Details

analyze571.0ms

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

25.0ms	256×	body	80	valid
2.0ms	25×	body	80	nan
1.0ms	9×	body	80	invalid

simplify924.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (393.0ms)

Iter	Nodes	Cost
0	2978	54
1	2978	54

prune9.0ms

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: 20.8b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

1.6b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
1.6b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite40.0ms

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` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 52

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
23.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series201.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
38.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
57.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
72.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify72.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5019	1222

prune114.0ms

Filtered

50 candidates to 64 candidates (-28.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	56	8	64
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	57	8	65

Merged error: 9.8b

Counts

65 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

1.6b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
3.7b	(/.f64 c (+.f64 b (-.f64 b (.f64 2 (/.f64 (.f64 c a) b)))))
7.4b	(/.f64 (*.f64 c a) b)
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

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

series232.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
120.0ms	(/.f64 c (+.f64 b (-.f64 b (.f64 2 (/.f64 (.f64 c a) b)))))
19.0ms	(/.f64 (*.f64 c a) b)
60.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify74.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4937	1648
1	4937	1648

prune136.0ms

Filtered

67 candidates to 92 candidates (-37.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	87	5	92
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	91	9	100

Merged error: 8.6b

Counts

100 → 9

localize29.0ms

Local error

Found 4 expressions with local error:

1.6b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
3.7b	(/.f64 c (+.f64 b (-.f64 b (.f64 2 (.f64 c (/.f64 a b))))))
5.1b	(*.f64 c (/.f64 a b))
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64` `times-frac_binary64`
13×	`associate-r_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64`
4×	`associate-/r*_binary64` `distribute-lft-out_binary64`
3×	`associate-l_binary64` `associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `-commutative_binary64`

Counts

4 → 91

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
8.0ms	(/.f64 c (+.f64 b (-.f64 b (.f64 2 (.f64 c (/.f64 a b))))))
7.0ms	(*.f64 c (/.f64 a b))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series236.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
118.0ms	(/.f64 c (+.f64 b (-.f64 b (.f64 2 (.f64 c (/.f64 a b))))))
20.0ms	(*.f64 c (/.f64 a b))
63.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify71.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4950	1777
1	4950	1777

prune137.0ms

Filtered

74 candidates to 103 candidates (-39.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	99	4	103
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	102	10	112

Merged error: 6.5b

Counts

112 → 10

localize39.0ms

Local error

Found 4 expressions with local error:

1.6b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
2.5b	(.f64 c (/.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (*.f64 (cbrt.f64 b) (cbrt.f64 b))))
3.7b	(/.f64 c (+.f64 b (-.f64 b (.f64 2 (.f64 (.f64 c (/.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (*.f64 (cbrt.f64 b) (cbrt.f64 b)))) (/.f64 (cbrt.f64 a) (cbrt.f64 b)))))))
23.4b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64` `add-exp-log_binary64`
20×	`add-sqr-sqrt_binary64`
16×	`add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
14×	`times-frac_binary64`
9×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64`
5×	`associate-r_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
4×	`associate-/r*_binary64` `distribute-lft-out_binary64`
3×	`associate-l_binary64` `associate-/l*_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `div-inv_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `-commutative_binary64`

Counts

4 → 89

Calls

4 calls:

5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
13.0ms	(.f64 c (/.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (*.f64 (cbrt.f64 b) (cbrt.f64 b))))
8.0ms	(/.f64 c (+.f64 b (-.f64 b (.f64 2 (.f64 (.f64 c (/.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (*.f64 (cbrt.f64 b) (cbrt.f64 b)))) (/.f64 (cbrt.f64 a) (cbrt.f64 b)))))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series315.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
97.0ms	(.f64 c (/.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (*.f64 (cbrt.f64 b) (cbrt.f64 b))))
124.0ms	(/.f64 c (+.f64 b (-.f64 b (.f64 2 (.f64 (.f64 c (/.f64 (.f64 (cbrt.f64 a) (cbrt.f64 a)) (*.f64 (cbrt.f64 b) (cbrt.f64 b)))) (/.f64 (cbrt.f64 a) (cbrt.f64 b)))))))
61.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify78.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4948	2060
1	4948	2060

prune115.0ms

Filtered

68 candidates to 101 candidates (-48.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	101	10	111

Merged error: 6.5b

Counts

111 → 10

regimes152.0ms

Accuracy

94.1% (0.9b remaining)

Error of 6.8b against oracle of 5.9b and baseline of 21.5b

bsearch79.0ms

Steps

Iters	Range		Point
10	4.1688745216488044e+138	3.975612975939537e+153	4.2377991560471444e+139
6	-2.789788358891522e+98	-2.748715332934914e+97	-1.4137242978488287e+98

simplify10.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	223	265
1	223	265

end0.0ms

sample1.1s

Algorithm

intervals

Results

766.0ms	8000×	body	80	valid
60.0ms	676×	body	80	nan
36.0ms	398×	body	80	invalid

Details

analyze571.0ms

sample40.0ms

simplify924.0ms

prune9.0ms

localize24.0ms

rewrite40.0ms

series201.0ms

simplify72.0ms

prune114.0ms

localize30.0ms

rewrite24.0ms

series232.0ms

simplify74.0ms

prune136.0ms

localize29.0ms

rewrite27.0ms

series236.0ms

simplify71.0ms

prune137.0ms

localize39.0ms

rewrite33.0ms

series315.0ms

simplify78.0ms

prune115.0ms

regimes152.0ms

bsearch79.0ms

simplify10.0ms

end0.0ms

sample1.1s

Profiling