Details

analyze6.0ms (0.2%)

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)

sample2.2s (84.4%)

Results

927.0ms	2736×	body	1024	valid
557.0ms	3136×	body	128	valid
355.0ms	1395×	body	512	valid
168.0ms	294×	body	2048	valid
106.0ms	695×	body	256	valid

Compiler

Compiled 23 to 17 computations (26.1% saved)

simplify19.0ms (0.7%)

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

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

0.0b

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)

series3.0ms (0.1%)

Counts

1 → 12

Calls

1 calls:

3.0ms

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

rewrite4.0ms (0.1%)

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)

simplify61.0ms (2.4%)

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 → 42

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

prune82.0ms (3.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	41	2	43

Error

Counts

43 → 2

Alt Table

Status	Error	Program
▶	22.5b	(fma.f64 x (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 3) 1))
✓	0.0b	(/.f64 (expm1.f64 x) x)

Compiler

Compiled 433 to 175 computations (59.6% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 3) 1))
✓	0.0b	(fma.f64 1/24 (pow.f64 x 3) 1)
✓	0.1b	(fma.f64 x 1/6 1/2)

series8.0ms (0.3%)

Counts

3 → 36

Calls

3 calls:

4.0ms	(fma.f64 x (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 3) 1))
3.0ms	(fma.f64 1/24 (pow.f64 x 3) 1)
2.0ms	(fma.f64 x 1/6 1/2)

rewrite2.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`*-un-lft-identity_binary64`
3×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
3×	`add-cbrt-cube_binary64`
3×	`add-exp-log_binary64`

Counts

3 → 30

Calls

3 calls:

0.0ms	(fma.f64 x 1/6 1/2)
0.0ms	(fma.f64 1/24 (pow.f64 x 3) 1)
0.0ms	(fma.f64 x (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 3) 1))

simplify67.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

608×	`associate-l_binary64`
535×	`associate-r_binary64`
462×	`fma-def_binary64`
371×	`associate-/l*_binary64`
351×	`exp-prod_binary64`

Counts

66 → 66

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	55	743
1	92	659
2	206	650
3	750	631
4	2903	631
5	3707	631
6	5137	631

prune45.0ms (1.8%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	66	2	68

Error

Counts

68 → 2

Alt Table

Status	Error	Program
✓	22.5b	(fma.f64 x (fma.f64 x 1/6 1/2) (fma.f64 1/24 (pow.f64 x 3) 1))
✓	0.0b	(/.f64 (expm1.f64 x) x)

Compiler

Compiled 1045 to 814 computations (22.1% saved)

regimes43.0ms (1.7%)

Accuracy

Total 0.0b remaining (70%)

Threshold costs 0.0b (70%)

Counts

20 → 1

Compiler

Compiled 403 to 281 computations (30.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4	6
1	4	6

end42.0ms (1.7%)

Compiler: Compiled 28 to 19 computations (32.1% 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

analyze6.0ms (0.2%)

sample2.2s (84.4%)

simplify19.0ms (0.7%)

prune3.0ms (0.1%)

localize3.0ms (0.1%)

series3.0ms (0.1%)

rewrite4.0ms (0.1%)

simplify61.0ms (2.4%)

prune82.0ms (3.2%)

localize7.0ms (0.3%)

series8.0ms (0.3%)

rewrite2.0ms (0.1%)

simplify67.0ms (2.6%)

prune45.0ms (1.8%)

regimes43.0ms (1.7%)

simplify2.0ms (0.1%)

end42.0ms (1.7%)

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