Details

analyze421.0ms (18.5%)

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)

sample43.0ms (1.9%)

Algorithm

1×

intervals

Results

14.0ms	10×	body	2048	valid
13.0ms	89×	body	1024	valid
4.0ms	43×	body	512	valid
3.0ms	93×	body	128	valid
1.0ms	21×	body	256	valid

Compiler

Compiled 18 to 12 computations (33.3% saved)

simplify9.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

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

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	8
1	12	8
2	13	8
3	11	8

prune6.0ms (0.3%)

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))

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 → 29

Calls

1 calls:

3.0ms

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

series16.0ms (0.7%)

Counts

1 → 12

Calls

1 calls:

16.0ms

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

simplify73.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

825×	`fma-def_binary64`
587×	`div-sub_binary64`
548×	`times-frac_binary64`
500×	`fma-neg_binary64`
317×	`distribute-rgt-in_binary64`

Counts

41 → 59

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	66	559
1	130	521
2	292	519
3	609	519
4	1403	519
5	4001	519
6	5294	519

prune19.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	56	3	59
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	56	4	60

Error

0.6b

Counts

60 → 4

Alt Table

Status	Error	Program
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))
	41.7b	(exp.f64 (-.f64 x (log.f64 (expm1.f64 x))))
	20.5b	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
▶	20.4b	(+.f64 1/2 (/.f64 1 x))

Compiler

Compiled 487 to 180 computations (63% saved)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify8.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	0	0
1	0	0

prune3.0ms (0.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Kept	Total
New	0	0
Fresh	2	2
Picked	1	1
Done	1	1
Total	4	4

Error

0.6b

Counts

4 → 4

Alt Table

Status	Error	Program
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))
	41.7b	(exp.f64 (-.f64 x (log.f64 (expm1.f64 x))))
▶	20.5b	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
✓	20.4b	(+.f64 1/2 (/.f64 1 x))

Compiler

Compiled 44 to 33 computations (25% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 x 1/12 (/.f64 1 x))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma.f64 x 1/12 (/.f64 1 x))

series10.0ms (0.5%)

Counts

1 → 12

Calls

1 calls:

10.0ms

(fma.f64 x 1/12 (/.f64 1 x))

simplify89.0ms (3.9%)

Algorithm

1×	egg-herbie

Rules

548×	`distribute-rgt-in_binary64`
507×	`distribute-lft-in_binary64`
453×	`distribute-rgt-out_binary64`
425×	`associate-/l/_binary64`
402×	`unswap-sqr_binary64`

Counts

22 → 34

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	208
1	22	191
2	45	191
3	114	191
4	324	191
5	1000	191
6	2257	191
7	3233	191
8	3784	191
9	4950	191
10	4875	191

prune9.0ms (0.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	34	0	34
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	34	4	38

Error

0.6b

Counts

38 → 4

Alt Table

Status	Error	Program
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))
▶	41.7b	(exp.f64 (-.f64 x (log.f64 (expm1.f64 x))))
✓	20.5b	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))
✓	20.4b	(+.f64 1/2 (/.f64 1 x))

Compiler

Compiled 213 to 165 computations (22.5% saved)

localize5.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 x (log.f64 (expm1.f64 x)))
✓	0.7b	(log.f64 (expm1.f64 x))
✓	2.1b	(exp.f64 (-.f64 x (log.f64 (expm1.f64 x))))

rewrite15.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
24×	`prod-diff_binary64`
23×	`add-cube-cbrt_binary64`
17×	`exp-sum_binary64`

Counts

3 → 87

Calls

3 calls:

5.0ms	(-.f64 x (log.f64 (expm1.f64 x)))
5.0ms	(exp.f64 (-.f64 x (log.f64 (expm1.f64 x))))
1.0ms	(log.f64 (expm1.f64 x))

series306.0ms (13.5%)

Counts

3 → 28

Calls

3 calls:

261.0ms	(log.f64 (expm1.f64 x))
42.0ms	(-.f64 x (log.f64 (expm1.f64 x)))
3.0ms	(exp.f64 (-.f64 x (log.f64 (expm1.f64 x))))

simplify129.0ms (5.7%)

Algorithm

1×	egg-herbie

Rules

1120×	`fma-neg_binary64`
541×	`cancel-sign-sub-inv_binary64`
376×	`associate-l_binary64`
359×	`fma-def_binary64`
318×	`associate-r_binary64`

Counts

115 → 195

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	145	1558
1	266	1192
2	755	1047
3	2806	1047
4	4561	1047
5	4993	1047
6	4882	1047

prune34.0ms (1.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	0	0	0
Picked	0	1	1
Done	1	2	3
Total	195	4	199

Error

0.6b

Counts

199 → 4

Alt Table

Status	Error	Program
✓	0.8b	(/.f64 (exp.f64 x) (expm1.f64 x))
	41.9b	(+.f64 (.f64 1/2 (.f64 (exp.f64 (neg.f64 (log.f64 x))) x)) (exp.f64 (neg.f64 (log.f64 x))))
✓	41.7b	(exp.f64 (-.f64 x (log.f64 (expm1.f64 x))))
✓	20.5b	(+.f64 1/2 (fma.f64 x 1/12 (/.f64 1 x)))

Compiler

Compiled 1842 to 543 computations (70.5% saved)

regimes28.0ms (1.2%)

Accuracy

Total 0.1b remaining (20.2%)

Threshold costs 0.1b (20.2%)

Compiler

Compiled 259 to 180 computations (30.5% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	8
1	5	8

end0.0ms (0%)

Compiler: Compiled 6 to 4 computations (33.3% saved)

sample1.0s (45.4%)

Algorithm

1×

intervals

Results

416.0ms	2587×	body	1024	valid
138.0ms	1360×	body	512	valid
111.0ms	3096×	body	128	valid
58.0ms	276×	body	2048	valid
41.0ms	681×	body	256	valid
1.0ms	4×	body	2048	invalid

Compiler

Compiled 52 to 35 computations (32.7% saved)

Details

analyze421.0ms (18.5%)

sample43.0ms (1.9%)

simplify9.0ms (0.4%)

prune6.0ms (0.3%)

localize3.0ms (0.1%)

rewrite4.0ms (0.2%)

series16.0ms (0.7%)

simplify73.0ms (3.2%)

prune19.0ms (0.8%)

localize3.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify8.0ms (0.4%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

rewrite1.0ms (0%)

series10.0ms (0.5%)

simplify89.0ms (3.9%)

prune9.0ms (0.4%)

localize5.0ms (0.2%)

rewrite15.0ms (0.7%)

series306.0ms (13.5%)

simplify129.0ms (5.7%)

prune34.0ms (1.5%)

regimes28.0ms (1.2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.0s (45.4%)

Profiling