Details

analyze529.0ms (4.8%)

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)

sample88.0ms (0.8%)

Algorithm

1×

intervals

Results

24.0ms	121×	body	256	valid
17.0ms	293×	pre	128	true
16.0ms	56×	body	512	valid
8.0ms	79×	body	128	valid
3.0ms	37×	body	128	nan

Compiler

Compiled 47 to 41 computations (12.8% saved)

simplify783.0ms (7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (604.0ms)

Iter	Nodes	Cost
0	1834	24
1	1834	24

prune7.0ms (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: 52.7b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize23.0ms (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))
22.8b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)

rewrite71.0ms (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:

24.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
17.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
9.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series510.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

207.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) b) (.f64 a 2))
125.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) b)
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
64.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify164.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	4899	1979
1	4899	1979

prune188.0ms (1.7%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	82	5	87

Merged error: 0.1b

Counts

87 → 5

Compiler

Compiled 2037 to 1207 computations (40.7% saved)

localize29.0ms (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))
0.3b	(/.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)))))

rewrite96.0ms (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:

27.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
22.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
16.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
8.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

series800.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

356.0ms	(/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))
274.0ms	(/.f64 (/.f64 (.f64 a (.f64 c -4)) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (.f64 a 2))
111.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
59.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify117.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4982	3037
1	4982	3037

prune279.0ms (2.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	105	6	111
Fresh	3	0	3
Picked	1	0	1
Done	1	0	1
Total	110	6	116

Merged error: 0b

Counts

116 → 6

Compiler

Compiled 3186 to 1962 computations (38.4% saved)

localize25.0ms (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)))

rewrite57.0ms (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:

16.0ms	(/.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)))))
9.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))
8.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))

series607.0ms (5.4%)

Counts

4 → 12

Calls

4 calls:

327.0ms	(/.f64 c (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))))
113.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))
103.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4))))
63.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify135.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4905	1972
1	4905	1972

prune189.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	84	6	90

Merged error: 0b

Counts

90 → 6

Compiler

Compiled 2283 to 1419 computations (37.8% saved)

localize29.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite98.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

50×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
17×	`cbrt-unprod_binary64_111` `prod-exp_binary64_127`
16×	`cbrt-undiv_binary64_112` `div-exp_binary64_129`
15×	`*-un-lft-identity_binary64_78`
11×	`add-sqr-sqrt_binary64_100`
10×	`associate-r_binary64_18`
9×	`add-cube-cbrt_binary64_113` `times-frac_binary64_84`
6×	`add-log-exp_binary64_117` `pow1_binary64_139`
5×	`associate-/r*_binary64_22`
4×	`associate-/r/_binary64_24`
3×	`associate-l_binary64_19` `div-inv_binary64_75` `distribute-lft-out_binary64_29`
2×	`flip-+_binary64_52` `frac-2neg_binary64_89` `associate-/l_binary64_23` `associate-r/_binary64_20` `clear-num_binary64_77` `flip3-+_binary64_81`
1×	`*-commutative_binary64_9` `flip3--_binary64_82` `diff-log_binary64_170` `flip--_binary64_53` `pow-prod-down_binary64_149` `unswap-sqr_binary64_46` `cancel-sign-sub-inv_binary64_44` `associate-/l/_binary64_25` `sub-neg_binary64_71`

Counts

4 → 97

Calls

4 calls:

28.0ms	(/.f64 (.f64 a (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))) (.f64 a 2))
23.0ms	(.f64 a (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
18.0ms	(/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))
9.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

series1.1s (9.8%)

Counts

4 → 12

Calls

4 calls:

375.0ms	(.f64 a (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))))))
356.0ms	(/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))
293.0ms	(/.f64 (.f64 a (/.f64 (.f64 c -4) (+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 a 4))))))) (.f64 a 2))
62.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 a 4)))

simplify141.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	5110	2689

prune234.0ms (2.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

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

Merged error: 0b

Counts

115 → 6

Compiler

Compiled 2856 to 1744 computations (38.9% saved)

regimes603.0ms (5.4%)

Compiler: Compiled 4264 to 3218 computations (24.5% saved)

bsearch0.0ms (0%)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	63	24
1	63	24

end0.0ms (0%)

sample4.2s (38.1%)

Algorithm

1×

intervals

Results

756.0ms	3769×	body	256	valid
529.0ms	8803×	pre	128	true
443.0ms	1502×	body	512	valid
276.0ms	2729×	body	128	valid
78.0ms	803×	body	128	nan

Compiler

Compiled 1102 to 833 computations (24.4% saved)

Details

analyze529.0ms (4.8%)

sample88.0ms (0.8%)

simplify783.0ms (7%)

prune7.0ms (0.1%)

localize23.0ms (0.2%)

rewrite71.0ms (0.6%)

series510.0ms (4.6%)

simplify164.0ms (1.5%)

prune188.0ms (1.7%)

localize29.0ms (0.3%)

rewrite96.0ms (0.9%)

series800.0ms (7.2%)

simplify117.0ms (1.1%)

prune279.0ms (2.5%)

localize25.0ms (0.2%)

rewrite57.0ms (0.5%)

series607.0ms (5.4%)

simplify135.0ms (1.2%)

prune189.0ms (1.7%)

localize29.0ms (0.3%)

rewrite98.0ms (0.9%)

series1.1s (9.8%)

simplify141.0ms (1.3%)

prune234.0ms (2.1%)

regimes603.0ms (5.4%)

bsearch0.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample4.2s (38.1%)

Profiling