Details

analyze260.0ms (4.9%)

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)

sample42.0ms (0.8%)

Algorithm

1×

intervals

Results

10.0ms	106×	body	256	valid
8.0ms	277×	pre	128	true
7.0ms	51×	body	512	valid
5.0ms	99×	body	128	valid
1.0ms	21×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify217.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune4.0ms (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: 52.6b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
27.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite37.0ms (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:

12.0ms	(/.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)
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series540.0ms (10.1%)

Counts

4 → 12

Calls

4 calls:

221.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
135.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
118.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
65.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify97.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4884	1963
1	4884	1963

prune99.0ms (1.9%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	77	5	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	5	83

Merged error: 0.1b

Counts

83 → 5

Compiler

Compiled 1980 to 1182 computations (40.3% saved)

localize14.0ms (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))))
0.1b	(-.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 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))

rewrite53.0ms (1%)

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:

15.0ms	(/.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))

series875.0ms (16.4%)

Counts

4 → 12

Calls

4 calls:

370.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
313.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
125.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify73.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4923	3030
1	4923	3030

prune153.0ms (2.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	104	6	110
Fresh	4	0	4
Picked	1	0	1
Done	0	0	0
Total	109	6	115

Merged error: 0b

Counts

115 → 6

Compiler

Compiled 3196 to 1966 computations (38.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(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)))))
0.1b	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

rewrite31.0ms (0.6%)

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:

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

series678.0ms (12.7%)

Counts

4 → 12

Calls

4 calls:

347.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
136.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
126.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
68.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify83.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4914	1962
1	4914	1962

prune108.0ms (2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	85	4	89

Merged error: 0b

Counts

89 → 4

Compiler

Compiled 2257 to 1399 computations (38% saved)

localize21.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))))
0.1b	(+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.2b	(.f64 c (.f64 (*.f64 c a) 16))
0.3b	(.f64 a (.f64 c (.f64 (.f64 c a) 16)))

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`pow1_binary64_135`
27×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110`
16×	`pow-prod-down_binary64_145` `cbrt-unprod_binary64_107` `prod-exp_binary64_123`
8×	`add-sqr-sqrt_binary64_98`
7×	`add-cube-cbrt_binary64_109` `*-un-lft-identity_binary64_77`
6×	`associate-l_binary64_20` `add-log-exp_binary64_113`
3×	`sqrt-prod_binary64_92`
2×	`sqrt-div_binary64_93` `-commutative_binary64_10` `associate-r*_binary64_19`
1×	`rem-sqrt-square_binary64_90` `sqrt-pow1_binary64_94` `flip-+_binary64_51` `flip3-+_binary64_80` `flip--_binary64_52` `+-commutative_binary64_9` `pow1/2_binary64_154` `flip3--_binary64_81` `sum-log_binary64_165`

Counts

4 → 71

Calls

4 calls:

11.0ms	(.f64 a (.f64 c (.f64 (.f64 c a) 16)))
7.0ms	(.f64 c (.f64 (*.f64 c a) 16))
5.0ms	(sqrt.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))))
5.0ms	(+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series262.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

114.0ms	(sqrt.f64 (-.f64 (pow.f64 b 4) (.f64 a (.f64 c (.f64 (.f64 c a) 16)))))
60.0ms	(+.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
55.0ms	(.f64 a (.f64 c (.f64 (.f64 c a) 16)))
34.0ms	(.f64 c (.f64 (*.f64 c a) 16))

simplify48.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5342	1285

prune130.0ms (2.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	83	0	83
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	83	4	87

Merged error: 0b

Counts

87 → 4

Compiler

Compiled 3062 to 1914 computations (37.5% saved)

regimes44.0ms (0.8%)

Compiler: Compiled 426 to 318 computations (25.4% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	97	47
1	97	47

end0.0ms (0%)

sample1.4s (26.3%)

Algorithm

1×

intervals

Results

366.0ms	3741×	body	256	valid
270.0ms	8812×	pre	128	true
209.0ms	1449×	body	512	valid
140.0ms	2810×	body	128	valid
41.0ms	812×	body	128	nan

Compiler

Compiled 201 to 150 computations (25.4% saved)

Details

analyze260.0ms (4.9%)

sample42.0ms (0.8%)

simplify217.0ms (4.1%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite37.0ms (0.7%)

series540.0ms (10.1%)

simplify97.0ms (1.8%)

prune99.0ms (1.9%)

localize14.0ms (0.3%)

rewrite53.0ms (1%)

series875.0ms (16.4%)

simplify73.0ms (1.4%)

prune153.0ms (2.9%)

localize12.0ms (0.2%)

rewrite31.0ms (0.6%)

series678.0ms (12.7%)

simplify83.0ms (1.5%)

prune108.0ms (2%)

localize21.0ms (0.4%)

rewrite38.0ms (0.7%)

series262.0ms (4.9%)

simplify48.0ms (0.9%)

prune130.0ms (2.4%)

regimes44.0ms (0.8%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (26.3%)

Profiling