Details

analyze1.3s (28.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.3%	24.4%	11
31.4%	44.3%	24.4%	12
31.4%	44%	24.5%	13
31.5%	43.8%	24.8%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample97.0ms (2.2%)

Algorithm

1×

intervals

Results

68.0ms	90×	body	1024	valid
9.0ms	49×	body	512	valid
6.0ms	88×	body	128	valid
3.0ms	10×	body	2048	valid
2.0ms	19×	body	256	valid

Compiler

Compiled 28 to 24 computations (14.3% saved)

simplify77.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

669×	`div-sub_binary64`
601×	`associate-/l*_binary64`
488×	`associate-/r*_binary64`
279×	`distribute-rgt-in_binary64`
273×	`associate-/l/_binary64`

Counts

1 → 1

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	11	19
1	23	19
2	32	19
3	55	19
4	116	11
5	296	8
6	987	8
7	4260	8
8	4954	8
9	5000	8
10	4831	8

prune3.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

0.0b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

Compiler

Compiled 18 to 15 computations (16.7% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 1 (exp.f64 x))
0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))

rewrite29.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Error

Rules

7×	`*-un-lft-identity_binary64`
4×	`sqrt-prod_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64`
3×	`add-cube-cbrt_binary64`

Counts

2 → 28

Calls

2 calls:

3.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
2.0ms	(+.f64 1 (exp.f64 x))

Compiler

Compiled 294 to 198 computations (32.7% saved)

series21.0ms (0.5%)

Error

0.0b

Counts

2 → 12

Calls

2 calls:

9.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
6.0ms	(+.f64 1 (exp.f64 x))

Compiler

Compiled 324 to 283 computations (12.7% saved)

simplify51.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

733×	`times-frac_binary64`
663×	`associate-/l*_binary64`
177×	`associate-/r/_binary64`
165×	`associate-+l+_binary64`
153×	`distribute-neg-frac_binary64`

Counts

40 → 15

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	82	545
1	205	521
2	543	490
3	1894	476
4	5062	476

prune12.0ms (0.3%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	14	1	15
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	15	1	16

Error

Counts

16 → 1

Alt Table

Status	Error	Program
▶	0b	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))

Compiler

Compiled 228 to 170 computations (25.4% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))
0.0b	(pow.f64 (exp.f64 x) 3)
0.0b	(pow.f64 (exp.f64 x) 2)
2.2b	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))

rewrite135.0ms (3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

107×	`*-un-lft-identity_binary64`
76×	`sqrt-prod_binary64`
56×	`times-frac_binary64`
54×	`add-sqr-sqrt_binary64`
46×	`add-cube-cbrt_binary64`

Counts

4 → 156

Calls

4 calls:

14.0ms	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))
5.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
3.0ms	(pow.f64 (exp.f64 x) 3)
2.0ms	(pow.f64 (exp.f64 x) 2)

Compiler

Compiled 3393 to 2311 computations (31.9% saved)

series91.0ms (2%)

Error

Counts

4 → 24

Calls

4 calls:

24.0ms	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))
8.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
8.0ms	(pow.f64 (exp.f64 x) 2)
8.0ms	(pow.f64 (exp.f64 x) 3)

Compiler

Compiled 1080 to 857 computations (20.6% saved)

simplify208.0ms (4.6%)

Algorithm

1×	egg-herbie

Rules

352×	`exp-prod_binary64`
347×	`log-prod_binary64`
281×	`unswap-sqr_binary64`
209×	`cancel-sign-sub-inv_binary64`
209×	`prod-exp_binary64`

Counts

180 → 146

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	253	5205
1	506	4969
2	1393	4909
3	3816	4889
4	4389	4889
5	4925	4889

prune65.0ms (1.5%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	146	1	147

Error

Counts

147 → 1

Alt Table

Status	Error	Program
	0b	(/.f64 (sqrt.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))

Compiler

Compiled 2149 to 1481 computations (31.1% saved)

regimes85.0ms (1.9%)

Accuracy

Total 0.0b remaining (0%)

Threshold costs 0.0b (0%)

Compiler

Compiled 1423 to 1119 computations (21.4% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	29
1	20	29
2	24	29
3	26	29
4	27	29
5	26	29

end1.0ms (0%)

Compiler: Compiled 19 to 14 computations (26.3% saved)

sample2.3s (51.4%)

Algorithm

1×

intervals

Results

1.2s	2672×	body	1024	valid
376.0ms	1329×	body	512	valid
170.0ms	3039×	body	128	valid
162.0ms	292×	body	2048	valid
84.0ms	668×	body	256	valid
0.0ms	3×	body	128	invalid

Compiler

Compiled 53 to 41 computations (22.6% saved)

Details

analyze1.3s (28.7%)

sample97.0ms (2.2%)

simplify77.0ms (1.7%)

prune3.0ms (0.1%)

localize4.0ms (0.1%)

rewrite29.0ms (0.7%)

series21.0ms (0.5%)

simplify51.0ms (1.1%)

prune12.0ms (0.3%)

localize12.0ms (0.3%)

rewrite135.0ms (3%)

series91.0ms (2%)

simplify208.0ms (4.6%)

prune65.0ms (1.5%)

regimes85.0ms (1.9%)

simplify4.0ms (0.1%)

end1.0ms (0%)

sample2.3s (51.4%)

Profiling