Details

analyze2.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample28.0ms (0.6%)

Algorithm

1×

intervals

Results

13.0ms	83×	body	1024	valid
5.0ms	125×	body	128	valid
3.0ms	30×	body	512	valid
1.0ms	18×	body	256	valid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify175.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	75	17
1	75	17

prune2.0ms (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: 19.9b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
0.3b	(/.f64 1 (sqrt.f64 x))
2.9b	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))

rewrite72.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

124×	`add-sqr-sqrt_binary64_1133`
118×	`times-frac_binary64_1117`
113×	`*-un-lft-identity_binary64_1111`
72×	`sqrt-prod_binary64_1127`
54×	`add-cube-cbrt_binary64_1146`
27×	`cancel-sign-sub-inv_binary64_1077`
25×	`difference-of-squares_binary64_1080`
13×	`associate-/r*_binary64_1055` `distribute-lft-out--_binary64_1063`
11×	`add-exp-log_binary64_1149`
10×	`distribute-lft-out_binary64_1062`
7×	`add-cbrt-cube_binary64_1147` `div-inv_binary64_1108` `pow1_binary64_1172`
6×	`pow-flip_binary64_1185` `associate-/l*_binary64_1056`
5×	`add-log-exp_binary64_1150`
4×	`sqrt-div_binary64_1128` `div-exp_binary64_1162` `associate-/r/_binary64_1057`
2×	`pow1/2_binary64_1191` `flip-+_binary64_1085` `frac-2neg_binary64_1122` `flip3-+_binary64_1114` `1-exp_binary64_1155` `rec-exp_binary64_1161` `cbrt-undiv_binary64_1145` `sqrt-pow1_binary64_1129` `clear-num_binary64_1110` `inv-pow_binary64_1196`
1×	`frac-sub_binary64_1120` `flip3--_binary64_1115` `diff-log_binary64_1203` `sub-neg_binary64_1104` `flip--_binary64_1086`

Counts

3 → 173

Calls

3 calls:

42.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
7.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (sqrt.f64 x))

series158.0ms (3.2%)

Counts

3 → 9

Calls

3 calls:

67.0ms	(-.f64 (/.f64 1 (sqrt.f64 x)) (/.f64 1 (sqrt.f64 (+.f64 x 1))))
53.0ms	(/.f64 1 (sqrt.f64 x))
37.0ms	(/.f64 1 (sqrt.f64 (+.f64 x 1)))

simplify75.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4920	3438
1	4920	3438

prune644.0ms (12.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	172	10	182
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	173	10	183

Merged error: 19.3b

Counts

183 → 10

Compiler

Compiled 10238 to 8232 computations (19.6% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
2.9b	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

rewrite48.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64_1133`
38×	`sqrt-prod_binary64_1127`
34×	`*-un-lft-identity_binary64_1111`
12×	`difference-of-squares_binary64_1080`
11×	`add-cube-cbrt_binary64_1146`
10×	`add-cbrt-cube_binary64_1147` `times-frac_binary64_1117` `associate-/l*_binary64_1056` `add-exp-log_binary64_1149`
9×	`distribute-lft-out--_binary64_1063`
7×	`associate-r_binary64_1051` `pow1_binary64_1172`
6×	`cancel-sign-sub-inv_binary64_1077` `associate-l_binary64_1052`
5×	`add-log-exp_binary64_1150`
4×	`sqrt-div_binary64_1128` `unswap-sqr_binary64_1079` `distribute-lft-out_binary64_1062` `associate-*r/_binary64_1053`
3×	`pow-prod-down_binary64_1182`
2×	`pow1/2_binary64_1191` `prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `flip-+_binary64_1085` `flip3--_binary64_1115` `associate-/l/_binary64_1058` `flip3-+_binary64_1114` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `sqrt-pow1_binary64_1129` `flip--_binary64_1086` `associate-/r/_binary64_1057`
1×	`-commutative_binary64_1042` `div-inv_binary64_1108` `associate-/r_binary64_1055` `frac-2neg_binary64_1122` `diff-log_binary64_1203` `sqrt-unprod_binary64_1131` `sub-neg_binary64_1104` `clear-num_binary64_1110` `div-sub_binary64_1116`

Counts

3 → 97

Calls

3 calls:

19.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
10.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series296.0ms (6%)

Counts

3 → 9

Calls

3 calls:

175.0ms	(/.f64 (-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
72.0ms	(-.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
50.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

simplify67.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5017	2435

prune174.0ms (3.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	105	1	106
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	114	2	116

Merged error: 0.3b

Counts

116 → 2

Compiler

Compiled 3137 to 2162 computations (31.1% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))
0.2b	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
0.3b	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))

rewrite74.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`*-un-lft-identity_binary64_1111`
78×	`times-frac_binary64_1117`
55×	`sqrt-prod_binary64_1127`
47×	`add-sqr-sqrt_binary64_1133`
45×	`distribute-lft-out_binary64_1062`
39×	`add-cube-cbrt_binary64_1146`
32×	`add-exp-log_binary64_1149`
27×	`associate-/l*_binary64_1056`
20×	`add-cbrt-cube_binary64_1147`
14×	`div-exp_binary64_1162`
9×	`pow1_binary64_1172`
8×	`associate-/r/_binary64_1057`
7×	`associate-/r_binary64_1055` `associate-r*_binary64_1051` `cbrt-undiv_binary64_1145`
6×	`flip-+_binary64_1085` `flip3-+_binary64_1114` `associate-l_binary64_1052` `add-log-exp_binary64_1150`
5×	`prod-exp_binary64_1160`
4×	`sqrt-div_binary64_1128` `div-inv_binary64_1108` `unswap-sqr_binary64_1079` `associate-*r/_binary64_1053`
3×	`cbrt-unprod_binary64_1144` `1-exp_binary64_1155` `rec-exp_binary64_1161` `pow-prod-down_binary64_1182`
2×	`pow1/2_binary64_1191` `frac-2neg_binary64_1122` `sqrt-pow1_binary64_1129` `clear-num_binary64_1110`
1×	`*-commutative_binary64_1042` `pow-flip_binary64_1185` `associate-/l/_binary64_1058` `+-commutative_binary64_1041` `sqrt-unprod_binary64_1131` `sum-log_binary64_1202` `inv-pow_binary64_1196`

Counts

4 → 166

Calls

4 calls:

22.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
11.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
10.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
8.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

series307.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

165.0ms	(/.f64 (/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))) (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x))))
55.0ms	(/.f64 1 (+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x)))
48.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 1 x)))
38.0ms	(+.f64 (sqrt.f64 (+.f64 1 x)) (sqrt.f64 x))

simplify86.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4944	4177
1	4944	4177

prune545.0ms (11%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	172	6	178
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	173	7	180

Merged error: 0.0b

Counts

180 → 7

Compiler

Compiled 9373 to 6753 computations (28% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))
0.1b	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
0.1b	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
0.3b	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))

rewrite69.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

234×	`times-frac_binary64_1117`
159×	`*-un-lft-identity_binary64_1111`
156×	`add-sqr-sqrt_binary64_1133`
119×	`add-cube-cbrt_binary64_1146`
87×	`sqrt-prod_binary64_1127`
49×	`distribute-lft-out_binary64_1062`
21×	`associate-/l*_binary64_1056`
20×	`associate-/r/_binary64_1057`
19×	`add-exp-log_binary64_1149`
13×	`add-cbrt-cube_binary64_1147`
12×	`flip-+_binary64_1085` `flip3-+_binary64_1114`
11×	`associate-/r*_binary64_1055`
10×	`div-inv_binary64_1108`
9×	`pow1_binary64_1172`
8×	`div-exp_binary64_1162`
7×	`associate-r_binary64_1051`
6×	`associate-l_binary64_1052` `add-log-exp_binary64_1150`
4×	`sqrt-div_binary64_1128` `cbrt-undiv_binary64_1145` `unswap-sqr_binary64_1079`
3×	`pow-prod-down_binary64_1182`
2×	`pow1/2_binary64_1191` `frac-2neg_binary64_1122` `1-exp_binary64_1155` `rec-exp_binary64_1161` `sqrt-pow1_binary64_1129` `clear-num_binary64_1110` `associate-*r/_binary64_1053`
1×	`*-commutative_binary64_1042` `prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `pow-flip_binary64_1185` `associate-/l/_binary64_1058` `+-commutative_binary64_1041` `sqrt-unprod_binary64_1131` `sum-log_binary64_1202` `inv-pow_binary64_1196`

Counts

4 → 252

Calls

4 calls:

17.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
11.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
5.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

series343.0ms (6.9%)

Counts

4 → 12

Calls

4 calls:

168.0ms	(/.f64 (/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))) (sqrt.f64 (+.f64 1 x)))
85.0ms	(/.f64 1 (+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))))
47.0ms	(*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1)))
42.0ms	(+.f64 x (*.f64 (sqrt.f64 x) (sqrt.f64 (+.f64 x 1))))

simplify160.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

264 → 264

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4947	9756
1	4947	9756

prune589.0ms (11.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	262	2	264
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	264	7	271

Merged error: 0b

Counts

271 → 7

Compiler

Compiled 9461 to 6929 computations (26.8% saved)

regimes21.0ms (0.4%)

Compiler: Compiled 150 to 122 computations (18.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	25
1	14	25

end0.0ms (0%)

sample1.0s (20.1%)

Algorithm

1×

intervals

Results

360.0ms	2301×	body	1024	valid
174.0ms	4198×	body	128	valid
112.0ms	996×	body	512	valid
41.0ms	505×	body	256	valid

Compiler

Compiled 191 to 157 computations (17.8% saved)

Details

analyze2.0ms (0%)

sample28.0ms (0.6%)

simplify175.0ms (3.5%)

prune2.0ms (0%)

localize7.0ms (0.1%)

rewrite72.0ms (1.5%)

series158.0ms (3.2%)

simplify75.0ms (1.5%)

prune644.0ms (12.9%)

localize8.0ms (0.2%)

rewrite48.0ms (1%)

series296.0ms (6%)

simplify67.0ms (1.3%)

prune174.0ms (3.5%)

localize8.0ms (0.2%)

rewrite74.0ms (1.5%)

series307.0ms (6.2%)

simplify86.0ms (1.7%)

prune545.0ms (11%)

localize10.0ms (0.2%)

rewrite69.0ms (1.4%)

series343.0ms (6.9%)

simplify160.0ms (3.2%)

prune589.0ms (11.9%)

regimes21.0ms (0.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.0s (20.1%)

Profiling