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

sample31.0ms

Algorithm

intervals

Results

9.0ms	256×	pre	80	true
6.0ms	191×	body	80	valid
4.0ms	23×	body	1280	valid
3.0ms	21×	body	640	valid
1.0ms	15×	body	320	valid
0.0ms	6×	body	160	valid

simplify229.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (226.0ms)

Iter	Nodes	Cost
0	5017	13

prune5.0ms

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: 15.2b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
2.1b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite32.0ms

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)

series20.0ms

Counts

2 → 6

Calls

2 calls:

8.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
12.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

simplify58.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	6347	994

prune102.0ms

Filtered

48 candidates to 71 candidates (-47.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	59	12	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	60	12	72

Merged error: 14.3b

Counts

72 → 12

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
2.1b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64`
34×	`add-sqr-sqrt_binary64`
33×	`times-frac_binary64`
24×	`distribute-lft-out_binary64`
23×	`add-cube-cbrt_binary64`
10×	`associate-/r*_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`associate-/l*_binary64`
5×	`add-log-exp_binary64`
4×	`associate-/r/_binary64` `difference-of-squares_binary64`
3×	`pow1_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`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

3 → 92

Calls

3 calls:

8.0ms	(/.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)

series26.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
6.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
12.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify42.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5515	1139

prune338.0ms

Filtered

68 candidates to 101 candidates (-48.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	91	10	101
Fresh	10	1	11
Picked	1	0	1
Done	0	0	0
Total	102	11	113

Merged error: 4.4b

Counts

113 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
0.1b	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)
2.1b	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

118×	`*-un-lft-identity_binary64`
75×	`add-sqr-sqrt_binary64`
67×	`times-frac_binary64`
43×	`add-cube-cbrt_binary64`
40×	`distribute-lft-out_binary64`
27×	`unpow-prod-down_binary64` `cube-prod_binary64`
21×	`associate-l_binary64`
14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`difference-of-squares_binary64`
8×	`associate-/r/_binary64`
7×	`pow1_binary64`
6×	`flip3-+_binary64` `add-log-exp_binary64` `difference-of-sqr-1_binary64` `flip-+_binary64`
5×	`associate-/r*_binary64`
4×	`associate-r_binary64` `sqr-pow_binary64` `div-inv_binary64`
3×	`pow-unpow_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64`
2×	`cbrt-unprod_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `rem-cube-cbrt_binary64` `prod-exp_binary64` `frac-times_binary64` `pow-exp_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `pow-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `cube-div_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `unpow3_binary64` `associate-l/_binary64` `-commutative_binary64` `cube-mult_binary64`

Counts

4 → 176

Calls

4 calls:

8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
25.0ms	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
11.0ms	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)
23.0ms	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)

series55.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
15.0ms	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (+.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 1))
12.0ms	(pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3)
22.0ms	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) 3) 1)

simplify68.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5000	2816

prune237.0ms

Filtered

103 candidates to 188 candidates (-82.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	187	12	199

Merged error: 4.4b

Counts

199 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 (+.f64 (+.f64 alpha beta) 2) beta)
0.4b	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))
2.1b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

184×	`*-un-lft-identity_binary64`
150×	`times-frac_binary64`
91×	`add-sqr-sqrt_binary64`
80×	`add-cube-cbrt_binary64`
60×	`distribute-lft-out_binary64`
27×	`associate-/r*_binary64`
19×	`add-exp-log_binary64`
13×	`add-cbrt-cube_binary64`
11×	`associate-/l*_binary64`
9×	`div-exp_binary64`
7×	`div-inv_binary64`
6×	`add-log-exp_binary64`
5×	`pow1_binary64` `cbrt-undiv_binary64`
4×	`difference-of-squares_binary64`
3×	`associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `1-exp_binary64` `difference-of-sqr-1_binary64` `rec-exp_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `inv-pow_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `pow-flip_binary64`

Counts

4 → 192

Calls

4 calls:

8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
11.0ms	(/.f64 (+.f64 (+.f64 alpha beta) 2) beta)
11.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))
14.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

series32.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
5.0ms	(/.f64 (+.f64 (+.f64 alpha beta) 2) beta)
8.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) beta))
12.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify74.0ms

Algorithm

egg-herbie

Counts

204 → 204

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4925	2528
1	4925	2528

prune155.0ms

Filtered

110 candidates to 204 candidates (-85.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	201	3	204
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	204	12	216

Merged error: 4.4b

Counts

216 → 12

regimes147.0ms

Accuracy

72.3% (3.4b remaining)

Error of 6.6b against oracle of 3.2b and baseline of 15.4b

bsearch17.0ms

Steps

Iters	Range		Point
8	1.0113532622146849e+24	8.315918103195864e+26	1.74995439910408e+24

simplify4.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	209	82
1	209	82

end0.0ms

sample728.0ms

Algorithm

intervals

Results

188.0ms	5878×	body	80	valid
137.0ms	823×	body	1280	valid
129.0ms	8000×	pre	80	true
89.0ms	689×	body	640	valid
36.0ms	385×	body	320	valid
14.0ms	225×	body	160	valid

Details

analyze2.0ms

sample31.0ms

simplify229.0ms

prune5.0ms

localize8.0ms

rewrite32.0ms

series20.0ms

simplify58.0ms

prune102.0ms

localize11.0ms

rewrite33.0ms

series26.0ms

simplify42.0ms

prune338.0ms

localize18.0ms

rewrite77.0ms

series55.0ms

simplify68.0ms

prune237.0ms

localize12.0ms

rewrite53.0ms

series32.0ms

simplify74.0ms

prune155.0ms

regimes147.0ms

bsearch17.0ms

simplify4.0ms

end0.0ms

sample728.0ms

Profiling