Details

analyze494.0ms (7.5%)

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 (0.5%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
2.0ms	22×	body	128	nan
1.0ms	8×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify468.0ms (7.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (372.0ms)

Iter	Nodes	Cost
0	4219	54
1	4219	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: 22.3b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
1.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite29.0ms (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:

8.0ms	(-.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)))
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)))

series242.0ms (3.7%)

Counts

4 → 12

Calls

4 calls:

63.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
63.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
58.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify94.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4936	1457
1	4936	1457

prune141.0ms (2.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	65	6	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	6	72

Merged error: 8.2b

Counts

72 → 6

Compiler

Compiled 3244 to 1947 computations (40% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.5b	(/.f64 (.f64 c 2) (-.f64 (-.f64 (.f64 2 (/.f64 (*.f64 a c) b)) b) b))
6.2b	(/.f64 (*.f64 a c) b)
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64_78`
14×	`add-cbrt-cube_binary64_114` `add-sqr-sqrt_binary64_100` `add-exp-log_binary64_116`
9×	`add-cube-cbrt_binary64_113`
8×	`times-frac_binary64_84` `associate-/r*_binary64_22`
6×	`add-log-exp_binary64_117`
5×	`pow1_binary64_139`
4×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
3×	`sqrt-prod_binary64_94`
2×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127` `distribute-lft-out--_binary64_30` `flip3--_binary64_82` `frac-2neg_binary64_89` `div-inv_binary64_75` `flip--_binary64_53` `associate-/l*_binary64_23` `sqrt-div_binary64_95` `difference-of-squares_binary64_47` `associate-/r/_binary64_24` `clear-num_binary64_77`
1×	`+-commutative_binary64_8` `sqrt-pow1_binary64_96` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `distribute-lft-out_binary64_29` `pow1/2_binary64_158` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 75

Calls

4 calls:

15.0ms	(/.f64 (.f64 c 2) (-.f64 (-.f64 (.f64 2 (/.f64 (*.f64 a c) b)) b) b))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(/.f64 (*.f64 a c) b)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series204.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(/.f64 (.f64 c 2) (-.f64 (-.f64 (.f64 2 (/.f64 (*.f64 a c) b)) b) b))
64.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
17.0ms	(/.f64 (*.f64 a c) b)

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4938	1545
1	4938	1545

prune145.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	84	3	87
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	86	7	93

Merged error: 7.7b

Counts

93 → 7

Compiler

Compiled 3760 to 2093 computations (44.3% saved)

localize28.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
2.7b	(.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))
4.5b	(/.f64 (.f64 c 2) (-.f64 (-.f64 (.f64 2 (.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))) b) b))
25.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite56.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64_100`
33×	`times-frac_binary64_84`
30×	`add-exp-log_binary64_116`
28×	`*-un-lft-identity_binary64_78`
23×	`add-cbrt-cube_binary64_114`
22×	`add-cube-cbrt_binary64_113` `associate-r_binary64_18`
11×	`cbrt-prod_binary64_109`
9×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129`
7×	`associate-l_binary64_19` `pow1_binary64_139`
6×	`add-log-exp_binary64_117` `unswap-sqr_binary64_46`
5×	`associate-/r*_binary64_22`
3×	`sqrt-prod_binary64_94` `div-inv_binary64_75`
2×	`distribute-lft-out--_binary64_30` `flip3--_binary64_82` `flip--_binary64_53` `sqrt-div_binary64_95` `difference-of-squares_binary64_47` `associate-/r/_binary64_24`
1×	`+-commutative_binary64_8` `-commutative_binary64_9` `sqrt-pow1_binary64_96` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `frac-2neg_binary64_89` `frac-times_binary64_88` `associate-/l_binary64_23` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `associate-r/_binary64_20` `clear-num_binary64_77` `distribute-lft-out_binary64_29` `pow1/2_binary64_158` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 113

Calls

4 calls:

21.0ms	(.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))
19.0ms	(/.f64 (.f64 c 2) (-.f64 (-.f64 (.f64 2 (.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))) b) b))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series320.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

145.0ms	(/.f64 (.f64 c 2) (-.f64 (-.f64 (.f64 2 (.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))) b) b))
62.0ms	(.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))
57.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
56.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify78.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4935	2438
1	4935	2438

prune237.0ms (3.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	121	4	125
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	123	9	132

Merged error: 7.2b

Counts

132 → 9

Compiler

Compiled 6088 to 3005 computations (50.6% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

2.7b	(.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))
3.6b	(/.f64 (+.f64 b (-.f64 b (.f64 2 (.f64 (/.f64 c b) a)))) a)
4.5b	(/.f64 (.f64 c 2) (-.f64 (-.f64 (.f64 2 (.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))) b) b))
5.6b	(*.f64 (/.f64 c b) a)

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite63.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-sqr-sqrt_binary64_100`
55×	`times-frac_binary64_84`
50×	`*-un-lft-identity_binary64_78`
38×	`add-cube-cbrt_binary64_113`
37×	`add-exp-log_binary64_116`
30×	`add-cbrt-cube_binary64_114`
25×	`associate-r_binary64_18`
20×	`associate-l_binary64_19`
11×	`cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `cbrt-prod_binary64_109`
8×	`associate-/r*_binary64_22` `unswap-sqr_binary64_46` `pow1_binary64_139`
5×	`div-inv_binary64_75` `associate-/l*_binary64_23`
4×	`add-log-exp_binary64_117` `distribute-lft-out_binary64_29`
2×	`-commutative_binary64_9` `distribute-lft-out--_binary64_30` `frac-2neg_binary64_89` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `difference-of-squares_binary64_47` `associate-/r/_binary64_24` `clear-num_binary64_77` `associate-/l/_binary64_25`
1×	`associate-+r-_binary64_12` `flip-+_binary64_52` `flip3--_binary64_82` `frac-times_binary64_88` `flip--_binary64_53` `associate-*r/_binary64_20` `div-sub_binary64_83` `flip3-+_binary64_81`

Counts

4 → 152

Calls

4 calls:

21.0ms	(.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))
19.0ms	(/.f64 (.f64 c 2) (-.f64 (-.f64 (.f64 2 (.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))) b) b))
8.0ms	(/.f64 (+.f64 b (-.f64 b (.f64 2 (.f64 (/.f64 c b) a)))) a)
7.0ms	(*.f64 (/.f64 c b) a)

series271.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

153.0ms	(/.f64 (.f64 c 2) (-.f64 (-.f64 (.f64 2 (.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))) b) b))
57.0ms	(.f64 (/.f64 a (.f64 (cbrt.f64 b) (cbrt.f64 b))) (/.f64 c (cbrt.f64 b)))
41.0ms	(/.f64 (+.f64 b (-.f64 b (.f64 2 (.f64 (/.f64 c b) a)))) a)
20.0ms	(*.f64 (/.f64 c b) a)

simplify83.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5007	2930

prune288.0ms (4.4%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	158	6	164
Fresh	1	7	8
Picked	1	0	1
Done	0	0	0
Total	160	13	173

Merged error: 7.1b

Counts

173 → 13

Compiler

Compiled 7370 to 3160 computations (57.1% saved)

regimes683.0ms (10.4%)

Compiler: Compiled 7538 to 4826 computations (36% saved)

bsearch189.0ms (2.9%)

Steps

Iters	Range		Point
9	2.0183891553962905e+62	6.256013624159553e+67	1.234913879083865e+67
10	-1.1129944088791664e-212	-4.2238277152251945e-229	-9.704665002374583e-213
6	-1.665541721458128e-166	-3.958105704941519e-167	-4.0127078141426725e-167
8	-1.047924617248767e+92	-3.176521970987605e+87	-1.0288136512639993e+92

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	174	406
1	174	406

end0.0ms (0%)

sample2.2s (34%)

Algorithm

1×

intervals

Results

680.0ms	8000×	body	128	valid
52.0ms	667×	body	128	nan
31.0ms	389×	body	128	invalid

Compiler

Compiled 2168 to 1354 computations (37.5% saved)

Details

analyze494.0ms (7.5%)

sample35.0ms (0.5%)

simplify468.0ms (7.1%)

prune5.0ms (0.1%)

localize21.0ms (0.3%)

rewrite29.0ms (0.4%)

series242.0ms (3.7%)

simplify94.0ms (1.4%)

prune141.0ms (2.2%)

localize24.0ms (0.4%)

rewrite33.0ms (0.5%)

series204.0ms (3.1%)

simplify58.0ms (0.9%)

prune145.0ms (2.2%)

localize28.0ms (0.4%)

rewrite56.0ms (0.9%)

series320.0ms (4.9%)

simplify78.0ms (1.2%)

prune237.0ms (3.6%)

localize27.0ms (0.4%)

rewrite63.0ms (1%)

series271.0ms (4.1%)

simplify83.0ms (1.3%)

prune288.0ms (4.4%)

regimes683.0ms (10.4%)

bsearch189.0ms (2.9%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample2.2s (34%)

Profiling