Details

analyze532.0ms (4.6%)

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)

sample73.0ms (0.6%)

Algorithm

1×

intervals

Results

20.0ms	281×	pre	128	true
17.0ms	176×	body	128	valid
15.0ms	80×	body	256	valid
2.0ms	25×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify431.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune8.0ms (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: 41.6b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize27.0ms (0.2%)

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))
36.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite75.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_98`
13×	`*-un-lft-identity_binary64_77`
9×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
8×	`add-log-exp_binary64_113`
7×	`add-cube-cbrt_binary64_109`
6×	`sqrt-prod_binary64_92` `times-frac_binary64_83` `associate-/l*_binary64_24` `difference-of-squares_binary64_46`
5×	`pow1_binary64_135`
4×	`flip--_binary64_52` `flip3--_binary64_81`
3×	`distribute-lft-out--_binary64_31`
2×	`cbrt-undiv_binary64_108` `sqrt-div_binary64_93` `sub-neg_binary64_70` `div-exp_binary64_125` `diff-log_binary64_166` `associate-/l/_binary64_26`
1×	`associate-/r*_binary64_23` `rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `cbrt-unprod_binary64_107` `div-sub_binary64_82` `prod-exp_binary64_123` `pow1/2_binary64_154` `clear-num_binary64_76` `frac-2neg_binary64_88` `div-inv_binary64_74`

Counts

4 → 70

Calls

4 calls:

26.0ms	(/.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)
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series1.0s (9.1%)

Counts

4 → 12

Calls

4 calls:

424.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
261.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
233.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
127.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify180.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (139.0ms)

Iter	Nodes	Cost
0	4884	1963
1	4884	1963

prune186.0ms (1.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	78	4	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	79	4	83

Merged error: 0.2b

Counts

83 → 4

Compiler

Compiled 1993 to 1186 computations (40.5% saved)

localize33.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite104.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
22×	`times-frac_binary64_83`
20×	`*-un-lft-identity_binary64_77`
17×	`cbrt-undiv_binary64_108` `div-exp_binary64_125`
13×	`cbrt-unprod_binary64_107` `prod-exp_binary64_123`
11×	`associate-/l*_binary64_24`
10×	`add-cube-cbrt_binary64_109` `add-sqr-sqrt_binary64_98`
8×	`add-log-exp_binary64_113`
6×	`associate-/r/_binary64_25`
5×	`associate-/r*_binary64_23` `distribute-lft-out_binary64_30`
4×	`flip-+_binary64_51` `flip3-+_binary64_80` `pow1_binary64_135` `div-inv_binary64_74`
2×	`clear-num_binary64_76` `frac-2neg_binary64_88`
1×	`sub-neg_binary64_70` `flip--_binary64_52` `+-commutative_binary64_9` `flip3--_binary64_81` `diff-log_binary64_166` `associate-/l/_binary64_26` `sum-log_binary64_165`

Counts

4 → 98

Calls

4 calls:

32.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
25.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
13.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series1.7s (14.6%)

Counts

4 → 12

Calls

4 calls:

724.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
571.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
252.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
134.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify134.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4923	3030
1	4923	3030

prune305.0ms (2.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	102	8	110
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	106	8	114

Merged error: 0.0b

Counts

114 → 8

Compiler

Compiled 3264 to 2016 computations (38.2% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite62.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64_77`
15×	`add-sqr-sqrt_binary64_98`
14×	`add-cube-cbrt_binary64_109`
12×	`times-frac_binary64_83`
8×	`add-log-exp_binary64_113`
6×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
5×	`pow1_binary64_135` `distribute-lft-out_binary64_30`
4×	`associate-/r*_binary64_23`
3×	`sqrt-prod_binary64_92` `associate-/l*_binary64_24`
2×	`flip-+_binary64_51` `sqrt-div_binary64_93` `flip3-+_binary64_80` `flip--_binary64_52` `associate-/r/_binary64_25` `flip3--_binary64_81`
1×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `cbrt-undiv_binary64_108` `sub-neg_binary64_70` `+-commutative_binary64_9` `div-exp_binary64_125` `pow1/2_binary64_154` `clear-num_binary64_76` `diff-log_binary64_166` `frac-2neg_binary64_88` `sum-log_binary64_165` `div-inv_binary64_74`

Counts

4 → 71

Calls

4 calls:

17.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
13.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
9.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
9.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series1.2s (10.5%)

Counts

4 → 12

Calls

4 calls:

633.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
231.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
223.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
122.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify153.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (113.0ms)

Iter	Nodes	Cost
0	4914	1962
1	4914	1962

prune207.0ms (1.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	84	7	91

Merged error: 0b

Counts

91 → 7

Compiler

Compiled 2349 to 1463 computations (37.7% saved)

localize30.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.2b	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
0.2b	(/.f64 (/.f64 a 1) (/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))))

rewrite138.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

230×	`times-frac_binary64_83`
99×	`*-un-lft-identity_binary64_77`
97×	`add-cube-cbrt_binary64_109` `add-sqr-sqrt_binary64_98`
59×	`add-exp-log_binary64_112`
45×	`add-cbrt-cube_binary64_110`
36×	`div-exp_binary64_125`
25×	`div-inv_binary64_74`
24×	`cbrt-undiv_binary64_108`
16×	`associate-/l*_binary64_24` `associate-/r/_binary64_25`
15×	`associate-*r/_binary64_21`
9×	`associate-/r*_binary64_23`
8×	`add-log-exp_binary64_113` `prod-exp_binary64_123`
6×	`cbrt-unprod_binary64_107`
4×	`1-exp_binary64_118` `pow1_binary64_135`
2×	`clear-num_binary64_76` `frac-2neg_binary64_88`
1×	`flip-+_binary64_51` `flip3-+_binary64_80` `sub-neg_binary64_70` `flip--_binary64_52` `+-commutative_binary64_9` `flip3--_binary64_81` `diff-log_binary64_166` `associate-/l/_binary64_26` `distribute-lft-out_binary64_30` `sum-log_binary64_165`

Counts

4 → 204

Calls

4 calls:

39.0ms	(/.f64 (/.f64 a 1) (/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))))
23.0ms	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
12.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
8.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series1.6s (13.8%)

Counts

4 → 12

Calls

4 calls:

669.0ms	(/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))))
563.0ms	(/.f64 (/.f64 a 1) (/.f64 a (.f64 -2 (/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4)))))))))
234.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
115.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify215.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

216 → 216

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4900	7891
1	4900	7891

prune511.0ms (4.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	215	1	216
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	216	7	223

Merged error: 0b

Counts

223 → 7

Compiler

Compiled 6215 to 3566 computations (42.6% saved)

regimes126.0ms (1.1%)

Compiler: Compiled 699 to 507 computations (27.5% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	60	24
1	60	24

end0.0ms (0%)

sample2.4s (21%)

Algorithm

1×

intervals

Results

526.0ms	2862×	body	256	valid
501.0ms	8826×	pre	128	true
496.0ms	5137×	body	128	valid
73.0ms	826×	body	128	nan
0.0ms	1×	body	512	valid

Compiler

Compiled 277 to 203 computations (26.7% saved)

Details

analyze532.0ms (4.6%)

sample73.0ms (0.6%)

simplify431.0ms (3.8%)

prune8.0ms (0.1%)

localize27.0ms (0.2%)

rewrite75.0ms (0.7%)

series1.0s (9.1%)

simplify180.0ms (1.6%)

prune186.0ms (1.6%)

localize33.0ms (0.3%)

rewrite104.0ms (0.9%)

series1.7s (14.6%)

simplify134.0ms (1.2%)

prune305.0ms (2.7%)

localize25.0ms (0.2%)

rewrite62.0ms (0.5%)

series1.2s (10.5%)

simplify153.0ms (1.3%)

prune207.0ms (1.8%)

localize30.0ms (0.3%)

rewrite138.0ms (1.2%)

series1.6s (13.8%)

simplify215.0ms (1.9%)

prune511.0ms (4.5%)

regimes126.0ms (1.1%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.4s (21%)

Profiling