Details

analyze265.0ms (3.8%)

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 (0.6%)

Algorithm

1×

intervals

Results

10.0ms	106×	body	256	valid
10.0ms	150×	body	128	valid
9.0ms	294×	pre	128	true
2.0ms	38×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify234.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

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: 44.0b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
0.1b	(-.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))
40.3b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite40.0ms (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:

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))

series544.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

215.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
144.0ms	(-.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)))
66.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify73.0ms (1%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5031	1979

prune105.0ms (1.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	82	5	87

Merged error: 0.2b

Counts

87 → 5

Compiler

Compiled 2082 to 1240 computations (40.4% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite54.0ms (0.8%)

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:

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

series929.0ms (13.2%)

Counts

4 → 12

Calls

4 calls:

409.0ms	(/.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))
131.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
75.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify75.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4960	3037
1	4960	3037

prune154.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	108	8	116

Merged error: 0b

Counts

116 → 8

Compiler

Compiled 3202 to 1972 computations (38.4% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite48.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64_78`
24×	`times-frac_binary64_84`
21×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113`
18×	`add-cbrt-cube_binary64_114` `associate-r_binary64_18` `add-exp-log_binary64_116`
9×	`pow1_binary64_139`
8×	`add-log-exp_binary64_117` `distribute-lft-out_binary64_29`
6×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
4×	`associate-/r*_binary64_22` `associate-/r/_binary64_24`
3×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip-+_binary64_52` `associate-/l*_binary64_23` `pow-prod-down_binary64_149` `flip3-+_binary64_81`
2×	`div-inv_binary64_75`
1×	`+-commutative_binary64_8` `-commutative_binary64_9` `associate-l_binary64_19` `flip3--_binary64_82` `diff-log_binary64_170` `frac-2neg_binary64_89` `flip--_binary64_53` `associate-r/_binary64_20` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

4 → 95

Calls

4 calls:

16.0ms	(.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)))

series768.0ms (10.9%)

Counts

4 → 12

Calls

4 calls:

363.0ms	(.f64 (.f64 c -4) (/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
221.0ms	(/.f64 1/2 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
122.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
62.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify67.0ms (1%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4921	2612
1	4921	2612

prune137.0ms (1.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	106	1	107
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	107	8	115

Merged error: 0b

Counts

115 → 8

Compiler

Compiled 2902 to 1849 computations (36.3% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite50.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

45×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
21×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
9×	`cbrt-undiv_binary64_112` `div-exp_binary64_129` `*-un-lft-identity_binary64_78` `pow1_binary64_139`
8×	`add-log-exp_binary64_117`
5×	`add-sqr-sqrt_binary64_100` `add-cube-cbrt_binary64_113`
4×	`associate-l_binary64_19` `associate-*l/_binary64_21`
3×	`flip-+_binary64_52` `pow-prod-down_binary64_149` `flip3-+_binary64_81`
2×	`associate-/r/_binary64_24` `distribute-lft-out_binary64_29`
1×	`+-commutative_binary64_8` `-commutative_binary64_9` `flip3--_binary64_82` `diff-log_binary64_170` `frac-2neg_binary64_89` `times-frac_binary64_84` `div-inv_binary64_75` `associate-r_binary64_18` `flip--_binary64_53` `associate-/l_binary64_23` `associate-/r*_binary64_22` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

4 → 78

Calls

4 calls:

16.0ms	(/.f64 (.f64 a (.f64 c -4)) (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (*.f64 a 2)))
12.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (*.f64 a 2))
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)))

series702.0ms (10%)

Counts

4 → 12

Calls

4 calls:

304.0ms	(/.f64 (.f64 a (.f64 c -4)) (.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (*.f64 a 2)))
215.0ms	(.f64 (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))) (*.f64 a 2))
117.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
66.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify72.0ms (1%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5142	2276

prune101.0ms (1.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	90	8	98

Merged error: 0b

Counts

98 → 8

Compiler

Compiled 2390 to 1415 computations (40.8% saved)

regimes405.0ms (5.8%)

Compiler: Compiled 5020 to 3802 computations (24.3% 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 (29.8%)

Algorithm

1×

intervals

Results

284.0ms	2868×	body	256	valid
262.0ms	8948×	pre	128	true
260.0ms	5132×	body	128	valid
46.0ms	948×	body	128	nan

Compiler

Compiled 1291 to 979 computations (24.2% saved)

Details

analyze265.0ms (3.8%)

sample41.0ms (0.6%)

simplify234.0ms (3.3%)

prune4.0ms (0.1%)

localize14.0ms (0.2%)

rewrite40.0ms (0.6%)

series544.0ms (7.7%)

simplify73.0ms (1%)

prune105.0ms (1.5%)

localize18.0ms (0.3%)

rewrite54.0ms (0.8%)

series929.0ms (13.2%)

simplify75.0ms (1.1%)

prune154.0ms (2.2%)

localize14.0ms (0.2%)

rewrite48.0ms (0.7%)

series768.0ms (10.9%)

simplify67.0ms (1%)

prune137.0ms (1.9%)

localize18.0ms (0.3%)

rewrite50.0ms (0.7%)

series702.0ms (10%)

simplify72.0ms (1%)

prune101.0ms (1.4%)

regimes405.0ms (5.8%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample2.1s (29.8%)

Profiling