Details

analyze26.0ms (0.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample30.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	64×	body	1024	valid
6.0ms	24×	body	512	valid
6.0ms	146×	body	128	valid
1.0ms	17×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 18 to 14 computations (22.2% saved)

simplify14.0ms (0.3%)

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 → 0

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	22	11
4	28	11
5	43	11
6	65	11
7	77	11
8	89	11
9	91	11
10	85	11
11	71	11

prune1.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

28.0b

Counts

1 → 1

Alt Table

Status	Error	Program
▶	28.0b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

Compiler

Compiled 16 to 12 computations (25% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(sqrt.f64 (+.f64 x 1))
3.9b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))

rewrite55.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

27.1b

Rules

15×	`sqrt-prod_binary64`
14×	`*-un-lft-identity_binary64`
14×	`add-sqr-sqrt_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`add-cube-cbrt_binary64`

Counts

2 → 40

Calls

2 calls:

7.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
2.0ms	(sqrt.f64 (+.f64 x 1))

Compiler

Compiled 459 to 303 computations (34% saved)

series16.0ms (0.3%)

Error

27.2b

Counts

2 → 9

Calls

2 calls:

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

Compiler

Compiled 232 to 177 computations (23.7% saved)

simplify55.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

732×	`associate-/l*_binary64`
324×	`cancel-sign-sub-inv_binary64`
278×	`distribute-rgt-in_binary64`
267×	`associate-/l/_binary64`
234×	`distribute-lft-in_binary64`

Counts

49 → 37

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	91	625
1	199	602
2	483	596
3	1673	589
4	4960	589

prune25.0ms (0.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	34	3	37
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	35	3	38

Error

0.1b

Counts

38 → 3

Alt Table

Status	Error	Program
	28.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))
	28.0b	(*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
▶	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 399 to 276 computations (30.8% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite102.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

52×	`*-un-lft-identity_binary64`
24×	`sqrt-prod_binary64`
21×	`distribute-lft-out_binary64`
18×	`times-frac_binary64`
16×	`add-sqr-sqrt_binary64`

Counts

3 → 75

Calls

3 calls:

10.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
6.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
3.0ms	(sqrt.f64 (+.f64 1 x))

Compiler

Compiled 1078 to 778 computations (27.8% saved)

series19.0ms (0.4%)

Error

0.1b

Counts

3 → 12

Calls

3 calls:

6.0ms	(sqrt.f64 (+.f64 1 x))
5.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
4.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 261 to 214 computations (18% saved)

simplify121.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

558×	`cancel-sign-sub-inv_binary64`
389×	`associate-l_binary64`
320×	`div-sub_binary64`
311×	`associate-r_binary64`
287×	`distribute-rgt-out_binary64`

Counts

87 → 48

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	93	1262
1	196	1181
2	404	1175
3	878	1168
4	2187	1168
5	4251	1168
6	4974	1168
7	4871	1168

prune31.0ms (0.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	45	3	48
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	45	6	51

Error

0.0b

Counts

51 → 6

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
	28.0b	(+.f64 (sqrt.f64 (+.f64 x 1)) (neg.f64 (sqrt.f64 x)))
	8.8b	(.f64 (/.f64 1 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (pow.f64 x 3/2))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	28.0b	(*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	8.3b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 556 to 408 computations (26.6% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite221.0ms (4.5%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

55×	`add-sqr-sqrt_binary64`
29×	`cbrt-prod_binary64`
28×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
17×	`sqrt-prod_binary64`

Counts

4 → 120

Calls

4 calls:

17.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
13.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
3.0ms	(cbrt.f64 (+.f64 1 x))
3.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 2925 to 2282 computations (22% saved)

series92.0ms (1.9%)

Error

0.0b

Counts

4 → 30

Calls

4 calls:

20.0ms	(*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x))))
17.0ms	(/.f64 1 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x)))
14.0ms	(cbrt.f64 (+.f64 1 x))
14.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 1894 to 1582 computations (16.5% saved)

simplify159.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

330×	`times-frac_binary64`
325×	`unswap-sqr_binary64`
296×	`*-commutative_binary64`
262×	`cancel-sign-sub-inv_binary64`
258×	`distribute-rgt-in_binary64`

Counts

150 → 127

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	225	3652
1	493	2843
2	1124	2334
3	2006	2297
4	4412	2297
5	4839	2297

prune93.0ms (1.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	125	2	127
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	127	6	133

Error

0.0b

Counts

133 → 6

Alt Table

Status	Error	Program
▶	0.3b	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
	0.4b	(/.f64 1 (+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 1 x)) (fabs.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))))) (sqrt.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))))) (sqrt.f64 x)))
	8.8b	(.f64 (/.f64 1 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (pow.f64 x 3/2))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	28.0b	(*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	8.3b	(cbrt.f64 (pow.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) 3))
✓	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 2022 to 1504 computations (25.6% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite710.0ms (14.3%)

Algorithm

1×	rewrite-expression-head

Error

Rules

414×	`times-frac_binary64`
383×	`*-un-lft-identity_binary64`
352×	`sqrt-prod_binary64`
204×	`add-sqr-sqrt_binary64`
204×	`add-cube-cbrt_binary64`

Counts

4 → 343

Calls

4 calls:

28.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
9.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
3.0ms	(cbrt.f64 (+.f64 1 x))
3.0ms	(cbrt.f64 (+.f64 1 x))

Compiler

Compiled 11339 to 8599 computations (24.2% saved)

series107.0ms (2.2%)

Error

0.0b

Counts

4 → 24

Calls

4 calls:

47.0ms	(/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
16.0ms	(cbrt.f64 (+.f64 1 x))
14.0ms	(cbrt.f64 (+.f64 1 x))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))

Compiler

Compiled 1993 to 1622 computations (18.6% saved)

simplify900.0ms (18.1%)

Algorithm

1×	egg-herbie

Rules

700×	`times-frac_binary64`
383×	`associate-l_binary64`
348×	`unswap-sqr_binary64`
298×	`associate-r_binary64`
285×	`log-prod_binary64`

Counts

367 → 335

Iterations

Useful iterations: 5 (0.0ms)

Iter	Nodes	Cost
0	262	21448
1	584	18247
2	1260	17843
3	2839	14366
4	3825	13353
5	4709	12993
6	4972	12993
7	4999	12993
8	4998	12993
9	4838	12993

prune228.0ms (4.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	330	5	335
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	332	9	341

Error

0.0b

Counts

341 → 9

Alt Table

Status	Error	Program
	8.8b	(.f64 (/.f64 1 (+.f64 (pow.f64 (sqrt.f64 (+.f64 1 x)) 3) (pow.f64 x 3/2))) (+.f64 (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 (+.f64 1 x))) (-.f64 (.f64 (sqrt.f64 x) (sqrt.f64 x)) (.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))
	0.5b	(/.f64 (/.f64 1 (sqrt.f64 (.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
	0.5b	(*.f64 (/.f64 1 (fabs.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (sqrt.f64 (cbrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
	0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
	0.8b	(.f64 (/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (.f64 (cbrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))) (cbrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))))) (/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (cbrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))
	0.2b	(/.f64 (pow.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) -1/2) (sqrt.f64 (+.f64 (*.f64 (fabs.f64 (cbrt.f64 (+.f64 1 x))) (sqrt.f64 (cbrt.f64 (+.f64 1 x)))) (sqrt.f64 x))))
	0.4b	(/.f64 1 (+.f64 (.f64 (.f64 (cbrt.f64 (+.f64 1 x)) (fabs.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))))) (sqrt.f64 (cbrt.f64 (cbrt.f64 (+.f64 1 x))))) (sqrt.f64 x)))
	28.0b	(*.f64 (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (sqrt.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))
	0.4b	(*.f64 (/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (/.f64 (sqrt.f64 (/.f64 1 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))) (sqrt.f64 (sqrt.f64 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))))))

Compiler

Compiled 3619 to 2642 computations (27% saved)

regimes832.0ms (16.8%)

Accuracy

Total 0.1b remaining (83.9%)

Threshold costs 0.1b (83.9%)

Compiler

Compiled 19309 to 15266 computations (20.9% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	14
1	12	14
2	11	14

end1.0ms (0%)

Compiler: Compiled 10 to 8 computations (20% saved)

sample1.1s (21.8%)

Algorithm

1×

intervals

Results

296.0ms	1992×	body	1024	valid
188.0ms	4260×	body	128	valid
122.0ms	1024×	body	512	valid
41.0ms	222×	body	2048	valid
37.0ms	502×	body	256	valid
0.0ms	2×	body	128	nan

Compiler

Compiled 306 to 231 computations (24.5% saved)

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	22	11
4	28	11
5	43	11
6	65	11
7	77	11
8	89	11
9	91	11
10	85	11
11	71	11

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	22	11
4	28	11
5	43	11
6	65	11
7	77	11
8	89	11
9	91	11
10	85	11
11	71	11

Details

analyze26.0ms (0.5%)

sample30.0ms (0.6%)

simplify14.0ms (0.3%)

prune1.0ms (0%)

localize5.0ms (0.1%)

rewrite55.0ms (1.1%)

series16.0ms (0.3%)

simplify55.0ms (1.1%)

prune25.0ms (0.5%)

localize6.0ms (0.1%)

rewrite102.0ms (2.1%)

series19.0ms (0.4%)

simplify121.0ms (2.4%)

prune31.0ms (0.6%)

localize10.0ms (0.2%)

rewrite221.0ms (4.5%)

series92.0ms (1.9%)

simplify159.0ms (3.2%)

prune93.0ms (1.9%)

localize17.0ms (0.3%)

rewrite710.0ms (14.3%)

series107.0ms (2.2%)

simplify900.0ms (18.1%)

prune228.0ms (4.6%)

regimes832.0ms (16.8%)

simplify3.0ms (0.1%)

end1.0ms (0%)

sample1.1s (21.8%)

Profiling

Iter	Nodes	Cost
0	7	11
1	12	11
2	16	11
3	22	11
4	28	11
5	43	11
6	65	11
7	77	11
8	89	11
9	91	11
10	85	11
11	71	11