Details

analyze77.0ms (2.4%)

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)

sample128.0ms (3.9%)

Algorithm

1×

intervals

Results

15.0ms	237×	body	128	valid
2.0ms	9×	body	512	valid
2.0ms	4×	body	1024	valid
1.0ms	1×	body	2048	valid
1.0ms	5×	body	256	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 25 to 19 computations (24% saved)

simplify99.0ms (3%)

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

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

0.3b

Counts

3 → 1

Alt Table

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

Compiler

Compiled 36 to 22 computations (38.9% 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))
✓	0.2b	(log1p.f64 (exp.f64 x))

series311.0ms (9.6%)

Counts

2 → 36

Calls

2 calls:

229.0ms	(log1p.f64 (exp.f64 x))
82.0ms	(-.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))

simplify80.0ms (2.5%)

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

prune29.0ms (0.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	54	3	57

Error

0.2b

Counts

57 → 3

Alt Table

Status	Error	Program
▶	11.1b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
	17.9b	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (+.f64 (.f64 (log1p.f64 (exp.f64 x)) (log1p.f64 (exp.f64 x))) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))))

Compiler

Compiled 847 to 310 computations (63.4% 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))

series11.0ms (0.3%)

Counts

1 → 24

Calls

1 calls:

11.0ms

(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))

simplify69.0ms (2.1%)

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

prune17.0ms (0.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	21	1	22
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	21	4	25

Error

0.2b

Counts

25 → 4

Alt Table

Status	Error	Program
	31.2b	(fma.f64 1/2 x (log.f64 2))
✓	11.1b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
▶	17.9b	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (+.f64 (.f64 (log1p.f64 (exp.f64 x)) (log1p.f64 (exp.f64 x))) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))))

Compiler

Compiled 312 to 211 computations (32.4% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(log1p.f64 (exp.f64 x))
✓	0.7b	(*.f64 (log1p.f64 (exp.f64 x)) (log1p.f64 (exp.f64 x)))
✓	0.7b	(pow.f64 (log1p.f64 (exp.f64 x)) 3)
✓	17.1b	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (+.f64 (.f64 (log1p.f64 (exp.f64 x)) (log1p.f64 (exp.f64 x))) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))))

series687.0ms (21.1%)

Counts

3 → 48

Calls

3 calls:

238.0ms

(pow.f64 (log1p.f64 (exp.f64 x)) 3)

235.0ms

(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (*.f64 x y) 3)) (+.f64 (*.f64 (log1p.f64 (exp.f64 x)) (log1p.f64 (exp.f64 x))) (+.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))))

213.0ms

(*.f64 (log1p.f64 (exp.f64 x)) (log1p.f64 (exp.f64 x)))

rewrite40.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`add-sqr-sqrt_binary64`
39×	`times-frac_binary64`
36×	`*-un-lft-identity_binary64`
32×	`difference-of-squares_binary64`
28×	`add-cube-cbrt_binary64`

Counts

3 → 126

Calls

3 calls:

18.0ms

(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (*.f64 x y) 3)) (+.f64 (*.f64 (log1p.f64 (exp.f64 x)) (log1p.f64 (exp.f64 x))) (+.f64 (*.f64 (*.f64 x y) (*.f64 x y)) (*.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))))

4.0ms

(*.f64 (log1p.f64 (exp.f64 x)) (log1p.f64 (exp.f64 x)))

1.0ms

(pow.f64 (log1p.f64 (exp.f64 x)) 3)

simplify221.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

556×	`fma-neg_binary64`
309×	`times-frac_binary64`
257×	`div-sub_binary64`
244×	`cancel-sign-sub-inv_binary64`
175×	`associate-l_binary64`

Counts

174 → 193

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	255	7022
1	626	6290
2	2399	6021
3	3950	6018
4	4934	6018
5	4949	6018

prune216.0ms (6.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	273	0	273
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	273	4	277

Error

0.2b

Counts

277 → 4

Alt Table

Status	Error	Program
▶	31.2b	(fma.f64 1/2 x (log.f64 2))
✓	11.1b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	17.9b	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (+.f64 (.f64 (log1p.f64 (exp.f64 x)) (log1p.f64 (exp.f64 x))) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))))

Compiler

Compiled 12872 to 3531 computations (72.6% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series6.0ms (0.2%)

Counts

1 → 12

Calls

1 calls:

6.0ms

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

simplify106.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

513×	`distribute-rgt-in_binary64`
464×	`distribute-rgt-out_binary64`
412×	`*-commutative_binary64`
408×	`associate-l_binary64`
387×	`associate-+l+_binary64`

Counts

22 → 16

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	17	186
1	20	171
2	43	171
3	103	170
4	282	170
5	916	170
6	1567	170
7	2139	170
8	2175	170
9	3975	170
10	4181	170
11	4654	170
12	4889	170
13	4872	170

prune10.0ms (0.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	15	1	16
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	16	4	20

Error

0.2b

Counts

20 → 4

Alt Table

Status	Error	Program
	31.7b	(exp.f64 (log.f64 (fma.f64 1/2 x (log.f64 2))))
✓	11.1b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.3b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	17.9b	(/.f64 (-.f64 (pow.f64 (log1p.f64 (exp.f64 x)) 3) (pow.f64 (.f64 x y) 3)) (+.f64 (.f64 (log1p.f64 (exp.f64 x)) (log1p.f64 (exp.f64 x))) (+.f64 (.f64 (.f64 x y) (.f64 x y)) (.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))))

Compiler

Compiled 195 to 148 computations (24.1% saved)

regimes143.0ms (4.4%)

Accuracy

Total 0.2b remaining (59.7%)

Threshold costs 0.2b (59.7%)

Counts

30 → 1

Compiler

Compiled 1856 to 1078 computations (41.9% 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)

sample961.0ms (29.6%)

Algorithm

1×

intervals

Results

464.0ms	7375×	body	128	valid
102.0ms	216×	body	1024	valid
61.0ms	238×	body	512	valid
27.0ms	169×	body	256	valid
3.0ms	44×	body	128	invalid
2.0ms	2×	body	2048	valid
0.0ms	10×	body	128	overflowed

Compiler

Compiled 87 to 54 computations (37.9% saved)

Details

analyze77.0ms (2.4%)

sample128.0ms (3.9%)

simplify99.0ms (3%)

prune3.0ms (0.1%)

localize5.0ms (0.2%)

series311.0ms (9.6%)

rewrite4.0ms (0.1%)

simplify80.0ms (2.5%)

prune29.0ms (0.9%)

localize5.0ms (0.2%)

series11.0ms (0.3%)

rewrite1.0ms (0%)

simplify69.0ms (2.1%)

prune17.0ms (0.5%)

localize15.0ms (0.5%)

series687.0ms (21.1%)

rewrite40.0ms (1.2%)

simplify221.0ms (6.8%)

prune216.0ms (6.7%)

localize4.0ms (0.1%)

series6.0ms (0.2%)

rewrite1.0ms (0%)

simplify106.0ms (3.3%)

prune10.0ms (0.3%)

regimes143.0ms (4.4%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample961.0ms (29.6%)

Profiling