Details

analyze941.0ms (1.9%)

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)

sample81.0ms (0.2%)

Algorithm

1×

intervals

Results

32.0ms	251×	body	128	valid
19.0ms	278×	pre	128	true
3.0ms	22×	body	128	nan
1.0ms	5×	body	256	valid

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify918.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (701.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune9.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 29.3b

Counts

2 → 2

Compiler

Compiled 49 to 40 computations (18.4% saved)

localize23.0ms (0%)

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))
0.2b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
29.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite79.0ms (0.2%)

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:

24.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
18.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
12.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series535.0ms (1.1%)

Counts

4 → 12

Calls

4 calls:

217.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
126.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
126.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify363.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (287.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune861.0ms (1.7%)

Pruning

42 alts after pruning (41 fresh and 1 done)

	Pruned	Kept	Total
New	46	40	86
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	46	42	88

Merged error: 0.4b

Counts

88 → 42

Compiler

Compiled 3083 to 1973 computations (36% saved)

localize125.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.2b	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
0.3b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
0.4b	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite174.0ms (0.3%)

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:

65.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
55.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
24.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
8.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series1.5s (3.1%)

Counts

4 → 12

Calls

4 calls:

649.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
506.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
315.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
78.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify274.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune2.1s (4.2%)

Pruning

76 alts after pruning (74 fresh and 2 done)

	Pruned	Kept	Total
New	62	49	111
Fresh	15	25	40
Picked	0	1	1
Done	0	1	1
Total	77	76	153

Merged error: 0.0b

Counts

153 → 76

Compiler

Compiled 5339 to 3515 computations (34.2% saved)

localize33.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite72.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_78`
15×	`add-sqr-sqrt_binary64_100`
14×	`add-cube-cbrt_binary64_113`
12×	`times-frac_binary64_84`
8×	`add-log-exp_binary64_117`
6×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
5×	`distribute-lft-out_binary64_29` `pow1_binary64_139`
4×	`associate-/r*_binary64_22`
3×	`sqrt-prod_binary64_94` `associate-/l*_binary64_23`
2×	`flip-+_binary64_52` `flip3--_binary64_82` `flip--_binary64_53` `sqrt-div_binary64_95` `associate-/r/_binary64_24` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `frac-2neg_binary64_89` `div-inv_binary64_75` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `pow1/2_binary64_158` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

4 → 72

Calls

4 calls:

20.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
15.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
13.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
12.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series810.0ms (1.6%)

Counts

4 → 12

Calls

4 calls:

452.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
138.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
133.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
86.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify189.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (142.0ms)

Iter	Nodes	Cost
0	4905	1972
1	4905	1972

prune3.1s (6.1%)

Pruning

109 alts after pruning (106 fresh and 3 done)

	Pruned	Kept	Total
New	43	41	84
Fresh	8	65	73
Picked	0	1	1
Done	0	2	2
Total	51	109	160

Merged error: 0b

Counts

160 → 109

Compiler

Compiled 5498 to 3761 computations (31.6% saved)

localize68.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.2b	(/.f64 c (+.f64 b (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))))
0.3b	(+.f64 b (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
0.4b	(.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))

rewrite179.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_100`
31×	`*-un-lft-identity_binary64_78`
21×	`add-cube-cbrt_binary64_113`
19×	`pow1_binary64_139`
18×	`sqrt-prod_binary64_94`
12×	`times-frac_binary64_84` `sqrt-div_binary64_95`
8×	`add-cbrt-cube_binary64_114` `add-log-exp_binary64_117` `sqrt-pow1_binary64_96` `swap-sqr_binary64_45` `add-exp-log_binary64_116` `pow1/2_binary64_158`
7×	`flip3--_binary64_82` `flip--_binary64_53`
6×	`associate-l_binary64_19` `associate-r_binary64_18`
5×	`pow-prod-up_binary64_148` `distribute-lft-out_binary64_29`
4×	`frac-times_binary64_88` `associate-/r*_binary64_22` `unswap-sqr_binary64_46`
3×	`pow-sqr_binary64_51` `associate-/l*_binary64_23` `pow-prod-down_binary64_149`
2×	`flip-+_binary64_52` `rem-sqrt-square_binary64_91` `associate-l/_binary64_21` `associate-/r/_binary64_24` `associate-r/_binary64_20` `flip3-+_binary64_81`
1×	`+-commutative_binary64_8` `pow2_binary64_159` `*-commutative_binary64_9` `sqr-abs_binary64_93` `cbrt-unprod_binary64_111` `cbrt-undiv_binary64_112` `prod-exp_binary64_127` `div-exp_binary64_129` `diff-log_binary64_170` `frac-2neg_binary64_89` `sqrt-unprod_binary64_98` `div-inv_binary64_75` `rem-square-sqrt_binary64_90` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `pow-plus_binary64_141` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

4 → 115

Calls

4 calls:

53.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
25.0ms	(/.f64 c (+.f64 b (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))))
22.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
15.0ms	(+.f64 b (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))

series956.0ms (1.9%)

Counts

4 → 12

Calls

4 calls:

487.0ms	(/.f64 c (+.f64 b (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))))
251.0ms	(+.f64 b (sqrt.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
151.0ms	(.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
66.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify194.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4959	2848
1	4959	2848

prune3.0s (6%)

Pruning

134 alts after pruning (130 fresh and 4 done)

	Pruned	Kept	Total
New	100	27	127
Fresh	2	103	105
Picked	0	1	1
Done	0	3	3
Total	102	134	236

Merged error: 0b

Counts

236 → 134

Compiler

Compiled 3864 to 2378 computations (38.5% saved)

regimes7.7s (15.3%)

Compiler: Compiled 27145 to 20216 computations (25.5% saved)

bsearch6.5s (12.9%)

simplify14.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	152	28
1	152	28

end0.0ms (0%)

sample19.5s (38.7%)

Algorithm

1×

intervals

Results

1.2s	7706×	body	128	valid
739.0ms	8869×	pre	128	true
105.0ms	869×	body	128	nan
84.0ms	294×	body	256	valid

Compiler

Compiled 6841 to 5094 computations (25.5% saved)

Pareto

Details

analyze941.0ms (1.9%)

sample81.0ms (0.2%)

simplify918.0ms (1.8%)

prune9.0ms (0%)

localize23.0ms (0%)

rewrite79.0ms (0.2%)

series535.0ms (1.1%)

simplify363.0ms (0.7%)

prune861.0ms (1.7%)

localize125.0ms (0.2%)

rewrite174.0ms (0.3%)

series1.5s (3.1%)

simplify274.0ms (0.5%)

prune2.1s (4.2%)

localize33.0ms (0.1%)

rewrite72.0ms (0.1%)

series810.0ms (1.6%)

simplify189.0ms (0.4%)

prune3.1s (6.1%)

localize68.0ms (0.1%)

rewrite179.0ms (0.4%)

series956.0ms (1.9%)

simplify194.0ms (0.4%)

prune3.0s (6%)

regimes7.7s (15.3%)

bsearch6.5s (12.9%)

simplify14.0ms (0%)

end0.0ms (0%)

sample19.5s (38.7%)

Profiling