Details

analyze3.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
62.5%	12.5%	25%	4
68.7%	6.2%	25%	5
71.8%	3.1%	25%	6
73.4%	1.6%	25%	7
74.2%	0.8%	25%	8
74.6%	0.4%	25%	9
74.8%	0.2%	25%	10
74.9%	0.1%	25%	11
74.9%	0%	25%	12
74.9%	0%	25%	13
74.9%	0%	25%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample12.0ms (0.5%)

Algorithm

1×

intervals

Results

7.0ms

256×

body

128

valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify166.0ms (6.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

prune2.0ms (0.1%)

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: 0.1b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

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

rewrite17.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`*-un-lft-identity_binary64_1111`
23×	`add-sqr-sqrt_binary64_1133`
18×	`times-frac_binary64_1117`
17×	`distribute-lft-out_binary64_1062`
14×	`add-cube-cbrt_binary64_1146`
12×	`sqrt-prod_binary64_1127`
6×	`associate-/r*_binary64_1055`
4×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
3×	`associate-/l*_binary64_1056` `pow1_binary64_1172`
2×	`sqrt-div_binary64_1128` `flip-+_binary64_1085` `flip3-+_binary64_1114` `add-log-exp_binary64_1150` `associate-/r/_binary64_1057`
1×	`pow1/2_binary64_1191` `rem-sqrt-square_binary64_1124` `div-inv_binary64_1108` `frac-2neg_binary64_1122` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145` `sqrt-pow1_binary64_1129` `clear-num_binary64_1110`

Counts

2 → 57

Calls

2 calls:

9.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
4.0ms	(sqrt.f64 (+.f64 x 1))

series148.0ms (5.5%)

Counts

2 → 6

Calls

2 calls:

122.0ms	(/.f64 x (+.f64 1 (sqrt.f64 (+.f64 x 1))))
26.0ms	(sqrt.f64 (+.f64 x 1))

simplify69.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4966	1265
1	4966	1265

prune140.0ms (5.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	61	2	63
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	3	64

Merged error: 0b

Counts

64 → 3

Compiler

Compiled 2267 to 1780 computations (21.5% saved)

localize16.0ms (0.6%)

Local error

Found 4 expressions with local error:

0.2b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))
0.2b	(pow.f64 (sqrt.f64 (+.f64 x 1)) 3)
2.6b	(-.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (.f64 1 (sqrt.f64 (+.f64 x 1))))
8.0b	(/.f64 x (+.f64 1 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))

rewrite71.0ms (2.7%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`sqrt-div_binary64_1128`
52×	`*-un-lft-identity_binary64_1111`
40×	`add-sqr-sqrt_binary64_1133`
34×	`sqrt-prod_binary64_1127`
32×	`flip-+_binary64_1085` `flip3-+_binary64_1114`
28×	`associate-*r/_binary64_1053`
26×	`add-cube-cbrt_binary64_1146`
21×	`pow1_binary64_1172`
16×	`frac-sub_binary64_1120`
12×	`times-frac_binary64_1117` `frac-times_binary64_1121` `distribute-lft-out_binary64_1062`
11×	`swap-sqr_binary64_1078`
9×	`pow1/2_binary64_1191` `add-cbrt-cube_binary64_1147` `sqrt-pow1_binary64_1129` `add-exp-log_binary64_1149`
8×	`associate-*l/_binary64_1054`
7×	`unpow-prod-down_binary64_1190` `associate-r_binary64_1051` `cube-prod_binary64_1139` `associate-l_binary64_1052`
6×	`add-log-exp_binary64_1150`
5×	`pow-prod-up_binary64_1181`
4×	`associate-/r*_binary64_1055` `sub-div_binary64_1118` `unswap-sqr_binary64_1079`
3×	`pow-unpow_binary64_1188` `associate-/l*_binary64_1056` `pow-sqr_binary64_1084` `pow-pow_binary64_1183` `pow-prod-down_binary64_1182`
2×	`cube-div_binary64_1140` `rem-sqrt-square_binary64_1124` `associate-/r/_binary64_1057`
1×	`*-commutative_binary64_1042` `cube-mult_binary64_1141` `prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `div-inv_binary64_1108` `cancel-sign-sub-inv_binary64_1077` `rem-square-sqrt_binary64_1123` `distribute-rgt-out--_binary64_1065` `frac-2neg_binary64_1122` `flip3--_binary64_1115` `diff-log_binary64_1203` `sqrt-pow2_binary64_1130` `pow-plus_binary64_1174` `div-exp_binary64_1162` `pow-exp_binary64_1179` `cbrt-undiv_binary64_1145` `rem-cube-cbrt_binary64_1134` `unpow3_binary64_1177` `pow2_binary64_1192` `sqrt-unprod_binary64_1131` `sqr-abs_binary64_1126` `sqr-pow_binary64_1083` `pow-to-exp_binary64_1180` `sub-neg_binary64_1104` `clear-num_binary64_1110` `flip--_binary64_1086`

Counts

4 → 165

Calls

4 calls:

15.0ms	(-.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (.f64 1 (sqrt.f64 (+.f64 x 1))))
14.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))
13.0ms	(/.f64 x (+.f64 1 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))
6.0ms	(pow.f64 (sqrt.f64 (+.f64 x 1)) 3)

series214.0ms (8%)

Counts

4 → 12

Calls

4 calls:

105.0ms	(/.f64 x (+.f64 1 (pow.f64 (sqrt.f64 (+.f64 x 1)) 3)))
50.0ms	(pow.f64 (sqrt.f64 (+.f64 x 1)) 3)
34.0ms	(-.f64 (.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1))) (.f64 1 (sqrt.f64 (+.f64 x 1))))
24.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (+.f64 x 1)))

simplify108.0ms (4%)

Algorithm

1×	egg-herbie

Counts

177 → 177

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4904	3339
1	4904	3339

prune609.0ms (22.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	177	0	177
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	177	3	180

Merged error: 0b

Counts

180 → 3

Compiler

Compiled 6499 to 5265 computations (19% saved)

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

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

rewrite58.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

113×	`*-un-lft-identity_binary64_1111`
89×	`add-sqr-sqrt_binary64_1133`
77×	`sqrt-prod_binary64_1127`
76×	`times-frac_binary64_1117`
53×	`distribute-lft-out_binary64_1062`
46×	`add-cube-cbrt_binary64_1146`
42×	`associate-r_binary64_1051`
10×	`add-cbrt-cube_binary64_1147` `add-exp-log_binary64_1149`
6×	`associate-/r_binary64_1055` `associate-/l_binary64_1056` `associate-l_binary64_1052` `unswap-sqr_binary64_1079` `pow1_binary64_1172`
4×	`associate-/r/_binary64_1057`
3×	`flip-+_binary64_1085` `flip3-+_binary64_1114` `add-log-exp_binary64_1150`
2×	`prod-exp_binary64_1160` `sqrt-div_binary64_1128` `cbrt-unprod_binary64_1144` `div-inv_binary64_1108` `div-exp_binary64_1162` `cbrt-undiv_binary64_1145`
1×	`pow1/2_binary64_1191` `-commutative_binary64_1042` `rem-sqrt-square_binary64_1124` `frac-2neg_binary64_1122` `pow-prod-down_binary64_1182` `sqrt-pow1_binary64_1129` `clear-num_binary64_1110` `associate-r/_binary64_1053`

Counts

3 → 146

Calls

3 calls:

28.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
10.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
4.0ms	(sqrt.f64 (+.f64 x 1))

series319.0ms (11.9%)

Counts

3 → 9

Calls

3 calls:

188.0ms	(/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1))))
106.0ms	(*.f64 (sqrt.f64 x) (/.f64 (sqrt.f64 x) (+.f64 1 (sqrt.f64 (+.f64 x 1)))))
25.0ms	(sqrt.f64 (+.f64 x 1))

simplify92.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4950	3539
1	4950	3539

prune167.0ms (6.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	155	3	158

Merged error: 0b

Counts

158 → 3

Compiler

Compiled 3324 to 2104 computations (36.7% saved)

regimes24.0ms (0.9%)

Compiler: Compiled 120 to 102 computations (15% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	10	12
1	10	12

end0.0ms (0%)

sample431.0ms (16.1%)

Algorithm

1×

intervals

Results

235.0ms	7997×	body	128	valid
0.0ms	3×	body	2048	valid

Compiler

Compiled 68 to 59 computations (13.2% saved)

Details

analyze3.0ms (0.1%)

sample12.0ms (0.5%)

simplify166.0ms (6.2%)

prune2.0ms (0.1%)

localize5.0ms (0.2%)

rewrite17.0ms (0.6%)

series148.0ms (5.5%)

simplify69.0ms (2.6%)

prune140.0ms (5.2%)

localize16.0ms (0.6%)

rewrite71.0ms (2.7%)

series214.0ms (8%)

simplify108.0ms (4%)

prune609.0ms (22.7%)

localize7.0ms (0.3%)

rewrite58.0ms (2.2%)

series319.0ms (11.9%)

simplify92.0ms (3.4%)

prune167.0ms (6.2%)

regimes24.0ms (0.9%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample431.0ms (16.1%)

Profiling