Details

analyze756.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
6.2%	93.6%	0.2%	9
18.7%	81.1%	0.2%	10
26.5%	71.5%	1.9%	11
28.8%	66%	5.2%	12
32.7%	58.7%	8.5%	13
41.9%	48.4%	9.7%	14

sample34.0ms

Algorithm

intervals

Results

10.0ms	246×	body	80	valid
3.0ms	72×	body	80	invalid
1.0ms	4×	body	1280	valid
1.0ms	4×	body	640	valid
0.0ms	2×	body	320	valid

simplify20.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (11.0ms)

Iter	Nodes	Cost
0	400	19
1	400	19

prune24.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 0.1b

Counts

2 → 1

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)) (*.f64 y 5))
0.0b	(.f64 x (+.f64 (.f64 (+.f64 y z) 2) t))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_1201`
4×	`*-un-lft-identity_binary64_1216` `add-cbrt-cube_binary64_1188` `pow1_binary64_1162` `add-exp-log_binary64_1180` `add-cube-cbrt_binary64_1187` `add-log-exp_binary64_1181`
3×	`associate-l_binary64_1276` `associate-r_binary64_1275`
2×	`flip-+_binary64_1241` `flip3-+_binary64_1214` `associate-*r/_binary64_1277` `distribute-lft-in_binary64_1258` `distribute-rgt-in_binary64_1259` `associate-+l+_binary64_1268`
1×	`sum-log_binary64_1131` `cbrt-unprod_binary64_1185` `pow-prod-down_binary64_1143` `unswap-sqr_binary64_1244` `prod-exp_binary64_1167` `*-commutative_binary64_1284` `+-commutative_binary64_1283`

Counts

2 → 35

Calls

2 calls:

11.0ms	(+.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)) (*.f64 y 5))
10.0ms	(.f64 x (+.f64 (.f64 (+.f64 y z) 2) t))

series92.0ms

Counts

2 → 6

Calls

2 calls:

51.0ms	(+.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)) (*.f64 y 5))
40.0ms	(.f64 x (+.f64 (.f64 (+.f64 y z) 2) t))

simplify74.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4987	763
1	4987	763

prune187.0ms

Filtered

31 candidates to 41 candidates (-32.3%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	36	5	41
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	36	6	42

Merged error: 0.0b

Counts

42 → 6

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 y y) 25)
0.3b	(.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)) (.f64 x (+.f64 (*.f64 (+.f64 y z) 2) t)))
4.4b	(-.f64 (.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)) (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t))) (.f64 (*.f64 y y) 25))
28.3b	(/.f64 (-.f64 (.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)) (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t))) (.f64 (.f64 y y) 25)) (-.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)) (.f64 y 5)))

rewrite83.0ms

Algorithm

rewrite-expression-head

Rules

48×	`pow1_binary64_1162`
23×	`add-cbrt-cube_binary64_1188` `add-exp-log_binary64_1180`
20×	`pow-prod-down_binary64_1143`
14×	`associate-*r/_binary64_1277` `add-sqr-sqrt_binary64_1201`
13×	`*-un-lft-identity_binary64_1216` `add-cube-cbrt_binary64_1187`
11×	`cbrt-unprod_binary64_1185` `prod-exp_binary64_1167`
9×	`times-frac_binary64_1211`
8×	`distribute-lft-in_binary64_1258` `distribute-rgt-in_binary64_1259`
6×	`flip-+_binary64_1241` `flip3-+_binary64_1214` `add-log-exp_binary64_1181`
4×	`frac-times_binary64_1208` `pow-prod-up_binary64_1142` `pow-sqr_binary64_1249` `associate--l+_binary64_1272` `associate-r_binary64_1275`
3×	`flip3--_binary64_1215` `associate-/r_binary64_1279` `associate-/l_binary64_1280` `flip--_binary64_1242`
2×	`pow-plus_binary64_1157` `associate-l/_binary64_1278` `associate-l_binary64_1276` `associate-/r/_binary64_1281` `-commutative_binary64_1284` `associate-/l/_binary64_1282`
1×	`div-exp_binary64_1169` `swap-sqr_binary64_1243` `div-inv_binary64_1217` `pow2_binary64_1153` `clear-num_binary64_1219` `unswap-sqr_binary64_1244` `diff-log_binary64_1132` `cbrt-undiv_binary64_1186` `sub-neg_binary64_1220` `frac-2neg_binary64_1209` `div-sub_binary64_1210`

Counts

4 → 112

Calls

4 calls:

5.0ms	(.f64 (.f64 y y) 25)
19.0ms	(.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)) (.f64 x (+.f64 (*.f64 (+.f64 y z) 2) t)))
22.0ms	(-.f64 (.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)) (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t))) (.f64 (*.f64 y y) 25))
33.0ms	(/.f64 (-.f64 (.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)) (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t))) (.f64 (.f64 y y) 25)) (-.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)) (.f64 y 5)))

series796.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(.f64 (.f64 y y) 25)
113.0ms	(.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)) (.f64 x (+.f64 (*.f64 (+.f64 y z) 2) t)))
272.0ms	(-.f64 (.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)) (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t))) (.f64 (*.f64 y y) 25))
389.0ms	(/.f64 (-.f64 (.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)) (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t))) (.f64 (.f64 y y) 25)) (-.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)) (.f64 y 5)))

simplify102.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4981	4710
1	4981	4710

prune372.0ms

Filtered

76 candidates to 124 candidates (-63.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	124	6	130

Merged error: 0.0b

Counts

130 → 6

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 x (+.f64 (.f64 (+.f64 y z) 2) t))
0.3b	(.f64 (sqrt.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t))) (sqrt.f64 (.f64 x (+.f64 (*.f64 (+.f64 y z) 2) t))))
1.0b	(sqrt.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)))
1.0b	(sqrt.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

61×	`pow1_binary64_1162`
32×	`sqrt-pow1_binary64_1197`
23×	`pow-prod-down_binary64_1143`
20×	`associate-*r/_binary64_1277`
16×	`sqrt-div_binary64_1196`
14×	`add-sqr-sqrt_binary64_1201`
12×	`pow1/2_binary64_1152`
10×	`*-un-lft-identity_binary64_1216` `pow-prod-up_binary64_1142` `add-cube-cbrt_binary64_1187`
9×	`flip-+_binary64_1241` `flip3-+_binary64_1214`
8×	`add-cbrt-cube_binary64_1188` `add-exp-log_binary64_1180`
7×	`associate-l_binary64_1276` `associate-r_binary64_1275`
6×	`pow-sqr_binary64_1249` `sqrt-prod_binary64_1195`
4×	`frac-times_binary64_1208` `swap-sqr_binary64_1243` `add-log-exp_binary64_1181`
2×	`associate-l/_binary64_1278` `cbrt-unprod_binary64_1185` `unswap-sqr_binary64_1244` `prod-exp_binary64_1167` `-commutative_binary64_1284`
1×	`pow-plus_binary64_1157` `pow2_binary64_1153` `sqrt-unprod_binary64_1199` `rem-square-sqrt_binary64_1203` `distribute-lft-in_binary64_1258` `distribute-rgt-in_binary64_1259`

Counts

4 → 105

Calls

4 calls:

9.0ms	(.f64 x (+.f64 (.f64 (+.f64 y z) 2) t))
19.0ms	(.f64 (sqrt.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t))) (sqrt.f64 (.f64 x (+.f64 (*.f64 (+.f64 y z) 2) t))))
7.0ms	(sqrt.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)))
14.0ms	(sqrt.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)))

series489.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(.f64 x (+.f64 (.f64 (+.f64 y z) 2) t))
43.0ms	(.f64 (sqrt.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t))) (sqrt.f64 (.f64 x (+.f64 (*.f64 (+.f64 y z) 2) t))))
206.0ms	(sqrt.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)))
204.0ms	(sqrt.f64 (.f64 x (+.f64 (.f64 (+.f64 y z) 2) t)))

simplify78.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4982	2246
1	4982	2246

prune36.0ms

Filtered: 70 candidates to 117 candidates (-67.1%)

Details

analyze756.0ms

sample34.0ms

simplify20.0ms

prune24.0ms

localize15.0ms

rewrite21.0ms

series92.0ms

simplify74.0ms

prune187.0ms

localize32.0ms

rewrite83.0ms

series796.0ms

simplify102.0ms

prune372.0ms

localize18.0ms

rewrite54.0ms

series489.0ms

simplify78.0ms

prune36.0ms

Profiling