Details

analyze24.0ms (0.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample37.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms	67×	body	1024	valid
7.0ms	134×	body	128	valid
6.0ms	36×	body	512	valid
2.0ms	19×	body	256	valid

Compiler

Compiled 26 to 22 computations (15.4% saved)

simplify16.0ms (0.2%)

Algorithm

1×	egg-herbie

Rules

15×	`sub-neg_binary64`
14×	`cancel-sign-sub-inv_binary64`
10×	`distribute-rgt-in_binary64`
9×	`neg-mul-1_binary64`
8×	`associate--r+_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	27	17
4	34	17
5	50	17
6	72	17
7	81	17
8	93	17
9	95	17
10	89	17
11	75	17

prune2.0ms (0%)

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

19.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	19.1b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 36 to 30 computations (16.7% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
2.4b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite254.0ms (3.6%)

Algorithm

1×	rewrite-expression-head

Error

18.6b

Rules

127×	`add-sqr-sqrt_binary64`
118×	`times-frac_binary64`
117×	`*-un-lft-identity_binary64`
76×	`sqrt-prod_binary64`
56×	`add-cube-cbrt_binary64`

Counts

4 → 189

Calls

4 calls:

33.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
5.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
3.0ms	(/.f64 1 (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 2812 to 2163 computations (23.1% saved)

series35.0ms (0.5%)

Error

18.8b

Counts

4 → 18

Calls

4 calls:

8.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(sqrt.f64 (+.f64 x 1))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
4.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 515 to 413 computations (19.8% saved)

simplify165.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

362×	`distribute-rgt-in_binary64`
300×	`distribute-lft-in_binary64`
263×	`neg-mul-1_binary64`
248×	`distribute-rgt-neg-in_binary64`
227×	`sub-neg_binary64`

Counts

207 → 183

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	180	3451
1	401	3364
2	890	3350
3	2507	3338
4	4526	3284
5	4941	3284

prune97.0ms (1.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	174	9	183
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	175	9	184

Error

18.6b

Counts

184 → 9

Alt Table

Status	Error	Program
	29.9b	(-.f64 (/.f64 1 (sqrt.f64 x)) (cbrt.f64 (pow.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) 3)))
▶	19.2b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))
	27.3b	(-.f64 (/.f64 1 (sqrt.f64 x)) (.f64 (/.f64 1 (.f64 (cbrt.f64 (sqrt.f64 (+.f64 1 x))) (cbrt.f64 (sqrt.f64 (+.f64 1 x))))) (/.f64 1 (cbrt.f64 (sqrt.f64 (+.f64 1 x))))))
	20.8b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	26.1b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (/.f64 1 (sqrt.f64 (sqrt.f64 (+.f64 1 x)))) (sqrt.f64 (sqrt.f64 (+.f64 x 1)))))
	31.0b	(/.f64 (+.f64 (/.f64 1 (pow.f64 x 3/2)) (/.f64 -1 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3))) (+.f64 (/.f64 1 x) (+.f64 (/.f64 1 (+.f64 1 x)) (/.f64 1 (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
	62.4b	(+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 (neg.f64 (sqrt.f64 (+.f64 -1 x))) (sqrt.f64 (+.f64 -1 (*.f64 x x)))))
	26.4b	(-.f64 (*.f64 (/.f64 1 (pow.f64 x 1/4)) (/.f64 1 (pow.f64 x 1/4))) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
	25.4b	(-.f64 (/.f64 1 (sqrt.f64 x)) (*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (+.f64 1 x)))) (/.f64 1 (sqrt.f64 (cbrt.f64 (+.f64 1 x))))))

Compiler

Compiled 1640 to 1280 computations (22% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.2b	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))
0.3b	(/.f64 1 (sqrt.f64 x))
2.4b	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))

rewrite721.0ms (10.3%)

Algorithm

1×	rewrite-expression-head

Error

18.1b

Rules

1332×	`*-un-lft-identity_binary64`
1249×	`times-frac_binary64`
725×	`add-sqr-sqrt_binary64`
429×	`distribute-lft-out_binary64`
304×	`sqrt-prod_binary64`

Counts

4 → 554

Calls

4 calls:

61.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))
18.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
8.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
4.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 10904 to 8671 computations (20.5% saved)

series46.0ms (0.7%)

Error

4.0b

Counts

4 → 20

Calls

4 calls:

9.0ms	(-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x)))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
7.0ms	(/.f64 (-.f64 (/.f64 1 x) (/.f64 1 (+.f64 1 x))) (+.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))
5.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 867 to 695 computations (19.8% saved)

simplify650.0ms (9.3%)

Algorithm

1×	egg-herbie

Rules

485×	`div-sub_binary64`
393×	`associate-/l*_binary64`
299×	`times-frac_binary64`
289×	`distribute-rgt-in_binary64`
276×	`associate-*l/_binary64`

Counts

574 → 493

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	281	22126
1	666	21928
2	1689	20863
3	4293	20857
4	4902	20857
5	4913	20857

prune81.0ms (1.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	490	3	493
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	498	4	502

Error

0.1b

Counts

502 → 4

Alt Table

Status	Error	Program
▶	4.2b	(/.f64 (/.f64 1 (+.f64 x (*.f64 x x))) (+.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))
	36.3b	(/.f64 (-.f64 (/.f64 1 (*.f64 x x)) (/.f64 1 (pow.f64 x 3))) (+.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))
	31.4b	(/.f64 (/.f64 (/.f64 1 x) (+.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))) x)
	20.8b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 2489 to 1901 computations (23.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (+.f64 x (*.f64 x x)))
0.2b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.3b	(/.f64 1 (sqrt.f64 x))
4.1b	(/.f64 (/.f64 1 (+.f64 x (*.f64 x x))) (+.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))

rewrite619.0ms (8.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

1041×	`times-frac_binary64`
965×	`*-un-lft-identity_binary64`
356×	`distribute-lft-out_binary64`
352×	`add-sqr-sqrt_binary64`
352×	`add-cube-cbrt_binary64`

Counts

4 → 530

Calls

4 calls:

41.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 x x))) (+.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))
5.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
4.0ms	(/.f64 1 (+.f64 x (*.f64 x x)))
3.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 11642 to 7482 computations (35.7% saved)

series48.0ms (0.7%)

Error

0.1b

Counts

4 → 20

Calls

4 calls:

12.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 x x))) (+.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))
9.0ms	(/.f64 1 (+.f64 x (*.f64 x x)))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
5.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 833 to 636 computations (23.6% saved)

simplify578.0ms (8.2%)

Algorithm

1×	egg-herbie

Rules

479×	`associate-/r*_binary64`
413×	`distribute-rgt-in_binary64`
372×	`distribute-lft-in_binary64`
354×	`times-frac_binary64`
341×	`associate-/l*_binary64`

Counts

550 → 477

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	268	18310
1	618	17849
2	1687	17841
3	4803	17835
4	4946	17835
5	4942	17835

prune201.0ms (2.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	472	5	477
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	474	7	481

Error

0.0b

Counts

481 → 7

Alt Table

Status	Error	Program
	31.4b	(/.f64 (/.f64 (/.f64 1 x) (+.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))) x)
	26.1b	(.f64 (/.f64 (/.f64 1 (+.f64 x (.f64 x x))) (+.f64 (pow.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) 3) (/.f64 1 (pow.f64 x 3/2)))) (+.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 (+.f64 1 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (*.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))))
	0.4b	(*.f64 (/.f64 1 x) (/.f64 (/.f64 1 (+.f64 1 x)) (+.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))
▶	0.3b	(/.f64 (/.f64 1 (+.f64 x 1)) (*.f64 x (+.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))
	6.1b	(.f64 (/.f64 (/.f64 1 (+.f64 x (.f64 x x))) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	4.3b	(/.f64 (/.f64 1 (+.f64 x (*.f64 x x))) (+.f64 (/.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (/.f64 1 (sqrt.f64 x))))
	20.8b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 3062 to 1969 computations (35.7% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
0.2b	(*.f64 x (+.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))
0.2b	(/.f64 (/.f64 1 (+.f64 x 1)) (*.f64 x (+.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))
0.3b	(/.f64 1 (sqrt.f64 x))

rewrite362.0ms (5.2%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

104×	`*-un-lft-identity_binary64`
99×	`times-frac_binary64`
61×	`add-sqr-sqrt_binary64`
59×	`add-cube-cbrt_binary64`
40×	`sqrt-prod_binary64`

Counts

4 → 195

Calls

4 calls:

36.0ms	(/.f64 (/.f64 1 (+.f64 x 1)) (*.f64 x (+.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))
33.0ms	(*.f64 x (+.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))
5.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
4.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 4615 to 3493 computations (24.3% saved)

series36.0ms (0.5%)

Error

0.0b

Counts

4 → 15

Calls

4 calls:

10.0ms	(/.f64 1 (sqrt.f64 (+.f64 1 x)))
8.0ms	(/.f64 (/.f64 1 (+.f64 x 1)) (*.f64 x (+.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))))
7.0ms	(*.f64 x (+.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))
5.0ms	(/.f64 1 (sqrt.f64 x))

Compiler

Compiled 597 to 469 computations (21.4% saved)

simplify180.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

693×	`distribute-rgt-in_binary64`
628×	`distribute-lft-in_binary64`
335×	`associate-/r/_binary64`
209×	`associate-l_binary64`
181×	`associate-/r*_binary64`

Counts

210 → 174

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	251	4167
1	616	3531
2	2143	3502
3	4743	3498
4	4970	3498
5	4980	3498

prune139.0ms (2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	170	4	174
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	174	7	181

Error

Counts

181 → 7

Alt Table

Status	Error	Program
	0.3b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 x 1))) (*.f64 (sqrt.f64 (+.f64 1 x)) (+.f64 (sqrt.f64 x) (/.f64 x (sqrt.f64 (+.f64 1 x))))))
	6.1b	(.f64 (/.f64 (/.f64 1 (+.f64 x (.f64 x x))) (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	0.6b	(.f64 (/.f64 (/.f64 1 (+.f64 1 x)) (+.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 x (pow.f64 (sqrt.f64 (+.f64 1 x)) 3)))) (+.f64 (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 (+.f64 1 x)))) (-.f64 (.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 x))) (.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x))))))
	0.2b	(/.f64 (/.f64 1 (+.f64 x 1)) (*.f64 (sqrt.f64 x) (+.f64 1 (/.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))))
	0.5b	(/.f64 1 (*.f64 (+.f64 1 x) (+.f64 (sqrt.f64 x) (/.f64 x (sqrt.f64 (+.f64 1 x))))))
	31.4b	(/.f64 (/.f64 (/.f64 1 x) (+.f64 (/.f64 1 (sqrt.f64 (+.f64 1 x))) (/.f64 1 (sqrt.f64 x)))) x)
	20.8b	(-.f64 (pow.f64 x -1/2) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

Compiler

Compiled 2028 to 1478 computations (27.1% saved)

regimes1.4s (20%)

Accuracy

Total 0.3b remaining (96.2%)

Threshold costs 0.3b (96.2%)

Compiler

Compiled 28091 to 21686 computations (22.8% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	23
1	16	23
2	15	23

end1.0ms (0%)

Compiler: Compiled 16 to 12 computations (25% saved)

sample1.3s (18.1%)

Algorithm

1×

intervals

Results

489.0ms	2262×	body	1024	valid
232.0ms	4259×	body	128	valid
167.0ms	974×	body	512	valid
53.0ms	505×	body	256	valid

Compiler

Compiled 196 to 149 computations (24% saved)

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	27	17
4	34	17
5	50	17
6	72	17
7	81	17
8	93	17
9	95	17
10	89	17
11	75	17

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	27	17
4	34	17
5	50	17
6	72	17
7	81	17
8	93	17
9	95	17
10	89	17
11	75	17

Details

analyze24.0ms (0.3%)

sample37.0ms (0.5%)

simplify16.0ms (0.2%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite254.0ms (3.6%)

series35.0ms (0.5%)

simplify165.0ms (2.3%)

prune97.0ms (1.4%)

localize13.0ms (0.2%)

rewrite721.0ms (10.3%)

series46.0ms (0.7%)

simplify650.0ms (9.3%)

prune81.0ms (1.1%)

localize16.0ms (0.2%)

rewrite619.0ms (8.8%)

series48.0ms (0.7%)

simplify578.0ms (8.2%)

prune201.0ms (2.9%)

localize13.0ms (0.2%)

rewrite362.0ms (5.2%)

series36.0ms (0.5%)

simplify180.0ms (2.6%)

prune139.0ms (2%)

regimes1.4s (20%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.3s (18.1%)

Profiling

Iter	Nodes	Cost
0	9	17
1	14	17
2	20	17
3	27	17
4	34	17
5	50	17
6	72	17
7	81	17
8	93	17
9	95	17
10	89	17
11	75	17