Details

analyze573.0ms

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

sample40.0ms

Algorithm

intervals

Results

24.0ms	256×	body	80	valid
1.0ms	14×	body	80	nan
1.0ms	7×	body	80	invalid

simplify678.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (262.0ms)

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: 21.9b

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)))))
1.5b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite29.0ms

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

series93.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
19.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
35.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify66.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4916	950
1	4916	950

prune142.0ms

Filtered

55 candidates to 68 candidates (-23.6%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	60	8	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	61	8	69

Merged error: 10.6b

Counts

69 → 8

localize23.0ms

Local error

Found 4 expressions with local error:

8.4b	(+.f64 b (.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)))))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

10×	`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×	`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` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 56

Calls

4 calls:

3.0ms	(+.f64 b (.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)))))))
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))))

series78.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(+.f64 b (.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)))))))
20.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify32.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5631	898

prune134.0ms

Filtered

56 candidates to 68 candidates (-21.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	68	8	76

Merged error: 10.6b

Counts

76 → 8

localize26.0ms

Local error

Found 4 expressions with local error:

10.5b	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) b)
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
25.9b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
25.9b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

10.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
4.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series118.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(-.f64 (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) b)
18.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
27.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
32.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify40.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	4940	1099
1	4940	1099

prune147.0ms

Filtered

58 candidates to 64 candidates (-10.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	63	1	64
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	63	9	72

Merged error: 10.6b

Counts

72 → 9

localize24.0ms

Local error

Found 4 expressions with local error:

1.1b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
3.4b	(/.f64 (.f64 2 (-.f64 (/.f64 (.f64 c a) b) b)) (*.f64 2 a))
7.1b	(/.f64 (*.f64 c a) b)
25.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`*-un-lft-identity_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
5×	`pow1_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`associate-/r*_binary64` `times-frac_binary64`
3×	`sqrt-prod_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `distribute-lft-out_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 71

Calls

4 calls:

6.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
13.0ms	(/.f64 (.f64 2 (-.f64 (/.f64 (.f64 c a) b) b)) (*.f64 2 a))
5.0ms	(/.f64 (*.f64 c a) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series60.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
15.0ms	(/.f64 (.f64 2 (-.f64 (/.f64 (.f64 c a) b) b)) (*.f64 2 a))
6.0ms	(/.f64 (*.f64 c a) b)
21.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify41.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5031	868

prune102.0ms

Filtered

59 candidates to 83 candidates (-40.7%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	77	6	83
Fresh	1	5	6
Picked	1	0	1
Done	0	2	2
Total	79	13	92

Merged error: 9.4b

Counts

92 → 13

regimes365.0ms

Accuracy

92.7% (0.9b remaining)

Error of 7.5b against oracle of 6.5b and baseline of 19.4b

bsearch64.0ms

Steps

Iters	Range		Point
9	4.133558150256362e+100	2.0370040434721257e+109	1.827145917976237e+108
9	-7.796098687113796e+132	-3.0791589294299004e+127	-3.6419385251769567e+130

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	129	117
1	129	117

end0.0ms

sample1.1s

Algorithm

intervals

Results

769.0ms	8000×	body	80	valid
59.0ms	663×	body	80	nan
34.0ms	375×	body	80	invalid

Details

analyze573.0ms

sample40.0ms

simplify678.0ms

prune12.0ms

localize23.0ms

rewrite29.0ms

series93.0ms

simplify66.0ms

prune142.0ms

localize23.0ms

rewrite19.0ms

series78.0ms

simplify32.0ms

prune134.0ms

localize26.0ms

rewrite25.0ms

series118.0ms

simplify40.0ms

prune147.0ms

localize24.0ms

rewrite31.0ms

series60.0ms

simplify41.0ms

prune102.0ms

regimes365.0ms

bsearch64.0ms

simplify3.0ms

end0.0ms

sample1.1s

Profiling