Details

analyze32.0ms (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
62.5%	25%	12.5%	4
68.7%	12.5%	18.8%	5
71.8%	6.2%	21.9%	6
73.4%	3.1%	23.5%	7
74.2%	1.6%	24.3%	8
74.6%	0.8%	24.6%	9
75%	0.4%	24.6%	10
75.1%	0.2%	24.7%	11
75.1%	0.1%	24.8%	12
75.1%	0%	24.8%	13
75.2%	0%	24.8%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample34.0ms (1.8%)

Algorithm

1×

intervals

Results

15.0ms	90×	body	1024	valid
6.0ms	50×	body	512	valid
3.0ms	88×	body	128	valid
2.0ms	13×	body	2048	valid
1.0ms	15×	body	256	valid

Compiler

Compiled 16 to 12 computations (25% saved)

simplify19.0ms (1%)

Algorithm

1×	egg-herbie

Rules

95×	`fma-def_binary64`
80×	`fma-neg_binary64`
32×	`distribute-rgt-in_binary64`
27×	`cancel-sign-sub-inv_binary64`
26×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	38	6
6	57	6
7	86	6
8	113	6
9	154	6
10	224	6
11	261	6
12	297	6
13	300	6
14	263	6

prune4.0ms (0.2%)

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

0.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	0.0b	(/.f64 (expm1.f64 x) x)

Compiler

Compiled 21 to 13 computations (38.1% saved)

localize3.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (expm1.f64 x) x)

rewrite4.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
9×	`times-frac_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64`
3×	`associate-/r*_binary64`

Counts

1 → 30

Calls

1 calls:

2.0ms

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

series9.0ms (0.5%)

Counts

1 → 12

Calls

1 calls:

9.0ms

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

simplify68.0ms (3.6%)

Algorithm

1×	egg-herbie

Rules

665×	`times-frac_binary64`
337×	`associate-/l*_binary64`
285×	`fma-def_binary64`
269×	`associate-l_binary64`
256×	`fma-neg_binary64`

Counts

42 → 60

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	76	468
1	144	440
2	345	437
3	884	430
4	4051	430
5	5063	430

prune24.0ms (1.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	2	61

Error

Counts

61 → 2

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (expm1.f64 x) x)
▶	19.6b	(+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3)))))

Compiler

Compiled 443 to 185 computations (58.2% saved)

localize10.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(*.f64 1/6 (pow.f64 x 2))
✓	0.3b	(*.f64 1/24 (pow.f64 x 3))
✓	8.5b	(+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3))))

rewrite19.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`add-sqr-sqrt_binary64`
20×	`associate-r_binary64`
13×	`add-exp-log_binary64`
10×	`*-un-lft-identity_binary64`
10×	`add-cube-cbrt_binary64`

Counts

3 → 78

Calls

3 calls:

6.0ms	(+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3))))
5.0ms	(*.f64 1/6 (pow.f64 x 2))
5.0ms	(*.f64 1/24 (pow.f64 x 3))

series32.0ms (1.7%)

Counts

3 → 8

Calls

3 calls:

13.0ms	(*.f64 1/24 (pow.f64 x 3))
10.0ms	(*.f64 1/6 (pow.f64 x 2))
8.0ms	(+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3))))

simplify111.0ms (5.9%)

Algorithm

1×	egg-herbie

Rules

599×	`fma-neg_binary64`
326×	`fma-def_binary64`
312×	`*-commutative_binary64`
287×	`distribute-rgt-in_binary64`
278×	`cancel-sign-sub-inv_binary64`

Counts

86 → 152

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	136	1168
1	298	1008
2	913	962
3	2749	939
4	4355	932
5	4834	932
6	4977	932

prune124.0ms (6.6%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	152	0	152
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	152	2	154

Error

Counts

154 → 2

Alt Table

Status	Error	Program
✓	0.0b	(/.f64 (expm1.f64 x) x)
✓	19.6b	(+.f64 1 (+.f64 (.f64 1/6 (pow.f64 x 2)) (+.f64 (.f64 1/2 x) (*.f64 1/24 (pow.f64 x 3)))))

Compiler

Compiled 2657 to 2144 computations (19.3% saved)

regimes43.0ms (2.3%)

Accuracy

Total 0.0b remaining (66.6%)

Threshold costs 0.0b (66.6%)

Compiler

Compiled 549 to 415 computations (24.4% saved)

simplify3.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	10
1	6	10

end0.0ms (0%)

Compiler: Compiled 7 to 5 computations (28.6% saved)

sample1.3s (71.2%)

Algorithm

1×

intervals

Results

763.0ms	2727×	body	1024	valid
127.0ms	1291×	body	512	valid
86.0ms	2989×	body	128	valid
59.0ms	714×	body	256	valid
56.0ms	279×	body	2048	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 39 to 30 computations (23.1% saved)

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	38	6
6	57	6
7	86	6
8	113	6
9	154	6
10	224	6
11	261	6
12	297	6
13	300	6
14	263	6

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	38	6
6	57	6
7	86	6
8	113	6
9	154	6
10	224	6
11	261	6
12	297	6
13	300	6
14	263	6

Details

analyze32.0ms (1.7%)

sample34.0ms (1.8%)

simplify19.0ms (1%)

prune4.0ms (0.2%)

localize3.0ms (0.1%)

rewrite4.0ms (0.2%)

series9.0ms (0.5%)

simplify68.0ms (3.6%)

prune24.0ms (1.3%)

localize10.0ms (0.5%)

rewrite19.0ms (1%)

series32.0ms (1.7%)

simplify111.0ms (5.9%)

prune124.0ms (6.6%)

regimes43.0ms (2.3%)

simplify3.0ms (0.2%)

end0.0ms (0%)

sample1.3s (71.2%)

Profiling

Iter	Nodes	Cost
0	6	6
1	15	6
2	18	6
3	22	6
4	30	6
5	38	6
6	57	6
7	86	6
8	113	6
9	154	6
10	224	6
11	261	6
12	297	6
13	300	6
14	263	6