Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
28.1%	28.1%	43.8%	2
56.2%	0%	43.8%	3

sample29.0ms

Algorithm

intervals

Results

6.0ms	175×	body	80	valid
5.0ms	34×	body	640	valid
4.0ms	26×	body	1280	valid
4.0ms	256×	pre	80	true
1.0ms	14×	body	320	valid
0.0ms	7×	body	160	valid

simplify213.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (211.0ms)

Iter	Nodes	Cost
0	5017	13

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 19.1b

Counts

2 → 1

localize13.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
2.0b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

58×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
19×	`distribute-lft-out_binary64`
14×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
5×	`associate-/r_binary64` `associate-/l_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `pow1_binary64` `associate-/r/_binary64` `div-sub_binary64` `flip-+_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `associate-+l-_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

2 → 65

Calls

2 calls:

11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
19.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

series23.0ms

Counts

2 → 6

Calls

2 calls:

9.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
14.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

simplify54.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	6347	994

prune102.0ms

Filtered

48 candidates to 71 candidates (-47.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	61	10	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	62	10	72

Merged error: 18.2b

Counts

72 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
2.0b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

73×	`*-un-lft-identity_binary64`
40×	`add-sqr-sqrt_binary64`
34×	`times-frac_binary64`
24×	`distribute-lft-out_binary64` `add-cube-cbrt_binary64`
11×	`add-log-exp_binary64`
10×	`associate-/r*_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64`
4×	`pow1_binary64` `diff-log_binary64` `associate-/r/_binary64` `distribute-lft-out--_binary64`
3×	`sub-neg_binary64` `flip3--_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `cbrt-undiv_binary64` `difference-of-sqr-1_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64` `frac-sub_binary64`
1×	`associate--r+_binary64` `associate--r-_binary64`

Counts

4 → 112

Calls

4 calls:

31.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
17.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

series46.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
10.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
14.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify50.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4921	1727
1	4921	1727

prune168.0ms

Filtered

87 candidates to 124 candidates (-42.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	117	7	124
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	125	9	134

Merged error: 3.8b

Counts

134 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
0.7b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
0.7b	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
2.0b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
18×	`add-sqr-sqrt_binary64`
15×	`cbrt-prod_binary64`
9×	`distribute-lft-out_binary64`
7×	`add-cube-cbrt_binary64`
6×	`cbrt-div_binary64` `add-log-exp_binary64`
4×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64`
3×	`flip3-+_binary64` `pow1/3_binary64` `times-frac_binary64` `flip-+_binary64`
2×	`difference-of-sqr-1_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 63

Calls

4 calls:

6.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
6.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
6.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
14.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

series73.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
19.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
19.0ms	(cbrt.f64 (+.f64 (+.f64 alpha beta) 2))
14.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify58.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4936	923
1	4936	923

prune123.0ms

Filtered

60 candidates to 75 candidates (-25.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	78	6	84

Merged error: 3.8b

Counts

84 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))
0.1b	(exp.f64 (log.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)))
2.0b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)
3.2b	(log.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64`
31×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
21×	`distribute-lft-out_binary64`
19×	`add-cube-cbrt_binary64`
8×	`log-prod_binary64`
7×	`add-exp-log_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
5×	`associate-/r_binary64` `associate-/l_binary64`
4×	`flip3-+_binary64` `exp-sum_binary64` `log-div_binary64` `flip-+_binary64` `exp-prod_binary64`
2×	`associate-/l/_binary64` `log-pow_binary64` `associate-/r/_binary64` `exp-diff_binary64` `div-sub_binary64`
1×	`flip3--_binary64` `cbrt-undiv_binary64` `rem-log-exp_binary64` `associate-+l-_binary64` `rem-exp-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 98

Calls

4 calls:

11.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))
19.0ms	(exp.f64 (log.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)))
20.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)
20.0ms	(log.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1))

series63.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2))
14.0ms	(exp.f64 (log.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)))
13.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1)
27.0ms	(log.f64 (+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 beta alpha) 2)) 1))

simplify58.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5849	1590

prune97.0ms

Filtered

74 candidates to 110 candidates (-48.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	111	5	116

Merged error: 3.8b

Counts

116 → 5

regimes112.0ms

Accuracy

76.1% (3.1b remaining)

Error of 6.4b against oracle of 3.2b and baseline of 16.3b

bsearch21.0ms

Steps

Iters	Range		Point
11	11.147105962075988	1.2795261915093277e+22	1957322.8552237058

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	234	46
1	234	46

end0.0ms

sample792.0ms

Algorithm

intervals

Results

209.0ms	5836×	body	80	valid
150.0ms	847×	body	1280	valid
133.0ms	8000×	pre	80	true
101.0ms	733×	body	640	valid
42.0ms	414×	body	320	valid
12.0ms	170×	body	160	valid

Details

analyze2.0ms

sample29.0ms

simplify213.0ms

prune6.0ms

localize13.0ms

rewrite33.0ms

series23.0ms

simplify54.0ms

prune102.0ms

localize12.0ms

rewrite68.0ms

series46.0ms

simplify50.0ms

prune168.0ms

localize23.0ms

rewrite34.0ms

series73.0ms

simplify58.0ms

prune123.0ms

localize12.0ms

rewrite73.0ms

series63.0ms

simplify58.0ms

prune97.0ms

regimes112.0ms

bsearch21.0ms

simplify7.0ms

end0.0ms

sample792.0ms

Profiling