Details

analyze86.0ms (3.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	43.7%	12.6%	6
53.1%	31.2%	15.7%	7
59.3%	18.7%	22%	8
62.4%	14%	23.5%	9
64.8%	8.6%	26.6%	10
66%	6.6%	27.4%	11
66.9%	4.1%	29%	12
67.4%	3.2%	29.4%	13
67.9%	2%	30.1%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample129.0ms (4.9%)

Algorithm

1×

intervals

Results

15.0ms	237×	body	128	valid
4.0ms	10×	body	1024	valid
2.0ms	6×	body	512	valid
1.0ms	3×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 25 to 19 computations (24% saved)

simplify97.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

837×	`fma-def_binary64`
741×	`fabs-mul_binary64`
531×	`fabs-div_binary64`
469×	`swap-sqr_binary64`
420×	`fma-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	19	11
2	28	11
3	45	11
4	59	11
5	89	11
6	120	11
7	148	11
8	188	11
9	201	11
10	231	11
11	257	11
12	336	11
13	544	11
14	967	11
15	2930	11
16	3463	11
17	3600	11
18	3896	11
19	4820	11
20	4969	11

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
	0.3b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))

Compiler

Compiled 58 to 38 computations (34.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	0.3b	(log1p.f64 (exp.f64 x))

series295.0ms (11.3%)

Counts

2 → 36

Calls

2 calls:

207.0ms	(log1p.f64 (exp.f64 x))
88.0ms	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-log-exp_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`fma-neg_binary64`

Counts

2 → 32

Calls

2 calls:

2.0ms	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
0.0ms	(log1p.f64 (exp.f64 x))

simplify76.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

620×	`cancel-sign-sub-inv_binary64`
339×	`unswap-sqr_binary64`
285×	`*-commutative_binary64`
285×	`unsub-neg_binary64`
252×	`distribute-rgt-in_binary64`

Counts

68 → 56

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	73	789
1	167	742
2	426	710
3	1507	707
4	3171	707
5	4588	701
6	4872	701

prune35.0ms (1.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	54	4	58

Error

0.2b

Counts

58 → 4

Alt Table

Status	Error	Program
▶	0.3b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
	12.1b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
	12.6b	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))

Compiler

Compiled 817 to 310 computations (62.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 1 (exp.f64 x))
✓	0.0b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
✓	0.3b	(log.f64 (+.f64 1 (exp.f64 x)))

series282.0ms (10.7%)

Counts

3 → 32

Calls

3 calls:

195.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
85.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
2.0ms	(+.f64 1 (exp.f64 x))

rewrite15.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`log-prod_binary64`
8×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64`

Counts

3 → 63

Calls

3 calls:

6.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
5.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
2.0ms	(+.f64 1 (exp.f64 x))

simplify114.0ms (4.4%)

Algorithm

1×	egg-herbie

Rules

343×	`fma-def_binary64`
310×	`distribute-rgt-in_binary64`
305×	`cancel-sign-sub-inv_binary64`
244×	`associate-+l+_binary64`
238×	`distribute-lft-in_binary64`

Counts

95 → 109

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	115	1097
1	272	1018
2	652	1004
3	2057	999
4	4440	999
5	4970	993
6	5000	993
7	4880	993

prune66.0ms (2.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	109	0	109
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	109	4	113

Error

0.2b

Counts

113 → 4

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
▶	12.1b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
	12.6b	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))

Compiler

Compiled 1698 to 876 computations (48.4% saved)

localize5.0ms (0.2%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))

series14.0ms (0.5%)

Counts

1 → 24

Calls

1 calls:

14.0ms

(fma.f64 x (-.f64 1/2 y) (log.f64 2))

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 (-.f64 1/2 y) (log.f64 2))

simplify64.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

855×	`fma-neg_binary64`
478×	`neg-sub0_binary64`
433×	`neg-mul-1_binary64`
375×	`*-commutative_binary64`
362×	`distribute-rgt-in_binary64`

Counts

34 → 22

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	28	459
1	52	346
2	104	346
3	328	346
4	1670	346
5	2981	346
6	4467	346
7	4969	346

prune15.0ms (0.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	22	4	26

Error

0.2b

Counts

26 → 4

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
✓	12.1b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
▶	12.6b	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))

Compiler

Compiled 257 to 191 computations (25.7% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))
	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
	0.3b	(log1p.f64 (exp.f64 x))
✓	1.1b	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))

series123.0ms (4.7%)

Counts

2 → 48

Calls

2 calls:

83.0ms	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
39.0ms	(log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))

rewrite3.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`expm1-log1p-u_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
2×	`add-cbrt-cube_binary64`

Counts

2 → 22

Calls

2 calls:

0.0ms	(log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))
0.0ms	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))

simplify87.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

668×	`fma-def_binary64`
354×	`distribute-neg-in_binary64`
303×	`sub-neg_binary64`
271×	`associate-+r+_binary64`
222×	`fma-neg_binary64`

Counts

70 → 89

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	222	2386
1	654	2314
2	2649	2270
3	4934	2268
4	5053	2268

prune96.0ms (3.7%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	145	4	149

Error

0.2b

Counts

149 → 4

Alt Table

Status	Error	Program
✓	0.3b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
✓	12.1b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	12.6b	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))

Compiler

Compiled 3892 to 2029 computations (47.9% saved)

regimes58.0ms (2.2%)

Accuracy

Total 0.2b remaining (52.8%)

Threshold costs 0.2b (52.8%)

Counts

20 → 1

Compiler

Compiled 557 to 430 computations (22.8% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

4×	`+-commutative_binary64`
4×	`*-commutative_binary64`
4×	`sub-neg_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	13	11
2	23	11
3	29	11
4	33	11
5	34	11
6	34	11

end0.0ms (0%)

Compiler: Compiled 9 to 6 computations (33.3% saved)

sample933.0ms (35.5%)

Algorithm

1×

intervals

Results

449.0ms	7403×	body	128	valid
106.0ms	217×	body	1024	valid
57.0ms	223×	body	512	valid
26.0ms	156×	body	256	valid
3.0ms	47×	body	128	invalid
1.0ms	1×	body	2048	valid
0.0ms	9×	body	128	overflowed

Compiler

Compiled 63 to 46 computations (27% saved)

Details

analyze86.0ms (3.3%)

sample129.0ms (4.9%)

simplify97.0ms (3.7%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series295.0ms (11.3%)

rewrite4.0ms (0.1%)

simplify76.0ms (2.9%)

prune35.0ms (1.3%)

localize6.0ms (0.2%)

series282.0ms (10.7%)

rewrite15.0ms (0.6%)

simplify114.0ms (4.4%)

prune66.0ms (2.5%)

localize5.0ms (0.2%)

series14.0ms (0.5%)

rewrite1.0ms (0%)

simplify64.0ms (2.5%)

prune15.0ms (0.6%)

localize9.0ms (0.4%)

series123.0ms (4.7%)

rewrite3.0ms (0.1%)

simplify87.0ms (3.3%)

prune96.0ms (3.7%)

regimes58.0ms (2.2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample933.0ms (35.5%)

Profiling