Details

analyze402.0ms (6.3%)

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
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

Compiler

Compiled 32 to 26 computations (18.8% saved)

sample4.1s (63.5%)

Results

2.2s	2020×	body	1024	valid
769.0ms	4424×	body	128	valid
505.0ms	1048×	body	512	valid
248.0ms	229×	body	2048	valid
165.0ms	535×	body	256	valid
90.0ms	459×	body	128	invalid
18.0ms	20×	body	1024	invalid
4.0ms	8×	body	512	invalid
2.0ms	5×	body	256	invalid

Compiler

Compiled 95 to 77 computations (18.9% saved)

simplify65.0ms (1%)

Algorithm

1×	egg-herbie

Rules

750×	`times-frac_binary64`
577×	`div-sub_binary64`
534×	`cancel-sign-sub-inv_binary64`
519×	`fma-neg_binary64`
467×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	45
1	57	45
2	153	37
3	394	37
4	1347	37
5	4048	37
6	4614	37
7	5259	37

prune5.0ms (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

30.8b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	30.8b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))) 2)
	43.5b	(*.f64 1/2 (fma.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 (+.f64 eps -1)) x) (/.f64 (-.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 eps x x)))))

Status

Error

Program

▶

30.8b

(/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))) (*.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x))))) 2)

43.5b

(*.f64 1/2 (fma.f64 (+.f64 1 (/.f64 1 eps)) (pow.f64 (exp.f64 (+.f64 eps -1)) x) (/.f64 (-.f64 1 (/.f64 1 eps)) (exp.f64 (fma.f64 eps x x)))))

Compiler

Compiled 172 to 133 computations (22.7% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 1 eps) x)
✓	0.0b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
✓	0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
✓	4.4b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

series62.0ms (1%)

Counts

4 → 84

Calls

4 calls:

46.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
7.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
5.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
4.0ms	(*.f64 (-.f64 1 eps) x)

rewrite90.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

495×	`prod-diff_binary64`
203×	`add-sqr-sqrt_binary64`
192×	`log1p-expm1-u_binary64`
192×	`expm1-log1p-u_binary64`
190×	`add-log-exp_binary64`

Counts

4 → 127

Calls

4 calls:

86.0ms	(*.f64 (-.f64 1 eps) x)
86.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
86.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
86.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	18	71
1	407	62
2	4376	62
3	5336	62

simplify104.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

542×	`associate--l+_binary64`
347×	`associate--r+_binary64`
302×	`cancel-sign-sub-inv_binary64`
260×	`fma-def_binary64`
189×	`distribute-rgt-out_binary64`

Counts

211 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	169	1994
1	538	1946
2	2064	1851
3	4864	1851
4	4998	1851
5	4958	1851

prune206.0ms (3.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	179	2	181
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	181	2	183

Error

0.0b

Counts

183 → 2

Alt Table

Status	Error	Program
	30.8b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (pow.f64 (exp.f64 -1) (.f64 x (+.f64 1 eps))))) 2)
▶	13.5b	(/.f64 (+.f64 (.f64 (pow.f64 eps 2) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))) (+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (+.f64 (.f64 1/3 (.f64 (pow.f64 eps 2) (.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))) (.f64 2 (exp.f64 (neg.f64 x)))))) 2)

Status

Error

Program

30.8b

(/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))) (*.f64 (-.f64 (/.f64 1 eps) 1) (pow.f64 (exp.f64 -1) (*.f64 x (+.f64 1 eps))))) 2)

▶

13.5b

(/.f64 (+.f64 (*.f64 (pow.f64 eps 2) (*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))) (+.f64 (*.f64 2 (*.f64 x (exp.f64 (neg.f64 x)))) (+.f64 (*.f64 1/3 (*.f64 (pow.f64 eps 2) (*.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))) (*.f64 2 (exp.f64 (neg.f64 x)))))) 2)

Compiler

Compiled 7807 to 5869 computations (24.8% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	5.4b	(.f64 (pow.f64 eps 2) (.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))
✓	5.5b	(.f64 (pow.f64 eps 2) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2)))
✓	8.4b	(*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))
✓	10.6b	(*.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x)))

series60.0ms (0.9%)

Counts

4 → 40

Calls

4 calls:

30.0ms	(.f64 (pow.f64 eps 2) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2)))
23.0ms	(.f64 (pow.f64 eps 2) (.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))
4.0ms	(*.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x)))
3.0ms	(*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))

rewrite64.0ms (1%)

Algorithm

1×	batch-egg-rewrite

Rules

644×	`log-prod_binary64`
212×	`expm1-udef_binary64`
212×	`log1p-udef_binary64`
195×	`log-pow_binary64`
191×	`pow3_binary64`

Counts

4 → 76

Calls

4 calls:

62.0ms	(.f64 (pow.f64 eps 2) (.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))
62.0ms	(.f64 (pow.f64 eps 2) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2)))
62.0ms	(*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))
62.0ms	(*.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x)))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	14	56
1	291	47
2	2857	47
3	4940	47

simplify70.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

653×	`unswap-sqr_binary64`
370×	`distribute-rgt-neg-in_binary64`
359×	`fma-def_binary64`
342×	`associate-l_binary64`
341×	`distribute-lft-neg-in_binary64`

Counts

116 → 115

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	61	662
1	180	648
2	608	568
3	2423	568
4	4743	568
5	5043	568

prune136.0ms (2.1%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	115	2	117

Error

0.0b

Counts

117 → 2

Alt Table

Status	Error	Program
▶	30.8b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (pow.f64 (exp.f64 -1) (.f64 x (+.f64 1 eps))))) 2)
✓	13.5b	(/.f64 (+.f64 (.f64 (pow.f64 eps 2) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))) (+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (+.f64 (.f64 1/3 (.f64 (pow.f64 eps 2) (.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))) (.f64 2 (exp.f64 (neg.f64 x)))))) 2)

Status

Error

Program

▶

30.8b

(/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))) (*.f64 (-.f64 (/.f64 1 eps) 1) (pow.f64 (exp.f64 -1) (*.f64 x (+.f64 1 eps))))) 2)

✓

13.5b

(/.f64 (+.f64 (*.f64 (pow.f64 eps 2) (*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))) (+.f64 (*.f64 2 (*.f64 x (exp.f64 (neg.f64 x)))) (+.f64 (*.f64 1/3 (*.f64 (pow.f64 eps 2) (*.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))) (*.f64 2 (exp.f64 (neg.f64 x)))))) 2)

Compiler

Compiled 5228 to 3016 computations (42.3% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (+.f64 1 eps))
	0.0b	(*.f64 (-.f64 1 eps) x)
	0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
✓	4.6b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (pow.f64 (exp.f64 -1) (.f64 x (+.f64 1 eps)))))

series35.0ms (0.5%)

Counts

2 → 48

Calls

2 calls:

31.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (pow.f64 (exp.f64 -1) (.f64 x (+.f64 1 eps)))))
4.0ms	(*.f64 x (+.f64 1 eps))

rewrite92.0ms (1.4%)

Algorithm

1×	batch-egg-rewrite

Rules

357×	`log1p-udef_binary64`
214×	`add-sqr-sqrt_binary64`
204×	`prod-diff_binary64`
203×	`log1p-expm1-u_binary64`
203×	`expm1-log1p-u_binary64`

Counts

2 → 77

Calls

2 calls:

87.0ms	(*.f64 x (+.f64 1 eps))
87.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (pow.f64 (exp.f64 -1) (.f64 x (+.f64 1 eps)))))

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	19	50
1	428	46
2	4541	46
3	5503	46

simplify69.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

770×	`associate-+r+_binary64`
445×	`associate-l_binary64`
426×	`associate--l+_binary64`
399×	`associate-r_binary64`
278×	`cancel-sign-sub-inv_binary64`

Counts

125 → 103

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	113	1318
1	329	1235
2	1212	1130
3	4776	1130
4	5093	1130

prune199.0ms (3.1%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	173	0	173
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	173	2	175

Error

0.0b

Counts

175 → 2

Alt Table

Status	Error	Program
✓	30.8b	(/.f64 (-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (pow.f64 (exp.f64 -1) (.f64 x (+.f64 1 eps))))) 2)
✓	13.5b	(/.f64 (+.f64 (.f64 (pow.f64 eps 2) (.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))) (+.f64 (.f64 2 (.f64 x (exp.f64 (neg.f64 x)))) (+.f64 (.f64 1/3 (.f64 (pow.f64 eps 2) (.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))) (.f64 2 (exp.f64 (neg.f64 x)))))) 2)

Status

Error

Program

✓

30.8b

(/.f64 (-.f64 (*.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))) (*.f64 (-.f64 (/.f64 1 eps) 1) (pow.f64 (exp.f64 -1) (*.f64 x (+.f64 1 eps))))) 2)

✓

13.5b

(/.f64 (+.f64 (*.f64 (pow.f64 eps 2) (*.f64 (exp.f64 (neg.f64 x)) (pow.f64 x 2))) (+.f64 (*.f64 2 (*.f64 x (exp.f64 (neg.f64 x)))) (+.f64 (*.f64 1/3 (*.f64 (pow.f64 eps 2) (*.f64 (pow.f64 x 3) (exp.f64 (neg.f64 x))))) (*.f64 2 (exp.f64 (neg.f64 x)))))) 2)

Compiler

Compiled 7445 to 5681 computations (23.7% saved)

regimes523.0ms (8.2%)

Accuracy

Total 0.5b remaining (94.4%)

Threshold costs 0.5b (94.4%)

Counts

89 → 1

Compiler

Compiled 11394 to 8638 computations (24.2% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	10	24
1	18	24
2	20	24
3	21	24
4	21	24

end87.0ms (1.4%)

Compiler: Compiled 109 to 78 computations (28.4% saved)

Details

analyze402.0ms (6.3%)

sample4.1s (63.5%)

simplify65.0ms (1%)

prune5.0ms (0.1%)

localize18.0ms (0.3%)

series62.0ms (1%)

rewrite90.0ms (1.4%)

simplify104.0ms (1.6%)

prune206.0ms (3.2%)

localize20.0ms (0.3%)

series60.0ms (0.9%)

rewrite64.0ms (1%)

simplify70.0ms (1.1%)

prune136.0ms (2.1%)

localize19.0ms (0.3%)

series35.0ms (0.5%)

rewrite92.0ms (1.4%)

simplify69.0ms (1.1%)

prune199.0ms (3.1%)

regimes523.0ms (8.2%)

simplify2.0ms (0%)

end87.0ms (1.4%)

Profiling