Details

analyze278.0ms (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)

sample42.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	84×	body	256	valid
10.0ms	300×	pre	128	true
9.0ms	172×	body	128	valid
2.0ms	44×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify226.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (61.0ms)

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: 42.8b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize11.0ms (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))
38.6b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite38.0ms (0.6%)

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:

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

series553.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
138.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
67.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify100.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4884	1963
1	4884	1963

prune101.0ms (1.7%)

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: 0.2b

Counts

83 → 5

Compiler

Compiled 2005 to 1194 computations (40.4% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite52.0ms (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:

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))
13.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (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))))
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series931.0ms (15.6%)

Counts

4 → 12

Calls

4 calls:

402.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
318.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
140.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
71.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify74.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4923	3030
1	4923	3030

prune159.0ms (2.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	102	8	110
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	105	10	115

Merged error: 0.0b

Counts

115 → 10

Compiler

Compiled 3264 to 2016 computations (38.2% saved)

localize12.0ms (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))))))
0.2b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
0.2b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))

rewrite32.0ms (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:

9.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
7.0ms	(+.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)))

series664.0ms (11.1%)

Counts

4 → 12

Calls

4 calls:

337.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
135.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
128.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
64.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify85.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4914	1962
1	4914	1962

prune109.0ms (1.8%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	80	3	83
Fresh	4	4	8
Picked	0	1	1
Done	0	1	1
Total	84	9	93

Merged error: 0b

Counts

93 → 9

Compiler

Compiled 2355 to 1469 computations (37.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1/2 (+.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 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
0.3b	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))

rewrite47.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64_77`
24×	`times-frac_binary64_83`
21×	`add-cube-cbrt_binary64_109` `add-sqr-sqrt_binary64_98`
18×	`add-exp-log_binary64_112` `add-cbrt-cube_binary64_110` `associate-r_binary64_19`
9×	`pow1_binary64_135`
8×	`add-log-exp_binary64_113` `distribute-lft-out_binary64_30`
6×	`cbrt-unprod_binary64_107` `prod-exp_binary64_123`
4×	`associate-/r*_binary64_23` `associate-/r/_binary64_25`
3×	`pow-prod-down_binary64_145` `flip-+_binary64_51` `cbrt-undiv_binary64_108` `flip3-+_binary64_80` `associate-/l*_binary64_24` `div-exp_binary64_125`
2×	`div-inv_binary64_74`
1×	`associate-l_binary64_20` `sub-neg_binary64_70` `flip--_binary64_52` `+-commutative_binary64_9` `associate-r/_binary64_21` `-commutative_binary64_10` `clear-num_binary64_76` `flip3--_binary64_81` `diff-log_binary64_166` `frac-2neg_binary64_88` `sum-log_binary64_165`

Counts

4 → 94

Calls

4 calls:

17.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
9.0ms	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series782.0ms (13.1%)

Counts

4 → 12

Calls

4 calls:

382.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
207.0ms	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
128.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
65.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify82.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4940	2605
1	4940	2605

prune126.0ms (2.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	106	0	106
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	106	9	115

Merged error: 0b

Counts

115 → 9

Compiler

Compiled 2726 to 1721 computations (36.9% saved)

regimes76.0ms (1.3%)

Compiler: Compiled 840 to 624 computations (25.7% 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%)

sample1.4s (22.8%)

Algorithm

1×

intervals

Results

295.0ms	8920×	pre	128	true
284.0ms	2872×	body	256	valid
263.0ms	5128×	body	128	valid
44.0ms	920×	body	128	nan

Compiler

Compiled 324 to 242 computations (25.3% saved)

Details

analyze278.0ms (4.6%)

sample42.0ms (0.7%)

simplify226.0ms (3.8%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite38.0ms (0.6%)

series553.0ms (9.2%)

simplify100.0ms (1.7%)

prune101.0ms (1.7%)

localize16.0ms (0.3%)

rewrite52.0ms (0.9%)

series931.0ms (15.6%)

simplify74.0ms (1.2%)

prune159.0ms (2.7%)

localize12.0ms (0.2%)

rewrite32.0ms (0.5%)

series664.0ms (11.1%)

simplify85.0ms (1.4%)

prune109.0ms (1.8%)

localize12.0ms (0.2%)

rewrite47.0ms (0.8%)

series782.0ms (13.1%)

simplify82.0ms (1.4%)

prune126.0ms (2.1%)

regimes76.0ms (1.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.4s (22.8%)

Profiling