computations (31.6% saved)

regimes71.0ms (2.9%)

Accuracy

Total 0.1b remaining (18.9%)

Threshold costs 0.1b (18.9%)

Counts

36 → 1

Compiler

Compiled 1019 to 772 computations (24.2% 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

end40.0ms (1.6%)

Compiler: Compiled 35 to 25 computations (28.6% saved)

Details

analyze455.0ms (18.9%)

sample1.6s (65%)

simplify6.0ms (0.2%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series7.0ms (0.3%)

rewrite34.0ms (1.4%)

simplify32.0ms (1.3%)

prune41.0ms (1.7%)

localize6.0ms (0.3%)

series24.0ms (1%)

rewrite42.0ms (1.7%)

simplify34.0ms (1.4%)

prune39.0ms (1.6%)

localize3.0ms (0.1%)

prune1.0ms (0.1%)

regimes71.0ms (2.9%)

simplify2.0ms (0.1%)

end40.0ms (1.6%)

Profiling