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

sample29.0ms

Algorithm

intervals

Results

10.0ms	41×	body	1024	valid
6.0ms	184×	body	128	valid
5.0ms	256×	pre	128	true
1.0ms	15×	body	512	valid
1.0ms	14×	body	256	valid
0.0ms	2×	body	2048	valid

simplify243.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (236.0ms)

Iter	Nodes	Cost
0	5018	19

prune2.0ms

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: 17.4b

Counts

2 → 1

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
1.0b	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

rewrite37.0ms

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))
20.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

series154.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2))
95.0ms	(+.f64 (/.f64 (-.f64 beta alpha) (+.f64 (+.f64 alpha beta) 2)) 1)

simplify68.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	6091	1488

prune81.0ms

Filtered

48 candidates to 71 candidates (-47.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	58	13	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	13	72

Merged error: 16.7b

Counts

72 → 13

localize11.0ms

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))
1.0b	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

rewrite78.0ms

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:

36.0ms	(-.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))
15.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

series316.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(-.f64 (/.f64 beta (+.f64 (+.f64 alpha beta) 2)) (-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1))
56.0ms	(/.f64 alpha (+.f64 (+.f64 beta alpha) 2))
64.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
110.0ms	(-.f64 (/.f64 alpha (+.f64 (+.f64 beta alpha) 2)) 1)

simplify83.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4943	2582
1	4943	2582

prune137.0ms

Filtered

87 candidates to 124 candidates (-42.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	117	7	124
Fresh	12	0	12
Picked	1	0	1
Done	0	0	0
Total	130	7	137

Merged error: 3.2b

Counts

137 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)))
1.0b	(+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1)

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

244×	`*-un-lft-identity_binary64`
130×	`times-frac_binary64`
96×	`distribute-lft-out_binary64`
84×	`add-sqr-sqrt_binary64`
72×	`add-cube-cbrt_binary64`
39×	`swap-sqr_binary64`
21×	`associate-r_binary64` `associate-l_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-/r/_binary64`
11×	`pow1_binary64`
10×	`associate-/r*_binary64`
7×	`flip3-+_binary64` `flip-+_binary64`
6×	`add-log-exp_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `div-inv_binary64` `div-exp_binary64`
4×	`cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-plus_binary64` `difference-of-sqr--1_binary64` `pow-sqr_binary64` `+-commutative_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 195

Calls

4 calls:

8.0ms	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
29.0ms	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)))
19.0ms	(+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1)

series336.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(/.f64 alpha (+.f64 (+.f64 alpha beta) 2))
59.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
87.0ms	(*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)))
134.0ms	(+.f64 (*.f64 (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)) (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) -1)

simplify69.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5055	4202

prune221.0ms

Filtered

118 candidates to 207 candidates (-75.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	206	1	207
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	208	6	214

Merged error: 3.2b

Counts

214 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
0.0b	(*.f64 alpha (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)))
0.1b	(.f64 (.f64 alpha (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
3.9b	(+.f64 (.f64 (.f64 alpha (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) -1)

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

83×	`*-un-lft-identity_binary64`
46×	`times-frac_binary64`
42×	`associate-r_binary64`
41×	`add-exp-log_binary64`
38×	`add-sqr-sqrt_binary64`
33×	`add-cube-cbrt_binary64`
32×	`add-cbrt-cube_binary64`
30×	`distribute-lft-out_binary64`
17×	`prod-exp_binary64`
12×	`cbrt-unprod_binary64`
11×	`pow1_binary64`
8×	`div-exp_binary64`
7×	`cbrt-undiv_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
5×	`associate-/r*_binary64`
4×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `associate-l*_binary64` `flip-+_binary64`
3×	`rec-exp_binary64` `associate-/l*_binary64` `div-inv_binary64`
2×	`unswap-sqr_binary64` `*-commutative_binary64`
1×	`clear-num_binary64` `frac-2neg_binary64` `un-div-inv_binary64` `+-commutative_binary64` `frac-times_binary64` `associate-*l/_binary64` `sum-log_binary64`

Counts

4 → 139

Calls

4 calls:

8.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
14.0ms	(*.f64 alpha (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)))
23.0ms	(.f64 (.f64 alpha (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
25.0ms	(+.f64 (.f64 (.f64 alpha (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) -1)

series338.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/.f64 beta (+.f64 (+.f64 alpha beta) 2))
53.0ms	(*.f64 alpha (/.f64 alpha (+.f64 (+.f64 alpha beta) 2)))
79.0ms	(.f64 (.f64 alpha (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) (/.f64 1 (+.f64 (+.f64 alpha beta) 2)))
138.0ms	(+.f64 (.f64 (.f64 alpha (/.f64 alpha (+.f64 (+.f64 alpha beta) 2))) (/.f64 1 (+.f64 (+.f64 alpha beta) 2))) -1)

simplify85.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4942	2586
1	4942	2586

prune168.0ms

Filtered

91 candidates to 151 candidates (-65.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	150	1	151
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	150	7	157

Merged error: 3.2b

Counts

157 → 7

regimes71.0ms

Accuracy

77.5% (2.9b remaining)

Error of 6.0b against oracle of 3.2b and baseline of 15.9b

bsearch22.0ms

Steps

Iters	Range		Point
9	7.429393406279412e+17	2.7681363267998034e+23	7.533781242299976e+17

simplify6.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	254	101
1	254	101

end0.0ms

sample647.0ms

Algorithm

intervals

Results

179.0ms	5951×	body	128	valid
126.0ms	1032×	body	1024	valid
117.0ms	8000×	pre	128	true
56.0ms	586×	body	512	valid
22.0ms	332×	body	256	valid
15.0ms	99×	body	2048	valid

Details

analyze3.0ms

sample29.0ms

simplify243.0ms

prune2.0ms

localize8.0ms

rewrite37.0ms

series154.0ms

simplify68.0ms

prune81.0ms

localize11.0ms

rewrite78.0ms

series316.0ms

simplify83.0ms

prune137.0ms

localize13.0ms

rewrite96.0ms

series336.0ms

simplify69.0ms

prune221.0ms

localize15.0ms

rewrite89.0ms

series338.0ms

simplify85.0ms

prune168.0ms

regimes71.0ms

bsearch22.0ms

simplify6.0ms

end0.0ms

sample647.0ms

Profiling