Details

analyze311.0ms (5.6%)

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)

sample69.0ms (1.2%)

Algorithm

1×

intervals

Results

32.0ms	72×	body	1024	valid
11.0ms	135×	body	128	valid
8.0ms	32×	body	512	valid
3.0ms	5×	body	2048	valid
2.0ms	12×	body	256	valid
1.0ms	7×	body	128	invalid
0.0ms	1×	body	1024	invalid
0.0ms	4×	body	128	overflowed

Compiler

Compiled 65 to 53 computations (18.5% saved)

simplify76.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

750×	`times-frac_binary64`
720×	`div-sub_binary64`
534×	`cancel-sign-sub-inv_binary64`
478×	`associate-/l*_binary64`
197×	`associate-/l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	45
1	56	45
2	151	41
3	373	41
4	1232	41
5	3992	41
6	4908	41
7	5212	41

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

29.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	29.5b	(/.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)

Compiler

Compiled 91 to 73 computations (19.8% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.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)))
0.7b	(-.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)))))

rewrite471.0ms (8.4%)

Algorithm

1×	rewrite-expression-head

Error

29.0b

Rules

81×	`frac-sub_binary64`
78×	`exp-neg_binary64`
76×	`frac-times_binary64`
59×	`neg-sub0_binary64` `exp-diff_binary64`
38×	`associate-l/_binary64` `associate-r/_binary64`

Counts

4 → 156

Calls

4 calls:

22.0ms	(-.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)))))
13.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
4.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
3.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))

Compiler

Compiled 9252 to 7479 computations (19.2% saved)

series207.0ms (3.7%)

Error

0.0b

Counts

4 → 48

Calls

4 calls:

60.0ms	(-.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)))))
40.0ms	(.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x))))
28.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
26.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))

Compiler

Compiled 3884 to 2665 computations (31.4% saved)

simplify253.0ms (4.5%)

Algorithm

1×	egg-herbie

Rules

772×	`times-frac_binary64`
442×	`associate-l_binary64`
440×	`associate-r_binary64`
241×	`*-commutative_binary64`
236×	`distribute-rgt-in_binary64`

Counts

204 → 173

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	477	10926
1	1241	9843
2	4312	9815
3	5517	9815

prune146.0ms (2.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	171	3	174

Error

0.0b

Counts

174 → 3

Alt Table

Status	Error	Program
	21.0b	(/.f64 (-.f64 (+.f64 2 (.f64 (.f64 x x) (.f64 eps eps))) (.f64 x x)) 2)
▶	16.4b	(/.f64 (+.f64 (+.f64 (.f64 x (/.f64 2 (exp.f64 x))) (.f64 (.f64 (.f64 eps eps) (pow.f64 x 3)) (/.f64 1/3 (exp.f64 x)))) (.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (.f64 (.f64 x x) (.f64 eps eps))))) 2)
✓	29.5b	(/.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)

Compiler

Compiled 4591 to 3216 computations (29.9% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.7b	(.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (.f64 (.f64 x x) (.f64 eps eps))))
4.0b	(.f64 (.f64 (*.f64 eps eps) (pow.f64 x 3)) (/.f64 1/3 (exp.f64 x)))
15.7b	(.f64 (.f64 eps eps) (pow.f64 x 3))
16.4b	(.f64 (.f64 x x) (*.f64 eps eps))

rewrite211.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

72×	`add-exp-log_binary64`
50×	`prod-exp_binary64`
44×	`add-cbrt-cube_binary64`
36×	`pow1_binary64`
29×	`associate-r_binary64`

Counts

4 → 134

Calls

4 calls:

12.0ms	(.f64 (.f64 (*.f64 eps eps) (pow.f64 x 3)) (/.f64 1/3 (exp.f64 x)))
10.0ms	(.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (.f64 (.f64 x x) (.f64 eps eps))))
9.0ms	(.f64 (.f64 x x) (*.f64 eps eps))
8.0ms	(.f64 (.f64 eps eps) (pow.f64 x 3))

Compiler

Compiled 5054 to 2366 computations (53.2% saved)

series162.0ms (2.9%)

Error

0.0b

Counts

4 → 32

Calls

4 calls:

48.0ms	(.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (.f64 (.f64 x x) (.f64 eps eps))))
38.0ms	(.f64 (.f64 (*.f64 eps eps) (pow.f64 x 3)) (/.f64 1/3 (exp.f64 x)))
28.0ms	(.f64 (.f64 x x) (*.f64 eps eps))
27.0ms	(.f64 (.f64 eps eps) (pow.f64 x 3))

Compiler

Compiled 2525 to 1756 computations (30.5% saved)

simplify132.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

548×	`associate-l_binary64`
466×	`unswap-sqr_binary64`
411×	`associate-r_binary64`
287×	`exp-prod_binary64`
273×	`log-prod_binary64`

Counts

166 → 125

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	235	3093
1	589	2611
2	2636	2542
3	4688	2503
4	5044	2503

prune74.0ms (1.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	125	3	128

Error

0.0b

Counts

128 → 3

Alt Table

Status	Error	Program
▶	21.0b	(/.f64 (-.f64 (+.f64 2 (.f64 (.f64 x x) (.f64 eps eps))) (.f64 x x)) 2)
✓	16.4b	(/.f64 (+.f64 (+.f64 (.f64 x (/.f64 2 (exp.f64 x))) (.f64 (.f64 (.f64 eps eps) (pow.f64 x 3)) (/.f64 1/3 (exp.f64 x)))) (.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (.f64 (.f64 x x) (.f64 eps eps))))) 2)
✓	29.5b	(/.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)

Compiler

Compiled 2121 to 1055 computations (50.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.8b	(-.f64 (+.f64 2 (.f64 (.f64 x x) (.f64 eps eps))) (.f64 x x))
16.4b	(.f64 (.f64 x x) (*.f64 eps eps))

rewrite60.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

30×	`pow1_binary64`
14×	`pow-prod-down_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`prod-exp_binary64` `cbrt-unprod_binary64`
7×	`add-log-exp_binary64`
4×	`pow-prod-up_binary64` `pow-plus_binary64`

Counts

2 → 44

Calls

2 calls:

9.0ms	(.f64 (.f64 x x) (*.f64 eps eps))
7.0ms	(-.f64 (+.f64 2 (.f64 (.f64 x x) (.f64 eps eps))) (.f64 x x))

Compiler

Compiled 872 to 323 computations (63% saved)

series62.0ms (1.1%)

Error

0.0b

Counts

2 → 18

Calls

2 calls:

37.0ms	(-.f64 (+.f64 2 (.f64 (.f64 x x) (.f64 eps eps))) (.f64 x x))
20.0ms	(.f64 (.f64 x x) (*.f64 eps eps))

Compiler

Compiled 532 to 427 computations (19.7% saved)

simplify86.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

688×	`associate-l_binary64`
530×	`associate-r_binary64`
216×	`distribute-rgt-in_binary64`
213×	`distribute-lft-in_binary64`
197×	`+-commutative_binary64`

Counts

62 → 41

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	80	1054
1	186	842
2	641	802
3	2567	787
4	4315	787
5	4947	787

prune23.0ms (0.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	41	3	44

Error

0.0b

Counts

44 → 3

Alt Table

Status	Error	Program
	21.0b	(/.f64 (-.f64 (+.f64 2 (.f64 (.f64 x x) (.f64 eps eps))) (.f64 x x)) 2)
	16.4b	(/.f64 (+.f64 (+.f64 (.f64 x (/.f64 2 (exp.f64 x))) (.f64 (.f64 (.f64 eps eps) (pow.f64 x 3)) (/.f64 1/3 (exp.f64 x)))) (.f64 (exp.f64 (neg.f64 x)) (+.f64 2 (.f64 (.f64 x x) (.f64 eps eps))))) 2)
	29.5b	(/.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)

Compiler

Compiled 437 to 234 computations (46.5% saved)

regimes1.0s (18.7%)

Accuracy

Total 0.9b remaining (97.1%)

Threshold costs 0.9b (97.1%)

Compiler

Compiled 25262 to 20274 computations (19.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

7×	`+-commutative_binary64`
5×	`sub-neg_binary64` `*-commutative_binary64`
4×	`neg-mul-1_binary64` `neg-sub0_binary64`
2×	`unsub-neg_binary64` `distribute-neg-in_binary64` `distribute-rgt-neg-in_binary64` `distribute-lft-neg-in_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	25
1	23	25
2	37	25
3	45	25
4	49	25
5	50	25
6	50	25

end1.0ms (0%)

Compiler: Compiled 18 to 11 computations (38.9% saved)

sample2.1s (38.3%)

Algorithm

1×

intervals

Results

857.0ms	1997×	body	1024	valid
356.0ms	4313×	body	128	valid
252.0ms	993×	body	512	valid
149.0ms	216×	body	2048	valid
81.0ms	481×	body	256	valid
19.0ms	225×	body	128	invalid
16.0ms	200×	body	128	overflowed
6.0ms	15×	body	1024	invalid
3.0ms	9×	body	512	invalid
1.0ms	4×	body	256	invalid

Compiler

Compiled 137 to 98 computations (28.5% saved)

Details

analyze311.0ms (5.6%)

sample69.0ms (1.2%)

simplify76.0ms (1.4%)

prune5.0ms (0.1%)

localize18.0ms (0.3%)

rewrite471.0ms (8.4%)

series207.0ms (3.7%)

simplify253.0ms (4.5%)

prune146.0ms (2.6%)

localize24.0ms (0.4%)

rewrite211.0ms (3.8%)

series162.0ms (2.9%)

simplify132.0ms (2.4%)

prune74.0ms (1.3%)

localize8.0ms (0.1%)

rewrite60.0ms (1.1%)

series62.0ms (1.1%)

simplify86.0ms (1.5%)

prune23.0ms (0.4%)

regimes1.0s (18.7%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample2.1s (38.3%)

Profiling