Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

sample33.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true

simplify294.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (285.0ms)

Iter	Nodes	Cost
0	5017	37

prune26.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 1.1b

Counts

2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
7.0b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
11.2b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64_1216`
34×	`add-cbrt-cube_binary64_1188` `add-exp-log_binary64_1180` `distribute-lft-out_binary64_1260`
24×	`flip-+_binary64_1241` `flip3-+_binary64_1214`
21×	`add-sqr-sqrt_binary64_1201` `associate-r_binary64_1275`
18×	`associate-/r/_binary64_1281`
16×	`frac-times_binary64_1208`
15×	`add-cube-cbrt_binary64_1187`
14×	`times-frac_binary64_1211`
13×	`pow1_binary64_1162`
11×	`swap-sqr_binary64_1243`
10×	`associate-*l/_binary64_1278` `div-exp_binary64_1169` `cbrt-unprod_binary64_1185` `cbrt-undiv_binary64_1186` `prod-exp_binary64_1167`
9×	`associate-l_binary64_1276`
8×	`associate-*r/_binary64_1277`
7×	`associate-/l/_binary64_1282`
6×	`associate-/r*_binary64_1279`
5×	`associate-/l*_binary64_1280`
4×	`add-log-exp_binary64_1181`
3×	`div-inv_binary64_1217` `unswap-sqr_binary64_1244`
2×	`pow-prod-down_binary64_1143` `clear-num_binary64_1219` `*-commutative_binary64_1284` `frac-2neg_binary64_1209`
1×	`pow-plus_binary64_1157` `pow-prod-up_binary64_1142` `pow2_binary64_1153` `pow-sqr_binary64_1249` `distribute-lft-in_binary64_1258` `distribute-rgt-in_binary64_1259`

Counts

4 → 158

Calls

4 calls:

14.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
33.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
24.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
17.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

series254.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
95.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
92.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
49.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

simplify85.0ms

Algorithm

egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5411	4425

prune656.0ms

Filtered

105 candidates to 170 candidates (-61.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	161	9	170
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	162	10	172

Merged error: 0.0b

Counts

172 → 10

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
0.2b	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
7.0b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))))

rewrite168.0ms

Algorithm

rewrite-expression-head

Rules

769×	`*-un-lft-identity_binary64_1216`
364×	`times-frac_binary64_1211`
331×	`distribute-lft-out_binary64_1260`
224×	`sqrt-prod_binary64_1195`
206×	`add-sqr-sqrt_binary64_1201`
131×	`add-cube-cbrt_binary64_1187`
127×	`swap-sqr_binary64_1243`
61×	`add-cbrt-cube_binary64_1188` `add-exp-log_binary64_1180`
45×	`associate-l_binary64_1276`
42×	`associate-r_binary64_1275`
22×	`cbrt-unprod_binary64_1185` `prod-exp_binary64_1167`
19×	`div-exp_binary64_1169` `frac-times_binary64_1208` `cbrt-undiv_binary64_1186`
16×	`pow1_binary64_1162`
15×	`flip-+_binary64_1241` `flip3-+_binary64_1214`
13×	`associate-*r/_binary64_1277` `associate-/l/_binary64_1282`
12×	`associate-/r/_binary64_1281`
11×	`associate-*l/_binary64_1278`
10×	`unswap-sqr_binary64_1244` `associate-/r*_binary64_1279`
8×	`associate-/l*_binary64_1280`
6×	`div-inv_binary64_1217`
4×	`pow-prod-down_binary64_1143` `add-log-exp_binary64_1181`
2×	`sqrt-div_binary64_1196` `clear-num_binary64_1219` `*-commutative_binary64_1284` `frac-2neg_binary64_1209`
1×	`pow-plus_binary64_1157` `pow-prod-up_binary64_1142` `pow2_binary64_1153` `pow-sqr_binary64_1249`

Counts

4 → 388

Calls

4 calls:

11.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))
37.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
51.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
32.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))))

series260.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))
92.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
46.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
93.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))))

simplify163.0ms

Algorithm

egg-herbie

Counts

400 → 400

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5760	12718

prune1.0s

Filtered

158 candidates to 400 candidates (-153.2%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	398	2	400
Fresh	2	7	9
Picked	0	1	1
Done	0	0	0
Total	400	10	410

Merged error: 0.0b

Counts

410 → 10

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))
0.1b	(.f64 (.f64 (+.f64 alpha 1) (*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
0.2b	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
7.0b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))))

rewrite175.0ms

Algorithm

rewrite-expression-head

Rules

781×	`*-un-lft-identity_binary64_1216`
374×	`times-frac_binary64_1211`
334×	`distribute-lft-out_binary64_1260`
224×	`sqrt-prod_binary64_1195`
213×	`add-sqr-sqrt_binary64_1201`
138×	`add-cube-cbrt_binary64_1187`
127×	`swap-sqr_binary64_1243`
117×	`add-exp-log_binary64_1180`
92×	`add-cbrt-cube_binary64_1188`
63×	`associate-r_binary64_1275`
58×	`prod-exp_binary64_1167`
46×	`associate-l_binary64_1276`
43×	`cbrt-unprod_binary64_1185`
39×	`frac-times_binary64_1208`
27×	`associate-*l/_binary64_1278` `div-exp_binary64_1169`
25×	`pow1_binary64_1162`
23×	`cbrt-undiv_binary64_1186`
20×	`associate-*r/_binary64_1277`
19×	`flip-+_binary64_1241` `flip3-+_binary64_1214`
12×	`associate-/r/_binary64_1281`
10×	`pow-prod-down_binary64_1143` `unswap-sqr_binary64_1244`
7×	`associate-/l*_binary64_1280`
6×	`rec-exp_binary64_1168` `div-inv_binary64_1217`
5×	`associate-/r*_binary64_1279`
4×	`add-log-exp_binary64_1181`
3×	`*-commutative_binary64_1284`
2×	`sqrt-div_binary64_1196` `associate-/l/_binary64_1282`
1×	`pow-plus_binary64_1157` `un-div-inv_binary64_1218` `pow-prod-up_binary64_1142` `pow2_binary64_1153` `clear-num_binary64_1219` `pow-sqr_binary64_1249` `frac-2neg_binary64_1209`

Counts

4 → 429

Calls

4 calls:

11.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))
41.0ms	(.f64 (.f64 (+.f64 alpha 1) (*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
50.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
32.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))))

series268.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))
94.0ms	(.f64 (.f64 (+.f64 alpha 1) (*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))) (/.f64 1 (+.f64 alpha (+.f64 beta 3))))
56.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)))
88.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))))

simplify176.0ms

Algorithm

egg-herbie

Counts

441 → 441

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5280	14364

prune1.1s

Filtered

168 candidates to 441 candidates (-162.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	440	1	441
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	440	11	451

Merged error: 0b

Counts

451 → 11

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt.f64 (+.f64 beta 1))
0.2b	(cbrt.f64 (+.f64 beta 1))
0.2b	(*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1)))
7.0b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (cbrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))))

rewrite62.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64_1216` `add-exp-log_binary64_1180`
32×	`cbrt-prod_binary64_1183`
26×	`add-cbrt-cube_binary64_1188`
23×	`add-sqr-sqrt_binary64_1201`
16×	`cbrt-unprod_binary64_1185` `pow1_binary64_1162` `prod-exp_binary64_1167` `cbrt-div_binary64_1184`
15×	`add-cube-cbrt_binary64_1187`
13×	`frac-times_binary64_1208`
12×	`flip-+_binary64_1241` `flip3-+_binary64_1214`
11×	`associate-l_binary64_1276`
9×	`swap-sqr_binary64_1243` `distribute-lft-out_binary64_1260`
8×	`associate-r/_binary64_1277` `pow1/3_binary64_1154` `associate-r*_binary64_1275`
7×	`associate-*l/_binary64_1278` `div-exp_binary64_1169` `cbrt-undiv_binary64_1186`
5×	`pow-prod-down_binary64_1143`
4×	`unswap-sqr_binary64_1244` `add-log-exp_binary64_1181`
2×	`pow-prod-up_binary64_1142` `pow-sqr_binary64_1249` `*-commutative_binary64_1284`
1×	`pow-plus_binary64_1157` `pow2_binary64_1153`

Counts

4 → 121

Calls

4 calls:

3.0ms	(cbrt.f64 (+.f64 beta 1))
3.0ms	(cbrt.f64 (+.f64 beta 1))
11.0ms	(*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1)))
40.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (cbrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))))

series172.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(cbrt.f64 (+.f64 beta 1))
27.0ms	(cbrt.f64 (+.f64 beta 1))
27.0ms	(*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1)))
94.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (*.f64 (cbrt.f64 (+.f64 beta 1)) (cbrt.f64 (+.f64 beta 1))) (+.f64 (+.f64 alpha beta) 2)) (/.f64 (cbrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 alpha beta) 2))))

simplify70.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5303	3027

prune560.0ms

Filtered

96 candidates to 133 candidates (-38.5%)

Pruning

11 alts after pruning (8 fresh and 3 done)

	Pruned	Kept	Total
New	133	0	133
Fresh	0	8	8
Picked	0	1	1
Done	0	2	2
Total	133	11	144

Merged error: 0b

Counts

144 → 11

regimes593.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	24	47
1	24	47

end0.0ms

sample829.0ms

Algorithm

intervals

Results

508.0ms	8000×	body	80	valid
127.0ms	8000×	pre	80	true

Details

analyze4.0ms

sample33.0ms

simplify294.0ms

prune26.0ms

localize20.0ms

rewrite94.0ms

series254.0ms

simplify85.0ms

prune656.0ms

localize23.0ms

rewrite168.0ms

series260.0ms

simplify163.0ms

prune1.0s

localize32.0ms

rewrite175.0ms

series268.0ms

simplify176.0ms

prune1.1s

localize27.0ms

rewrite62.0ms

series172.0ms

simplify70.0ms

prune560.0ms

regimes593.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample829.0ms

Profiling