Details

analyze433.0ms (5.8%)

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%	56.2%	0.1%	6
53.1%	42.1%	4.8%	7
59.3%	35.9%	4.8%	8
62.4%	30.4%	7.1%	9
64.8%	28.1%	7.1%	10
66%	25.8%	8.3%	11
66.9%	24.8%	8.3%	12
67.4%	23.7%	8.9%	13
67.9%	23.3%	8.9%	14

Compiler

Compiled 12 to 9 computations (25% saved)

sample4.3s (57.2%)

Results

2.7s	2562×	body	8192	exit
1.1s	7622×	body	128	valid
140.0ms	216×	body	1024	valid
112.0ms	246×	body	512	valid
51.0ms	171×	body	256	valid
8.0ms	62×	body	128	invalid
1.0ms	1×	body	2048	valid

Compiler

Compiled 35 to 26 computations (25.7% saved)

simplify101.0ms (1.4%)

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%)

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

Compiler

Compiled 36 to 22 computations (38.9% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series297.0ms (4%)

Counts

2 → 36

Calls

2 calls:

209.0ms	(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))

simplify86.0ms (1.2%)

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

prune31.0ms (0.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	53	3	56
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	53	4	57

Error

0.0b

Counts

57 → 4

Alt Table

Status	Error	Program
	12.5b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
✓	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
	17.6b	(/.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)))))
▶	11.9b	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))

Compiler

Compiled 869 to 326 computations (62.5% saved)

localize13.0ms (0.2%)

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))
	0.0b	(log1p.f64 (exp.f64 x))
✓	1.2b	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))

series133.0ms (1.8%)

Counts

2 → 48

Calls

2 calls:

87.0ms	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))
46.0ms	(log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y)))

rewrite1.0ms (0%)

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))))

simplify93.0ms (1.3%)

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

prune103.0ms (1.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	144	5	149

Error

Counts

149 → 5

Alt Table

Status	Error	Program
▶	12.5b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
	30.8b	(expm1.f64 (log.f64 (+.f64 1 (log.f64 2))))
✓	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
	17.6b	(/.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)))))
✓	11.9b	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))

Compiler

Compiled 3980 to 2076 computations (47.8% saved)

localize5.0ms (0.1%)

Local error

Found 1 expressions with local error:

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

series12.0ms (0.2%)

Counts

1 → 24

Calls

1 calls:

12.0ms

(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))

simplify65.0ms (0.9%)

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 (0.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	22	0	22
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	22	5	27

Error

Counts

27 → 5

Alt Table

Status	Error	Program
✓	12.5b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
	30.8b	(expm1.f64 (log.f64 (+.f64 1 (log.f64 2))))
✓	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
▶	17.6b	(/.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)))))
✓	11.9b	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))

Compiler

Compiled 325 to 223 computations (31.4% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (log1p.f64 (exp.f64 x)) (.f64 x y))
✓	0.7b	(pow.f64 (log1p.f64 (exp.f64 x)) 3)
✓	0.7b	(*.f64 (log1p.f64 (exp.f64 x)) (log1p.f64 (exp.f64 x)))
✓	17.0b	(/.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)))))

series1.1s (15.3%)

Counts

4 → 72

Calls

4 calls:

502.0ms	(.f64 (log1p.f64 (exp.f64 x)) (.f64 x y))
227.0ms	(/.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)))))
204.0ms	(*.f64 (log1p.f64 (exp.f64 x)) (log1p.f64 (exp.f64 x)))
203.0ms	(pow.f64 (log1p.f64 (exp.f64 x)) 3)

rewrite49.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
39×	`times-frac_binary64`
38×	`*-un-lft-identity_binary64`
32×	`difference-of-squares_binary64`
30×	`add-cube-cbrt_binary64`

Counts

4 → 146

Calls

4 calls:

21.0ms	(/.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)) (.f64 x y))
3.0ms	(*.f64 (log1p.f64 (exp.f64 x)) (log1p.f64 (exp.f64 x)))
2.0ms	(pow.f64 (log1p.f64 (exp.f64 x)) 3)

simplify211.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

335×	`fma-neg_binary64`
318×	`times-frac_binary64`
287×	`cancel-sign-sub-inv_binary64`
275×	`associate-l_binary64`
273×	`associate-r_binary64`

Counts

218 → 232

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	296	7651
1	732	6860
2	2871	6609
3	4244	6608
4	4948	6608

prune188.0ms (2.5%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	232	0	232
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	232	5	237

Error

Counts

237 → 5

Alt Table

Status	Error	Program
✓	12.5b	(fma.f64 x (-.f64 1/2 y) (log.f64 2))
	30.8b	(expm1.f64 (log.f64 (+.f64 1 (log.f64 2))))
✓	0.0b	(-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))
✓	17.6b	(/.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)))))
✓	11.9b	(expm1.f64 (log1p.f64 (-.f64 (log1p.f64 (exp.f64 x)) (*.f64 x y))))

Compiler

Compiled 11326 to 3143 computations (72.2% saved)

regimes103.0ms (1.4%)

Accuracy

Total 0.3b remaining (59.6%)

Threshold costs 0.3b (59.6%)

Counts

32 → 1

Compiler

Compiled 1816 to 1071 computations (41% saved)

simplify3.0ms (0%)

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

end71.0ms (1%)

Compiler: Compiled 92 to 57 computations (38% saved)

Details

analyze433.0ms (5.8%)

sample4.3s (57.2%)

simplify101.0ms (1.4%)

prune3.0ms (0%)

localize6.0ms (0.1%)

series297.0ms (4%)

rewrite4.0ms (0.1%)

simplify86.0ms (1.2%)

prune31.0ms (0.4%)

localize13.0ms (0.2%)

series133.0ms (1.8%)

rewrite1.0ms (0%)

simplify93.0ms (1.3%)

prune103.0ms (1.4%)

localize5.0ms (0.1%)

series12.0ms (0.2%)

rewrite1.0ms (0%)

simplify65.0ms (0.9%)

prune17.0ms (0.2%)

localize15.0ms (0.2%)

series1.1s (15.3%)

rewrite49.0ms (0.7%)

simplify211.0ms (2.8%)

prune188.0ms (2.5%)

regimes103.0ms (1.4%)

simplify3.0ms (0%)

end71.0ms (1%)

Profiling