Details

analyze255.0ms (4.4%)

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)

sample41.0ms (0.7%)

Algorithm

1×

intervals

Results

11.0ms	120×	body	256	valid
9.0ms	284×	pre	128	true
5.0ms	38×	body	512	valid
5.0ms	98×	body	128	valid
1.0ms	28×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify395.0ms (6.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (301.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune3.0ms (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: 50.5b

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 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
24.1b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite34.0ms (0.6%)

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:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
4.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series263.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

99.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
71.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
32.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify87.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune99.0ms (1.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	83	4	87

Merged error: 0.1b

Counts

87 → 4

Compiler

Compiled 2063 to 1224 computations (40.7% saved)

localize14.0ms (0.2%)

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))
0.3b	(/.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)))))

rewrite51.0ms (0.9%)

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:

14.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
11.0ms	(/.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))

series444.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

193.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
158.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
60.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
33.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify60.0ms (1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune150.0ms (2.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	106	5	111
Fresh	3	0	3
Picked	1	0	1
Done	0	0	0
Total	110	5	115

Merged error: 0b

Counts

115 → 5

Compiler

Compiled 3154 to 1937 computations (38.6% 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 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)))))
0.1b	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

rewrite29.0ms (0.5%)

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:

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

series325.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

175.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
59.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
59.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
32.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify76.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4905	1972
1	4905	1972

prune101.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	84	5	89

Merged error: 0b

Counts

89 → 5

Compiler

Compiled 2251 to 1394 computations (38.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite67.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

145×	`times-frac_binary64_84`
77×	`*-un-lft-identity_binary64_78`
53×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113`
50×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
36×	`associate-/l*_binary64_23`
25×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
15×	`div-inv_binary64_75`
12×	`distribute-lft-out_binary64_29`
10×	`associate-/r*_binary64_22`
8×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
6×	`add-log-exp_binary64_117`
4×	`pow1_binary64_139`
3×	`frac-2neg_binary64_89` `associate-/r/_binary64_24` `clear-num_binary64_77` `associate-/l/_binary64_25`
1×	`flip-+_binary64_52` `flip3--_binary64_82` `diff-log_binary64_170` `flip--_binary64_53` `cancel-sign-sub-inv_binary64_44` `sub-neg_binary64_71` `flip3-+_binary64_81`

Counts

4 → 175

Calls

4 calls:

17.0ms	(/.f64 (/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (.f64 c -4))) (*.f64 a 2))
11.0ms	(/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (.f64 c -4)))
10.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (.f64 c -4))
7.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series511.0ms (8.8%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (.f64 c -4)))
174.0ms	(/.f64 (/.f64 a (/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (.f64 c -4))) (*.f64 a 2))
80.0ms	(/.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (.f64 c -4))
34.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify105.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

187 → 187

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4965	6374
1	4965	6374

prune253.0ms (4.4%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	187	0	187
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	187	5	192

Merged error: 0b

Counts

192 → 5

Compiler

Compiled 5836 to 3430 computations (41.2% saved)

regimes308.0ms (5.3%)

Compiler: Compiled 4224 to 3190 computations (24.5% 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%)

sample2.1s (35.8%)

Algorithm

1×

intervals

Results

362.0ms	3884×	body	256	valid
261.0ms	8800×	pre	128	true
200.0ms	1446×	body	512	valid
134.0ms	2670×	body	128	valid
40.0ms	800×	body	128	nan

Compiler

Compiled 1092 to 826 computations (24.4% saved)

Details

analyze255.0ms (4.4%)

sample41.0ms (0.7%)

simplify395.0ms (6.8%)

prune3.0ms (0.1%)

localize10.0ms (0.2%)

rewrite34.0ms (0.6%)

series263.0ms (4.5%)

simplify87.0ms (1.5%)

prune99.0ms (1.7%)

localize14.0ms (0.2%)

rewrite51.0ms (0.9%)

series444.0ms (7.7%)

simplify60.0ms (1%)

prune150.0ms (2.6%)

localize12.0ms (0.2%)

rewrite29.0ms (0.5%)

series325.0ms (5.6%)

simplify76.0ms (1.3%)

prune101.0ms (1.7%)

localize14.0ms (0.2%)

rewrite67.0ms (1.2%)

series511.0ms (8.8%)

simplify105.0ms (1.8%)

prune253.0ms (4.4%)

regimes308.0ms (5.3%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.1s (35.8%)

Profiling