Details

analyze3.0ms

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

sample25.0ms

Algorithm

intervals

Results

6.0ms	188×	body	80	valid
4.0ms	28×	body	1280	valid
4.0ms	256×	pre	80	true
2.0ms	19×	body	640	valid
1.0ms	15×	body	320	valid
0.0ms	6×	body	160	valid

simplify227.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (224.0ms)

Iter	Nodes	Cost
0	5017	13

prune4.0ms

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: 15.7b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
1.7b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite35.0ms

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:

10.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
22.0ms	(+.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))
13.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

simplify53.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	6347	994

prune70.0ms

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: 14.9b

Counts

72 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
0.0b	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
1.7b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

100×	`*-un-lft-identity_binary64`
67×	`add-sqr-sqrt_binary64`
58×	`times-frac_binary64`
36×	`add-cube-cbrt_binary64`
24×	`distribute-lft-out_binary64`
13×	`associate-/r_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64`
12×	`difference-of-squares_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`add-log-exp_binary64`
4×	`associate-/l/_binary64` `pow1_binary64` `associate-/r/_binary64`
3×	`flip3--_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64`
2×	`flip3-+_binary64` `difference-of-sqr-1_binary64` `flip-+_binary64` `frac-sub_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `div-sub_binary64`

Counts

4 → 140

Calls

4 calls:

34.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
8.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
13.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

series39.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)) 2)
7.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
7.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
12.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify55.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	4928	2528
1	4928	2528

prune140.0ms

Filtered

107 candidates to 152 candidates (-42.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	145	7	152
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	154	8	162

Merged error: 3.3b

Counts

162 → 8

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)))
0.1b	(/.f64 (-.f64 (.f64 beta (+.f64 (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 alpha (+.f64 (+.f64 beta alpha) 2))) (+.f64 (.f64 1 1) (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)))) (.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 3) (pow.f64 1 3)))) (.f64 2 (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 (.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 beta alpha) 2)) 3)
1.7b	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 3) (pow.f64 1 3))

rewrite155.0ms

Algorithm

rewrite-expression-head

Rules

258×	`*-un-lft-identity_binary64`
145×	`add-sqr-sqrt_binary64` `times-frac_binary64`
107×	`associate-*r/_binary64`
90×	`distribute-lft-out_binary64`
73×	`add-cube-cbrt_binary64`
68×	`flip3-+_binary64` `flip-+_binary64`
66×	`associate-/l/_binary64`
64×	`frac-sub_binary64`
53×	`frac-times_binary64`
49×	`unpow-prod-down_binary64` `cube-prod_binary64`
48×	`frac-add_binary64`
39×	`swap-sqr_binary64`
36×	`difference-of-squares_binary64`
35×	`associate-*l/_binary64`
28×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
26×	`flip3--_binary64` `flip--_binary64`
21×	`associate-r_binary64` `associate-l_binary64`
20×	`associate-/r/_binary64`
13×	`sqr-pow_binary64`
12×	`pow1_binary64`
8×	`cbrt-undiv_binary64` `div-exp_binary64`
7×	`cbrt-unprod_binary64` `prod-exp_binary64` `div-inv_binary64`
6×	`add-log-exp_binary64` `distribute-lft-out--_binary64`
4×	`unswap-sqr_binary64`
3×	`pow-unpow_binary64` `associate-/l*_binary64`
2×	`rem-cube-cbrt_binary64` `pow-exp_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `pow-prod-down_binary64` `difference-cubes_binary64` `associate-/r_binary64` `sub-neg_binary64` `diff-log_binary64` `pow-prod-up_binary64` `pow-pow_binary64` `pow-plus_binary64` `cube-div_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-sqr_binary64` `pow2_binary64` `unpow3_binary64` `-commutative_binary64`

Counts

4 → 323

Calls

4 calls:

27.0ms	(*.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)))
55.0ms	(/.f64 (-.f64 (.f64 beta (+.f64 (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 alpha (+.f64 (+.f64 beta alpha) 2))) (+.f64 (.f64 1 1) (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)))) (.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 3) (pow.f64 1 3)))) (.f64 2 (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 (.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 beta alpha) 2)) 3)
38.0ms	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 3) (pow.f64 1 3))

series176.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(*.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)))
131.0ms	(/.f64 (-.f64 (.f64 beta (+.f64 (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) (/.f64 alpha (+.f64 (+.f64 beta alpha) 2))) (+.f64 (.f64 1 1) (.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)))) (.f64 (+.f64 (+.f64 alpha beta) 2) (-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 3) (pow.f64 1 3)))) (.f64 2 (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 (.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 beta alpha) 2)) 3)
22.0ms	(-.f64 (pow.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 3) (pow.f64 1 3))

simplify84.0ms

Algorithm

egg-herbie

Counts

335 → 335

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	6100	11141

prune2.2s

Filtered

199 candidates to 335 candidates (-68.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	331	4	335
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	335	8	343

Merged error: 3.3b

Counts

343 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 beta)
0.6b	(cbrt.f64 beta)
0.6b	(cbrt.f64 beta)
1.7b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

1.0ms	(cbrt.f64 beta)
1.0ms	(cbrt.f64 beta)
1.0ms	(cbrt.f64 beta)
13.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

series55.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(cbrt.f64 beta)
14.0ms	(cbrt.f64 beta)
15.0ms	(cbrt.f64 beta)
12.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify40.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5113	482

prune43.0ms

Filtered

51 candidates to 63 candidates (-23.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	58	5	63
Fresh	2	5	7
Picked	1	0	1
Done	0	0	0
Total	61	10	71

Merged error: 3.3b

Counts

71 → 10

regimes129.0ms

Accuracy

76.7% (2.9b remaining)

Error of 6.0b against oracle of 3.1b and baseline of 15.6b

bsearch1.0ms

Steps

Iters	Range		Point
0	2.887432631723143e+23	2.9640236399885602e+23	2.9257281358558516e+23

simplify7.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	237	59
1	237	59

end0.0ms

sample730.0ms

Algorithm

intervals

Results

192.0ms	5889×	body	80	valid
137.0ms	832×	body	1280	valid
124.0ms	8000×	pre	80	true
85.0ms	679×	body	640	valid
38.0ms	404×	body	320	valid
14.0ms	196×	body	160	valid

Details

analyze3.0ms

sample25.0ms

simplify227.0ms

prune4.0ms

localize8.0ms

rewrite35.0ms

series20.0ms

simplify53.0ms

prune70.0ms

localize12.0ms

rewrite68.0ms

series39.0ms

simplify55.0ms

prune140.0ms

localize28.0ms

rewrite155.0ms

series176.0ms

simplify84.0ms

prune2.2s

localize17.0ms

rewrite18.0ms

series55.0ms

simplify40.0ms

prune43.0ms

regimes129.0ms

bsearch1.0ms

simplify7.0ms

end0.0ms

sample730.0ms

Profiling