Details

analyze462.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

sample42.0ms

Algorithm

intervals

Results

11.0ms	41×	body	2560	valid
8.0ms	160×	body	80	valid
7.0ms	32×	body	1280	valid
2.0ms	9×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	9×	body	320	valid
1.0ms	25×	body	80	nan
1.0ms	15×	body	80	invalid
0.0ms	1×	body	160	valid

simplify111.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	928	24
1	928	24

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 34.5b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
2.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `insert-posit16` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 74

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
6.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series3.2s

Counts

4 → 12

Calls

4 calls:

1.3s	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
868.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
422.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
649.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	1297	800
1	1297	800
0	1297	800
1	1297	800
0	5075	5
0	1221	404
1	1221	404
0	1221	404
1	1221	404
0	1	3
1	1	3
0	1845	860
1	1845	860
0	1845	860
1	1845	860
0	5075	5
0	2954	1631
1	2954	1631
0	2954	1631
1	2954	1631
0	1	3
1	1	3

simplify116.0ms

Counts

86 → 86

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5003	1907

prune114.0ms

Filtered

63 candidates to 86 candidates (-36.5%)

Pruning

16 alts after pruning (15 fresh and 1 done)

	Pruned	Kept	Total
New	71	15	86
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	71	16	87

Merged error: 27.5b

Counts

87 → 16

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
2.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64` `add-cube-cbrt_binary64`
10×	`times-frac_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
6×	`associate-l_binary64`
5×	`flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64`
4×	`difference-of-squares_binary64` `insert-posit16`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `div-exp_binary64` `-commutative_binary64`

Counts

4 → 83

Calls

4 calls:

18.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series3.4s

Counts

4 → 12

Calls

4 calls:

1.5s	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
869.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
421.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
643.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	1297	800
1	1297	800
0	1297	800
1	1297	800
0	5075	5
0	1221	404
1	1221	404
0	1221	404
1	1221	404
0	1	3
1	1	3
0	1845	860
1	1845	860
0	1845	860
1	1845	860
0	5075	5
0	4751	1114
1	4751	1114
0	4751	1114
1	4751	1114
0	1	3
1	1	3

simplify122.0ms

Counts

95 → 95

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	5002	2155

prune101.0ms

Filtered

70 candidates to 95 candidates (-35.7%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	91	4	95
Fresh	3	11	14
Picked	0	1	1
Done	0	1	1
Total	94	17	111

Merged error: 27.5b

Counts

111 → 17

localize14.0ms

Local error

Found 4 expressions with local error:

2.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
2.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-log-exp_binary64` `add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 56

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
6.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series2.1s

Counts

4 → 12

Calls

4 calls:

424.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
425.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
647.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
645.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	1297	800
1	1297	800
0	1297	800
1	1297	800
0	5075	5
0	1297	800
1	1297	800
0	1297	800
1	1297	800
0	5075	5
0	1221	404
1	1221	404
0	1221	404
1	1221	404
0	1	3
1	1	3
0	1221	404
1	1221	404
0	1221	404
1	1221	404
0	1	3
1	1	3

simplify119.0ms

Counts

68 → 68

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	5245	1138

prune95.0ms

Filtered

52 candidates to 68 candidates (-30.8%)

Pruning

17 alts after pruning (14 fresh and 3 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	14	14
Picked	0	1	1
Done	0	2	2
Total	68	17	85

Merged error: 27.5b

Counts

85 → 17

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.0b	(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))
2.0b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
23.6b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
16×	`cbrt-prod_binary64`
15×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`
12×	`pow1_binary64`
8×	`add-log-exp_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `pow1/3_binary64` `add-exp-log_binary64` `associate-l_binary64`
4×	`add-cbrt-cube_binary64` `unswap-sqr_binary64` `insert-posit16` `sqrt-prod_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `pow-prod-up_binary64` `difference-of-squares_binary64` `pow-sqr_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-unprod_binary64` `pow-plus_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 84

Calls

4 calls:

10.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
7.0ms	(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))
5.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series1.9s

Counts

4 → 10

Calls

4 calls:

859.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
0.0ms	(*.f64 (cbrt.f64 1/2) (cbrt.f64 1/2))
428.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
644.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	1297	800
1	1297	800
0	1297	800
1	1297	800
0	5075	5
0	1221	404
1	1221	404
0	1221	404
1	1221	404
0	1	3
1	1	3
0	1845	860
1	1845	860
0	1845	860
1	1845	860
0	5075	5

simplify72.0ms

Counts

94 → 94

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5018	1391

prune100.0ms

Filtered

66 candidates to 94 candidates (-42.4%)

Pruning

14 alts after pruning (10 fresh and 4 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	6	7	13
Picked	0	1	1
Done	0	3	3
Total	97	14	111

Merged error: 21.8b

Counts

111 → 14

regimes143.0ms

Accuracy

96.9% (0.4b remaining)

Error of 22.1b against oracle of 21.7b and baseline of 34.8b

bsearch115.0ms

Steps

Iters	Range	Point
9	3.966937236639783e+145	9.564940306668997e+153	9.382688758558198e+153
10	1.355234608594972e-131	8.035481738455187e-122	5.58280276704199e-129
8	-3.1166058458792097e+155	-1.9581447245194372e+151	-1.353329681310028e+154

Iters

Range

Point

3.966937236639783e+145

9.564940306668997e+153

9.382688758558198e+153

1.355234608594972e-131

8.035481738455187e-122

5.58280276704199e-129

-3.1166058458792097e+155

-1.9581447245194372e+151

-1.353329681310028e+154

simplify8.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	105	106
1	105	106

end0.0ms

sample1.2s

Algorithm

intervals

Results

303.0ms	1085×	body	2560	valid
262.0ms	5126×	body	80	valid
213.0ms	898×	body	1280	valid
81.0ms	440×	body	640	valid
42.0ms	124×	body	5120	valid
31.0ms	653×	body	80	nan
30.0ms	222×	body	320	valid
20.0ms	397×	body	80	invalid
10.0ms	105×	body	160	valid

Details

analyze462.0ms

sample42.0ms

simplify111.0ms

prune4.0ms

localize14.0ms

rewrite38.0ms

series3.2s

simplify116.0ms

prune114.0ms

localize11.0ms

rewrite43.0ms

series3.4s

simplify122.0ms

prune101.0ms

localize14.0ms

rewrite23.0ms

series2.1s

simplify119.0ms

prune95.0ms

localize14.0ms

rewrite30.0ms

series1.9s

simplify72.0ms

prune100.0ms

regimes143.0ms

bsearch115.0ms

simplify8.0ms

end0.0ms

sample1.2s

Profiling