Details

analyze701.0ms

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
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

sample42.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
1.0ms	15×	body	80	nan
1.0ms	11×	body	80	invalid

simplify697.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (263.0ms)

Iter	Nodes	Cost
0	2747	36
1	2747	36

prune12.0ms

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: 20.0b

Counts

2 → 1

localize29.0ms

Local error

Found 4 expressions with local error:

1.7b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
2.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
8×	`add-log-exp_binary64`
7×	`sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `distribute-lft-out--_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 56

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series81.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
16.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
26.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify68.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4916	950
1	4916	950

prune141.0ms

Filtered

55 candidates to 68 candidates (-23.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	61	7	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	7	69

Merged error: 5.6b

Counts

69 → 7

localize22.0ms

Local error

Found 4 expressions with local error:

11.7b	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) b)
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `difference-of-squares_binary64`

Counts

4 → 57

Calls

4 calls:

18.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series67.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) b)
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify46.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5116	926

prune126.0ms

Filtered

58 candidates to 69 candidates (-19.0%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	69	7	76

Merged error: 5.6b

Counts

76 → 7

localize21.0ms

Local error

Found 4 expressions with local error:

2.6b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `sqrt-prod_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `distribute-lft-out_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 57

Calls

4 calls:

7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series64.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify30.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5224	910

prune123.0ms

Filtered

57 candidates to 69 candidates (-21.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	69	7	76

Merged error: 5.6b

Counts

76 → 7

localize28.0ms

Local error

Found 4 expressions with local error:

22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 60

Calls

4 calls:

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

series66.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
17.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
15.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify34.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	4927	924
1	4927	924

prune133.0ms

Filtered

60 candidates to 72 candidates (-20.0%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	72	7	79

Merged error: 5.6b

Counts

79 → 7

regimes216.0ms

Accuracy

90% (1.3b remaining)

Error of 8.9b against oracle of 7.6b and baseline of 20.4b

bsearch46.0ms

Steps

Iters	Range		Point
8	1.631248782496957e+100	1.2588914441016629e+103	1.2789809966277235e+101
6	-5.917785821803394e+50	-7.650404129414556e+49	-5.831678047639542e+50

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	125	125
1	125	125

end0.0ms

sample955.0ms

Algorithm

intervals

Results

679.0ms	8000×	body	80	valid
53.0ms	642×	body	80	nan
27.0ms	339×	body	80	invalid

Details

analyze701.0ms

sample42.0ms

simplify697.0ms

prune12.0ms

localize29.0ms

rewrite30.0ms

series81.0ms

simplify68.0ms

prune141.0ms

localize22.0ms

rewrite33.0ms

series67.0ms

simplify46.0ms

prune126.0ms

localize21.0ms

rewrite24.0ms

series64.0ms

simplify30.0ms

prune123.0ms

localize28.0ms

rewrite20.0ms

series66.0ms

simplify34.0ms

prune133.0ms

regimes216.0ms

bsearch46.0ms

simplify3.0ms

end0.0ms

sample955.0ms

Profiling