Details

analyze6.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	50%	0%	4
75%	25%	0%	5
87.5%	12.5%	0%	6
93.7%	6.2%	0%	7
96.8%	3.1%	0%	8
98.4%	1.6%	0%	9
99.2%	0.8%	0%	10
99.6%	0.4%	0%	11
99.8%	0.2%	0%	12
99.9%	0.1%	0%	13
99.9%	0.1%	0.1%	14

sample30.0ms

Algorithm

intervals

Results

8.0ms	62×	body	640	valid
5.0ms	127×	body	80	valid
3.0ms	34×	body	320	valid
3.0ms	17×	body	1280	valid
1.0ms	16×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	192	22
1	192	22

prune15.0ms

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: 11.2b

Counts

2 → 1

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 1 (-.f64 x 1))
0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
2.9b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

98×	`*-un-lft-identity_binary64_1216`
58×	`add-sqr-sqrt_binary64_1201`
56×	`times-frac_binary64_1211`
25×	`add-cube-cbrt_binary64_1187`
18×	`distribute-lft-out--_binary64_1261`
17×	`distribute-lft-out_binary64_1260`
14×	`difference-of-squares_binary64_1245`
11×	`add-log-exp_binary64_1181` `associate-/r*_binary64_1279`
10×	`add-exp-log_binary64_1180`
8×	`div-inv_binary64_1217` `add-cbrt-cube_binary64_1188`
6×	`pow1_binary64_1162` `associate-/l*_binary64_1280`
4×	`associate-/r/_binary64_1281` `difference-of-sqr-1_binary64_1246`
3×	`flip3--_binary64_1215` `frac-add_binary64_1206` `flip--_binary64_1242`
2×	`sum-log_binary64_1131` `div-exp_binary64_1169` `rec-exp_binary64_1168` `frac-sub_binary64_1207` `flip-+_binary64_1241` `clear-num_binary64_1219` `flip3-+_binary64_1214` `pow-flip_binary64_1146` `diff-log_binary64_1132` `cbrt-undiv_binary64_1186` `sub-neg_binary64_1220` `inv-pow_binary64_1138` `frac-2neg_binary64_1209`
1×	`+-commutative_binary64_1283` `associate-+l+_binary64_1268` `associate-+l-_binary64_1270`

Counts

4 → 133

Calls

4 calls:

6.0ms	(/.f64 1 (-.f64 x 1))
6.0ms	(/.f64 1 (+.f64 x 1))
21.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
36.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/.f64 1 (-.f64 x 1))
7.0ms	(/.f64 1 (+.f64 x 1))
12.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
47.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

simplify104.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5071	2562

prune416.0ms

Filtered

85 candidates to 145 candidates (-70.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	141	4	145
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	142	4	146

Merged error: 0.0b

Counts

146 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (+.f64 x 1))
0.3b	(cbrt.f64 (+.f64 x 1))
0.3b	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))
19.2b	(+.f64 (-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (+.f64 x 1))) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

64×	`*-un-lft-identity_binary64_1216`
32×	`cbrt-prod_binary64_1183`
22×	`add-sqr-sqrt_binary64_1201`
16×	`distribute-lft-out_binary64_1260` `cbrt-div_binary64_1184`
14×	`add-cube-cbrt_binary64_1187`
12×	`times-frac_binary64_1211`
11×	`pow1_binary64_1162`
9×	`swap-sqr_binary64_1243` `flip-+_binary64_1241` `flip3-+_binary64_1214` `add-log-exp_binary64_1181`
8×	`distribute-lft-out--_binary64_1261` `pow1/3_binary64_1154`
7×	`associate-l_binary64_1276` `associate-r_binary64_1275`
6×	`add-exp-log_binary64_1180`
4×	`frac-times_binary64_1208` `div-inv_binary64_1217` `add-cbrt-cube_binary64_1188` `unswap-sqr_binary64_1244`
3×	`frac-add_binary64_1206`
2×	`sum-log_binary64_1131` `associate-l/_binary64_1278` `pow-prod-up_binary64_1142` `pow-prod-down_binary64_1143` `pow-sqr_binary64_1249` `associate-r/_binary64_1277`
1×	`flip3--_binary64_1215` `pow-plus_binary64_1157` `cbrt-unprod_binary64_1185` `frac-sub_binary64_1207` `pow2_binary64_1153` `diff-log_binary64_1132` `sub-neg_binary64_1220` `prod-exp_binary64_1167` `*-commutative_binary64_1284` `+-commutative_binary64_1283` `flip--_binary64_1242` `associate-+l+_binary64_1268` `associate-+l-_binary64_1270`

Counts

4 → 106

Calls

4 calls:

3.0ms	(cbrt.f64 (+.f64 x 1))
3.0ms	(cbrt.f64 (+.f64 x 1))
10.0ms	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))
106.0ms	(+.f64 (-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (+.f64 x 1))) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

series138.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(cbrt.f64 (+.f64 x 1))
29.0ms	(cbrt.f64 (+.f64 x 1))
28.0ms	(*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))
55.0ms	(+.f64 (-.f64 (/.f64 (/.f64 1 (*.f64 (cbrt.f64 (+.f64 x 1)) (cbrt.f64 (+.f64 x 1)))) (cbrt.f64 (+.f64 x 1))) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

simplify99.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5275	2278

prune483.0ms

Filtered

83 candidates to 118 candidates (-42.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	118	4	122

Merged error: 0.0b

Counts

122 → 4

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 x (*.f64 2 (+.f64 x 1)))
0.0b	(.f64 (-.f64 x 1) (-.f64 x (.f64 2 (+.f64 x 1))))
0.0b	(*.f64 x (+.f64 x 1))
17.3b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 2 (+.f64 x 1)))) (*.f64 x (+.f64 x 1)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

24×	`associate-*r/_binary64_1277`
19×	`flip3--_binary64_1215` `flip--_binary64_1242`
16×	`add-sqr-sqrt_binary64_1201` `frac-add_binary64_1206`
13×	`*-un-lft-identity_binary64_1216`
12×	`frac-times_binary64_1208`
10×	`flip-+_binary64_1241` `flip3-+_binary64_1214` `associate-l_binary64_1276`
8×	`add-cbrt-cube_binary64_1188` `pow1_binary64_1162` `add-exp-log_binary64_1180` `add-cube-cbrt_binary64_1187` `add-log-exp_binary64_1181`
7×	`associate-r_binary64_1275`
6×	`associate-*l/_binary64_1278`
5×	`sub-neg_binary64_1220` `distribute-lft-in_binary64_1258` `distribute-rgt-in_binary64_1259`
2×	`cbrt-unprod_binary64_1185` `pow-prod-down_binary64_1143` `unswap-sqr_binary64_1244` `associate-+r+_binary64_1267` `prod-exp_binary64_1167` `*-commutative_binary64_1284` `associate--r+_binary64_1271` `difference-of-squares_binary64_1245` `associate-+l+_binary64_1268`
1×	`sum-log_binary64_1131` `distribute-lft-out--_binary64_1261` `diff-log_binary64_1132` `distribute-lft-out_binary64_1260` `+-commutative_binary64_1283` `difference-of-sqr-1_binary64_1246`

Counts

4 → 99

Calls

4 calls:

3.0ms	(-.f64 x (*.f64 2 (+.f64 x 1)))
8.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 2 (+.f64 x 1))))
6.0ms	(*.f64 x (+.f64 x 1))
11.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 2 (+.f64 x 1)))) (*.f64 x (+.f64 x 1)))

series60.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(-.f64 x (*.f64 2 (+.f64 x 1)))
11.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 2 (+.f64 x 1))))
33.0ms	(*.f64 x (+.f64 x 1))
4.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 2 (+.f64 x 1)))) (*.f64 x (+.f64 x 1)))

simplify64.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	6242	2822

prune401.0ms

Filtered

87 candidates to 111 candidates (-27.6%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	2	0	2
Picked	1	0	1
Done	1	0	1
Total	114	1	115

Merged error: 0.0b

Counts

115 → 1

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b	(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64_1216`
21×	`times-frac_binary64_1211`
13×	`add-sqr-sqrt_binary64_1201` `add-cube-cbrt_binary64_1187`
8×	`distribute-rgt-out_binary64_1262` `distribute-lft-out_binary64_1260` `unpow3_binary64_1160`
7×	`associate-/r*_binary64_1279`
4×	`distribute-rgt-neg-in_binary64_1251` `distribute-lft-neg-in_binary64_1250` `neg-mul-1_binary64_1223`
3×	`add-cbrt-cube_binary64_1188` `add-exp-log_binary64_1180` `associate-/l*_binary64_1280`
2×	`associate-/r/_binary64_1281`
1×	`div-exp_binary64_1169` `div-inv_binary64_1217` `flip-+_binary64_1241` `pow1_binary64_1162` `clear-num_binary64_1219` `flip3-+_binary64_1214` `cbrt-undiv_binary64_1186` `frac-2neg_binary64_1209` `add-log-exp_binary64_1181`

Counts

1 → 45

Calls

1 calls:

11.0ms

(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))

series22.0ms

Counts

1 → 3

Calls

1 calls:

22.0ms

(/.f64 2 (+.f64 (pow.f64 x 3) (neg.f64 x)))

simplify75.0ms

Algorithm

egg-herbie

Counts

48 → 48

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5291	778

prune142.0ms

Filtered

32 candidates to 48 candidates (-50.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	46	2	48
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	46	3	49

Merged error: 0b

Counts

49 → 3

regimes49.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	10
1	17	10

end0.0ms

sample795.0ms

Algorithm

intervals

Results

266.0ms	1921×	body	640	valid
154.0ms	4108×	body	80	valid
107.0ms	577×	body	1280	valid
107.0ms	911×	body	320	valid
34.0ms	483×	body	160	valid
0.0ms	1×	body	80	invalid

Details

analyze6.0ms

sample30.0ms

simplify17.0ms

prune15.0ms

localize14.0ms

rewrite74.0ms

series75.0ms

simplify104.0ms

prune416.0ms

localize19.0ms

rewrite126.0ms

series138.0ms

simplify99.0ms

prune483.0ms

localize21.0ms

rewrite32.0ms

series60.0ms

simplify64.0ms

prune401.0ms

localize8.0ms

rewrite13.0ms

series22.0ms

simplify75.0ms

prune142.0ms

regimes49.0ms

bsearch0.0ms

simplify3.0ms

end0.0ms

sample795.0ms

Profiling