Details

analyze255.0ms (3.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 30 to 24 computations (20% saved)

sample32.0ms (0.4%)

Algorithm

1×

intervals

Results

12.0ms	247×	body	128	valid
9.0ms	279×	pre	128	true
1.0ms	23×	body	128	nan
1.0ms	9×	body	256	valid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify236.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune4.0ms (0%)

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: 30.3b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
30.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite38.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series540.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

216.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
134.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
76.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify70.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5031	1979

prune103.0ms (1.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	5	87

Merged error: 0.4b

Counts

87 → 5

Compiler

Compiled 2083 to 1240 computations (40.5% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.3b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
0.3b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))

rewrite54.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
22×	`times-frac_binary64_84`
20×	`*-un-lft-identity_binary64_78`
17×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
13×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
11×	`associate-/l*_binary64_23`
10×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113`
8×	`add-log-exp_binary64_117`
6×	`associate-/r/_binary64_24`
5×	`associate-/r*_binary64_22` `distribute-lft-out_binary64_29`
4×	`flip-+_binary64_52` `div-inv_binary64_75` `pow1_binary64_139` `flip3-+_binary64_81`
2×	`frac-2neg_binary64_89` `clear-num_binary64_77`
1×	`+-commutative_binary64_8` `flip3--_binary64_82` `diff-log_binary64_170` `flip--_binary64_53` `cancel-sign-sub-inv_binary64_44` `associate-/l/_binary64_25` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

4 → 99

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
12.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
5.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series1.0s (12.5%)

Counts

4 → 12

Calls

4 calls:

485.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
325.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
134.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
63.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify76.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4960	3037
1	4960	3037

prune160.0ms (2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	101	10	111
Fresh	4	0	4
Picked	0	1	1
Done	0	0	0
Total	105	11	116

Merged error: 0.0b

Counts

116 → 11

Compiler

Compiled 3343 to 2071 computations (38% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.3b	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
0.3b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.3b	(/.f64 (/.f64 a 1) (/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))))

rewrite79.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

242×	`times-frac_binary64_84`
114×	`*-un-lft-identity_binary64_78`
106×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113`
61×	`add-exp-log_binary64_116`
47×	`add-cbrt-cube_binary64_114`
37×	`div-exp_binary64_129`
26×	`div-inv_binary64_75`
25×	`cbrt-undiv_binary64_112`
19×	`associate-/l*_binary64_23`
18×	`associate-/r/_binary64_24`
15×	`associate-*r/_binary64_20`
13×	`associate-/r*_binary64_22`
8×	`prod-exp_binary64_127`
6×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111`
4×	`1-exp_binary64_122` `distribute-lft-out_binary64_29` `pow1_binary64_139`
3×	`frac-2neg_binary64_89` `clear-num_binary64_77`
1×	`flip-+_binary64_52` `flip3--_binary64_82` `diff-log_binary64_170` `flip--_binary64_53` `cancel-sign-sub-inv_binary64_44` `associate-/l/_binary64_25` `sub-neg_binary64_71` `flip3-+_binary64_81`

Counts

4 → 226

Calls

4 calls:

19.0ms	(/.f64 (/.f64 a 1) (/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))))
14.0ms	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
8.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series1.1s (13.8%)

Counts

4 → 12

Calls

4 calls:

371.0ms	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
352.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
315.0ms	(/.f64 (/.f64 a 1) (/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))))
71.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify132.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

238 → 238

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4905	8594
1	4905	8594

prune337.0ms (4.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	236	2	238
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	239	10	249

Merged error: 0b

Counts

249 → 10

Compiler

Compiled 7168 to 4150 computations (42.1% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.4b	(.f64 (/.f64 (.f64 -2 c) a) (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))

rewrite53.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

39×	`*-un-lft-identity_binary64_78`
28×	`add-sqr-sqrt_binary64_100` `times-frac_binary64_84`
27×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
23×	`add-cube-cbrt_binary64_113`
18×	`associate-r_binary64_18`
8×	`add-log-exp_binary64_117` `cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `distribute-lft-out_binary64_29`
7×	`associate-l_binary64_19`
6×	`pow1_binary64_139`
4×	`associate-/r*_binary64_22` `associate-/r/_binary64_24`
3×	`flip-+_binary64_52` `div-inv_binary64_75` `associate-/l*_binary64_23` `flip3-+_binary64_81`
2×	`unswap-sqr_binary64_46`
1×	`+-commutative_binary64_8` `-commutative_binary64_9` `flip3--_binary64_82` `diff-log_binary64_170` `frac-2neg_binary64_89` `frac-times_binary64_88` `flip--_binary64_53` `associate-l/_binary64_21` `pow-prod-down_binary64_149` `associate-*r/_binary64_20` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

4 → 108

Calls

4 calls:

21.0ms	(.f64 (/.f64 (.f64 -2 c) a) (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
9.0ms	(/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series903.0ms (11.2%)

Counts

4 → 12

Calls

4 calls:

385.0ms	(.f64 (/.f64 (.f64 -2 c) a) (/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
331.0ms	(/.f64 a (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
123.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
64.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify70.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4972	3093
1	4972	3093

prune137.0ms (1.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	118	2	120
Fresh	2	5	7
Picked	0	1	1
Done	0	2	2
Total	120	10	130

Merged error: 0b

Counts

130 → 10

Compiler

Compiled 3247 to 1848 computations (43.1% saved)

regimes559.0ms (7%)

Compiler: Compiled 5268 to 3974 computations (24.6% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample2.0s (25.3%)

Algorithm

1×

intervals

Results

384.0ms	7706×	body	128	valid
274.0ms	8853×	pre	128	true
39.0ms	853×	body	128	nan
30.0ms	294×	body	256	valid

Compiler

Compiled 1353 to 1022 computations (24.5% saved)

Details

analyze255.0ms (3.2%)

sample32.0ms (0.4%)

simplify236.0ms (2.9%)

prune4.0ms (0%)

localize11.0ms (0.1%)

rewrite38.0ms (0.5%)

series540.0ms (6.7%)

simplify70.0ms (0.9%)

prune103.0ms (1.3%)

localize14.0ms (0.2%)

rewrite54.0ms (0.7%)

series1.0s (12.5%)

simplify76.0ms (0.9%)

prune160.0ms (2%)

localize14.0ms (0.2%)

rewrite79.0ms (1%)

series1.1s (13.8%)

simplify132.0ms (1.6%)

prune337.0ms (4.2%)

localize13.0ms (0.2%)

rewrite53.0ms (0.7%)

series903.0ms (11.2%)

simplify70.0ms (0.9%)

prune137.0ms (1.7%)

regimes559.0ms (7%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.0s (25.3%)

Profiling