Details

analyze556.0ms

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

sample38.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
2.0ms	19×	body	80	nan
1.0ms	10×	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

prune10.0ms

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: 19.4b

Counts

2 → 1

localize23.0ms

Local error

Found 4 expressions with local error:

1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
1.6b	(-.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))))

rewrite45.0ms

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:

7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
23.0ms	(-.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))))
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series76.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
17.0ms	(-.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))))
27.0ms	(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

prune118.0ms

Filtered

55 candidates to 68 candidates (-23.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	59	9	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	9	69

Merged error: 7.8b

Counts

69 → 9

localize26.0ms

Local error

Found 4 expressions with local error:

12.3b	(-.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:

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)
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:

19.0ms	(-.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)
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))))
16.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify47.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5116	926

prune105.0ms

Filtered

57 candidates to 69 candidates (-21.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	69	9	78

Merged error: 7.8b

Counts

78 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

1.6b	(-.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))))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
10×	`sqrt-prod_binary64`
9×	`*-un-lft-identity_binary64`
7×	`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`
2×	`difference-of-squares_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `distribute-lft-out--_binary64`

Counts

4 → 59

Calls

4 calls:

8.0ms	(-.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))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series63.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify46.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4958	966
1	4958	966

prune110.0ms

Filtered

58 candidates to 71 candidates (-22.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	71	9	80

Merged error: 7.8b

Counts

80 → 9

localize25.0ms

Local error

Found 4 expressions with local error:

5.4b	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
16.2b	(+.f64 b (exp.f64 (log.f64 (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

11×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
9×	`add-cube-cbrt_binary64` `sqrt-prod_binary64`
8×	`pow1_binary64`
6×	`add-log-exp_binary64` `log-prod_binary64` `exp-sum_binary64` `sqrt-div_binary64` `exp-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/2_binary64` `flip3--_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `flip--_binary64`
2×	`exp-diff_binary64` `rem-sqrt-square_binary64` `log-div_binary64`
1×	`flip3-+_binary64` `distribute-lft-out_binary64` `rem-exp-log_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 64

Calls

4 calls:

7.0ms	(exp.f64 (log.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))))
12.0ms	(+.f64 b (exp.f64 (log.f64 (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))))

series63.0ms

Counts

4 → 12

Calls

4 calls:

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

76 → 76

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5296	981

prune77.0ms

Filtered

57 candidates to 76 candidates (-33.3%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	0	6	6
Picked	1	0	1
Done	0	2	2
Total	75	10	85

Merged error: 7.8b

Counts

85 → 10

regimes216.0ms

Accuracy

89.3% (1.3b remaining)

Error of 8.6b against oracle of 7.3b and baseline of 19.5b

bsearch66.0ms

Steps

Iters	Range		Point
9	1.7102570126301476e+35	2.4064393717816498e+41	2.3718123998214835e+41
9	-3.999860267026533e+154	-3.833436215723568e+149	-1.3606679773833112e+154

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	121	125
1	121	125

end0.0ms

sample997.0ms

Algorithm

intervals

Results

696.0ms	8000×	body	80	valid
56.0ms	678×	body	80	nan
31.0ms	380×	body	80	invalid

Details

analyze556.0ms

sample38.0ms

simplify697.0ms

prune10.0ms

localize23.0ms

rewrite45.0ms

series76.0ms

simplify68.0ms

prune118.0ms

localize26.0ms

rewrite33.0ms

series66.0ms

simplify47.0ms

prune105.0ms

localize23.0ms

rewrite26.0ms

series63.0ms

simplify46.0ms

prune110.0ms

localize25.0ms

rewrite30.0ms

series63.0ms

simplify30.0ms

prune77.0ms

regimes216.0ms

bsearch66.0ms

simplify3.0ms

end0.0ms

sample997.0ms

Profiling