Details

analyze466.0ms (2.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
6.2%	93.6%	0.2%	5
6.2%	68.6%	25.1%	6
6.2%	49.9%	43.9%	7
6.2%	35.9%	57.9%	8
6.2%	25.3%	68.4%	9
6.2%	20.1%	73.7%	10
6.2%	15.7%	78.1%	11
6.2%	12%	81.7%	12
6.2%	9%	84.8%	13
6.2%	7.5%	86.3%	14

Compiler

Compiled 32 to 28 computations (12.5% saved)

sample239.0ms (1.2%)

Algorithm

1×

intervals

Results

82.0ms	144×	body	512	valid
50.0ms	275×	body	128	nan
48.0ms	60×	body	1024	valid
11.0ms	30×	body	256	valid
4.0ms	22×	body	128	valid

Compiler

Compiled 63 to 59 computations (6.3% saved)

simplify256.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	5168	50

prune7.0ms (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

5.1b

Counts

2 → 1

Compiler

Compiled 62 to 54 computations (12.9% saved)

localize51.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (+.f64 (+.f64 (-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x)) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
0.0b	(sqrt.f64 (+.f64 x 1))
0.0b	(sqrt.f64 (+.f64 t 1))
0.0b	(sqrt.f64 (+.f64 y 1))
1.8b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
1.8b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
3.1b	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
3.3b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

rewrite103.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`sqrt-prod_binary64_13740` `add-sqr-sqrt_binary64_13746`
40×	`*-un-lft-identity_binary64_13724`
24×	`cancel-sign-sub-inv_binary64_13690`
16×	`difference-of-squares_binary64_13693`
12×	`add-log-exp_binary64_13763` `add-cube-cbrt_binary64_13759` `distribute-lft-out--_binary64_13676`
4×	`add-exp-log_binary64_13762` `distribute-lft-out_binary64_13675` `sub-neg_binary64_13717` `flip3--_binary64_13728` `flip--_binary64_13699` `pow1_binary64_13785` `diff-log_binary64_13816` `add-cbrt-cube_binary64_13760`

Counts

4 → 96

Calls

8 calls:

23.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
21.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
20.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
17.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
0.0ms	(sqrt.f64 (+.f64 y 1))

series247.0ms (1.2%)

Counts

4 → 12

Calls

4 calls:

65.0ms	(-.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 x))
61.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
61.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
59.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

Compiler

Compiled 928 to 800 computations (13.8% saved)

simplify86.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4912	1588
1	4912	1588

prune581.0ms (2.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	101	7	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	7	109

Error

0.6b

Counts

109 → 7

Compiler

Compiled 4109 to 2640 computations (35.8% saved)

localize54.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(sqrt.f64 (+.f64 t 1))
0.0b	(sqrt.f64 (+.f64 y 1))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
1.8b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
1.8b	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
3.3b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

rewrite79.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

70×	`*-un-lft-identity_binary64_13724`
49×	`sqrt-prod_binary64_13740`
45×	`add-sqr-sqrt_binary64_13746`
21×	`add-cube-cbrt_binary64_13759`
19×	`distribute-lft-out_binary64_13675`
18×	`cancel-sign-sub-inv_binary64_13690` `times-frac_binary64_13730`
12×	`difference-of-squares_binary64_13693`
10×	`add-log-exp_binary64_13763`
9×	`distribute-lft-out--_binary64_13676`
8×	`add-exp-log_binary64_13762`
6×	`associate-/r*_binary64_13668` `add-cbrt-cube_binary64_13760`
5×	`pow1_binary64_13785`
3×	`associate-/l*_binary64_13669` `sub-neg_binary64_13717` `flip3--_binary64_13728` `flip--_binary64_13699` `diff-log_binary64_13816`
2×	`associate-/r/_binary64_13670` `div-exp_binary64_13775`
1×	`1-exp_binary64_13768` `flip-+_binary64_13698` `inv-pow_binary64_13809` `clear-num_binary64_13723` `cbrt-undiv_binary64_13758` `frac-2neg_binary64_13735` `rec-exp_binary64_13774` `flip3-+_binary64_13727` `pow-flip_binary64_13798` `div-inv_binary64_13721`

Counts

4 → 117

Calls

8 calls:

18.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
11.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
9.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
0.0ms	(sqrt.f64 (+.f64 y 1))

series223.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(-.f64 (sqrt.f64 (+.f64 y 1)) (sqrt.f64 y))
67.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
58.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
29.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))

Compiler

Compiled 918 to 804 computations (12.4% saved)

simplify133.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4879	2015
1	4879	2015

prune516.0ms (2.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	125	4	129
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	129	7	136

Error

0.0b

Counts

136 → 7

Compiler

Compiled 5151 to 3419 computations (33.6% saved)

localize36.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (+.f64 (+.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))) (-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))) (-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t)))
0.0b	(sqrt.f64 (+.f64 1 y))
0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(sqrt.f64 (+.f64 t 1))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
1.8b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
3.3b	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))

rewrite65.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

100×	`*-un-lft-identity_binary64_13724`
54×	`sqrt-prod_binary64_13740`
46×	`add-sqr-sqrt_binary64_13746`
36×	`times-frac_binary64_13730`
34×	`distribute-lft-out_binary64_13675`
30×	`add-cube-cbrt_binary64_13759`
12×	`add-exp-log_binary64_13762` `associate-/r*_binary64_13668` `cancel-sign-sub-inv_binary64_13690`
8×	`difference-of-squares_binary64_13693` `add-log-exp_binary64_13763` `add-cbrt-cube_binary64_13760`
6×	`associate-/l*_binary64_13669` `pow1_binary64_13785` `distribute-lft-out--_binary64_13676`
4×	`associate-/r/_binary64_13670` `div-exp_binary64_13775`
2×	`1-exp_binary64_13768` `sub-neg_binary64_13717` `flip3--_binary64_13728` `flip-+_binary64_13698` `flip--_binary64_13699` `inv-pow_binary64_13809` `clear-num_binary64_13723` `cbrt-undiv_binary64_13758` `frac-2neg_binary64_13735` `rec-exp_binary64_13774` `diff-log_binary64_13816` `flip3-+_binary64_13727` `pow-flip_binary64_13798` `div-inv_binary64_13721`

Counts

4 → 138

Calls

8 calls:

12.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
10.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
9.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
0.0ms	(sqrt.f64 (+.f64 t 1))

series190.0ms (0.9%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
56.0ms	(-.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
38.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
31.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))

Compiler

Compiled 908 to 808 computations (11% saved)

simplify126.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4879	2442
1	4879	2442

prune600.0ms (2.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	150	7	157

Error

0.0b

Counts

157 → 7

Compiler

Compiled 6282 to 4284 computations (31.8% saved)

localize60.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z))
0.0b	(sqrt.f64 (+.f64 1 y))
0.0b	(sqrt.f64 (+.f64 1 x))
0.0b	(sqrt.f64 (+.f64 t 1))
0.1b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
1.8b	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))

rewrite132.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

130×	`*-un-lft-identity_binary64_13724`
59×	`sqrt-prod_binary64_13740`
54×	`times-frac_binary64_13730`
49×	`distribute-lft-out_binary64_13675`
47×	`add-sqr-sqrt_binary64_13746`
39×	`add-cube-cbrt_binary64_13759`
18×	`associate-/r*_binary64_13668`
16×	`add-exp-log_binary64_13762`
10×	`add-cbrt-cube_binary64_13760`
9×	`associate-/l*_binary64_13669`
7×	`pow1_binary64_13785`
6×	`associate-/r/_binary64_13670` `add-log-exp_binary64_13763` `div-exp_binary64_13775` `cancel-sign-sub-inv_binary64_13690`
4×	`difference-of-squares_binary64_13693`
3×	`1-exp_binary64_13768` `flip-+_binary64_13698` `inv-pow_binary64_13809` `clear-num_binary64_13723` `cbrt-undiv_binary64_13758` `frac-2neg_binary64_13735` `rec-exp_binary64_13774` `flip3-+_binary64_13727` `pow-flip_binary64_13798` `div-inv_binary64_13721` `distribute-lft-out--_binary64_13676`
1×	`sub-neg_binary64_13717` `flip3--_binary64_13728` `flip--_binary64_13699` `diff-log_binary64_13816`

Counts

4 → 159

Calls

8 calls:

21.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
20.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))
19.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
17.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
0.0ms	(sqrt.f64 (+.f64 t 1))

series163.0ms (0.8%)

Counts

4 → 12

Calls

4 calls:

47.0ms	(-.f64 (sqrt.f64 (+.f64 t 1)) (sqrt.f64 t))
45.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
42.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 y)) (sqrt.f64 y)))
29.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 z 1)) (sqrt.f64 z)))

Compiler

Compiled 898 to 812 computations (9.6% saved)

simplify122.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5016	2869

prune701.0ms (3.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	169	2	171
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	171	7	178

Error

0.0b

Counts

178 → 7

Compiler

Compiled 7211 to 4987 computations (30.8% saved)

simplify64.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (8.0ms)

Iter	Nodes	Cost
0	395	2235
1	395	2235

regimes979.0ms (4.8%)

Accuracy

Total 0.0b remaining (54.8%)

Threshold costs 0.0b (54.8%)

Compiler

Compiled 7836 to 6903 computations (11.9% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	62
1	41	62

end0.0ms (0%)

sample14.1s (69.2%)

Algorithm

1×

intervals

Results

2.3s	4369×	body	512	valid
1.7s	9614×	body	128	nan
1.3s	1762×	body	1024	valid
364.0ms	1045×	body	256	valid
146.0ms	824×	body	128	valid

Compiler

Compiled 4326 to 3801 computations (12.1% saved)

Pareto

0.26311009961118803

Details

analyze466.0ms (2.3%)

sample239.0ms (1.2%)

simplify256.0ms (1.3%)

prune7.0ms (0%)

localize51.0ms (0.2%)

rewrite103.0ms (0.5%)

series247.0ms (1.2%)

simplify86.0ms (0.4%)

prune581.0ms (2.8%)

localize54.0ms (0.3%)

rewrite79.0ms (0.4%)

series223.0ms (1.1%)

simplify133.0ms (0.7%)

prune516.0ms (2.5%)

localize36.0ms (0.2%)

rewrite65.0ms (0.3%)

series190.0ms (0.9%)

simplify126.0ms (0.6%)

prune600.0ms (2.9%)

localize60.0ms (0.3%)

rewrite132.0ms (0.6%)

series163.0ms (0.8%)

simplify122.0ms (0.6%)

prune701.0ms (3.4%)

simplify64.0ms (0.3%)

regimes979.0ms (4.8%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample14.1s (69.2%)

Profiling