Details

analyze508.0ms (8.1%)

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
18.7%	81.1%	0.1%	6
26.5%	67.1%	6.4%	7
35.1%	58.5%	6.4%	8
41.3%	49.9%	8.7%	9
46.4%	40.2%	13.4%	10
50.8%	34.2%	15%	11
55.2%	26.7%	18.1%	12
57.4%	22%	20.6%	13
59.8%	17.9%	22.3%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample35.0ms (0.6%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
1.0ms	15×	body	128	nan
1.0ms	11×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify248.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (84.0ms)

Iter	Nodes	Cost
0	1224	54
1	1224	54

prune5.0ms (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

Merged error: 22.8b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
25.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
25.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_100`
11×	`*-un-lft-identity_binary64_78`
8×	`add-log-exp_binary64_117`
7×	`sqrt-prod_binary64_94` `add-cube-cbrt_binary64_113`
6×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `sqrt-div_binary64_95`
3×	`flip3--_binary64_82` `flip--_binary64_53` `cancel-sign-sub-inv_binary64_44`
2×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `difference-of-squares_binary64_47` `pow1/2_binary64_158`
1×	`+-commutative_binary64_8` `flip-+_binary64_52` `distribute-lft-out--_binary64_30` `diff-log_binary64_170` `distribute-lft-out_binary64_29` `sub-neg_binary64_71` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 59

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series472.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

127.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
115.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5169	1454

prune149.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	64	7	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	7	72

Merged error: 9.4b

Counts

72 → 7

Compiler

Compiled 3318 to 1995 computations (39.9% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.3b	(/.f64 (+.f64 b (-.f64 b (.f64 2 (/.f64 (.f64 a c) b)))) a)
5.5b	(/.f64 (*.f64 a c) b)
25.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64_78`
22×	`add-sqr-sqrt_binary64_100`
17×	`add-cube-cbrt_binary64_113`
15×	`times-frac_binary64_84`
11×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
6×	`add-log-exp_binary64_117` `associate-/r*_binary64_22`
5×	`associate-/l*_binary64_23` `pow1_binary64_139`
4×	`sqrt-prod_binary64_94` `distribute-lft-out_binary64_29`
3×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `cancel-sign-sub-inv_binary64_44`
2×	`flip3--_binary64_82` `frac-2neg_binary64_89` `div-inv_binary64_75` `flip--_binary64_53` `sqrt-div_binary64_95` `difference-of-squares_binary64_47` `clear-num_binary64_77` `associate-/l/_binary64_25`
1×	`sqrt-pow1_binary64_96` `associate-+r-_binary64_12` `cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `distribute-lft-out--_binary64_30` `diff-log_binary64_170` `div-sub_binary64_83` `pow1/2_binary64_158` `sub-neg_binary64_71` `flip3-+_binary64_81`

Counts

4 → 87

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
8.0ms	(/.f64 (+.f64 b (-.f64 b (.f64 2 (/.f64 (.f64 a c) b)))) a)
5.0ms	(/.f64 (*.f64 a c) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series340.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

116.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
107.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
78.0ms	(/.f64 (+.f64 b (-.f64 b (.f64 2 (/.f64 (.f64 a c) b)))) a)
38.0ms	(/.f64 (*.f64 a c) b)

simplify63.0ms (1%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5180	1847

prune191.0ms (3.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	92	7	99
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	94	12	106

Merged error: 8.6b

Counts

106 → 12

Compiler

Compiled 4527 to 2508 computations (44.6% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 4 a) c)
0.4b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
25.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64_100`
10×	`pow1_binary64_139`
9×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116` `*-un-lft-identity_binary64_78`
8×	`add-log-exp_binary64_117`
7×	`add-cube-cbrt_binary64_113`
4×	`sqrt-prod_binary64_94` `cancel-sign-sub-inv_binary64_44`
3×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `flip3--_binary64_82` `associate-r_binary64_18` `flip--_binary64_53` `pow-prod-down_binary64_149`
2×	`diff-log_binary64_170` `sqrt-div_binary64_95` `difference-of-squares_binary64_47` `sub-neg_binary64_71`
1×	`-commutative_binary64_9` `associate-l*_binary64_19` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `distribute-lft-out--_binary64_30` `pow1/2_binary64_158`

Counts

4 → 62

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
6.0ms	(.f64 (.f64 4 a) c)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series326.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

125.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
108.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
64.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
29.0ms	(.f64 (.f64 4 a) c)

simplify83.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4883	1223
1	4883	1223

prune132.0ms (2.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	72	2	74
Fresh	3	8	11
Picked	1	0	1
Done	0	0	0
Total	76	10	86

Merged error: 8.6b

Counts

86 → 10

Compiler

Compiled 3225 to 1871 computations (42% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 c)
0.6b	(cbrt.f64 c)
0.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 (.f64 4 a) (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (cbrt.f64 c)))) b)
25.9b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 (.f64 4 a) (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (cbrt.f64 c))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-sqr-sqrt_binary64_100`
10×	`*-un-lft-identity_binary64_78`
8×	`add-cube-cbrt_binary64_113`
6×	`add-log-exp_binary64_117` `cbrt-prod_binary64_109`
5×	`pow1_binary64_139`
4×	`add-cbrt-cube_binary64_114` `sqrt-prod_binary64_94` `add-exp-log_binary64_116`
3×	`cancel-sign-sub-inv_binary64_44`
2×	`flip3--_binary64_82` `pow1/3_binary64_160` `flip--_binary64_53` `sqrt-div_binary64_95` `difference-of-squares_binary64_47`
1×	`sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `distribute-lft-out--_binary64_30` `diff-log_binary64_170` `pow1/2_binary64_158` `sub-neg_binary64_71`

Counts

4 → 54

Calls

4 calls:

10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 (.f64 4 a) (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (cbrt.f64 c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 (.f64 4 a) (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (cbrt.f64 c))))
1.0ms	(cbrt.f64 c)
1.0ms	(cbrt.f64 c)

series633.0ms (10.1%)

Counts

4 → 12

Calls

4 calls:

164.0ms	(cbrt.f64 c)
164.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 (.f64 4 a) (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (cbrt.f64 c))))
156.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 (.f64 4 a) (*.f64 (cbrt.f64 c) (cbrt.f64 c))) (cbrt.f64 c)))) b)
148.0ms	(cbrt.f64 c)

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4800	947
1	4800	947

prune107.0ms (1.7%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	65	1	66
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	65	11	76

Merged error: 8.6b

Counts

76 → 11

Compiler

Compiled 2779 to 1455 computations (47.6% saved)

regimes543.0ms (8.7%)

Compiler: Compiled 5326 to 3702 computations (30.5% saved)

bsearch8.0ms (0.1%)

Compiler: Compiled 38 to 26 computations (31.6% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	193	486
1	193	486

end0.0ms (0%)

sample2.0s (32.6%)

Algorithm

1×

intervals

Results

696.0ms	8000×	body	128	valid
56.0ms	679×	body	128	nan
33.0ms	397×	body	128	invalid

Compiler

Compiled 1673 to 1132 computations (32.3% saved)

Details

analyze508.0ms (8.1%)

sample35.0ms (0.6%)

simplify248.0ms (4%)

prune5.0ms (0.1%)

localize21.0ms (0.3%)

rewrite27.0ms (0.4%)

series472.0ms (7.6%)

simplify71.0ms (1.1%)

prune149.0ms (2.4%)

localize29.0ms (0.5%)

rewrite31.0ms (0.5%)

series340.0ms (5.4%)

simplify63.0ms (1%)

prune191.0ms (3.1%)

localize24.0ms (0.4%)

rewrite29.0ms (0.5%)

series326.0ms (5.2%)

simplify83.0ms (1.3%)

prune132.0ms (2.1%)

localize29.0ms (0.5%)

rewrite20.0ms (0.3%)

series633.0ms (10.1%)

simplify79.0ms (1.3%)

prune107.0ms (1.7%)

regimes543.0ms (8.7%)

bsearch8.0ms (0.1%)

simplify7.0ms (0.1%)

end0.0ms (0%)

sample2.0s (32.6%)

Profiling