Details

analyze263.0ms (7.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	50%	25%	4
25%	37.5%	37.5%	5
25%	31.2%	43.8%	6
25%	28.1%	46.9%	7
25%	26.5%	48.5%	8
25%	25.8%	49.2%	9
25%	25.4%	49.6%	10
25%	25.2%	49.8%	11
25%	25.1%	49.9%	12
25%	25%	50%	13
25%	25%	50%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample52.0ms (1.5%)

Algorithm

1×

intervals

Results

19.0ms	122×	body	2048	nan
11.0ms	256×	body	128	valid
6.0ms	50×	body	1024	nan
4.0ms	12×	body	256	nan
3.0ms	31×	body	512	nan
0.0ms	9×	body	128	nan

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify273.0ms (7.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	5604	14

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: 31.1b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
29.0b	(sqrt.f64 (-.f64 (*.f64 x x) 1))

rewrite15.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64_1111` `sqrt-prod_binary64_1127`
5×	`add-sqr-sqrt_binary64_1133`
4×	`add-log-exp_binary64_1150`
3×	`add-cube-cbrt_binary64_1146` `pow1_binary64_1172`
2×	`add-cbrt-cube_binary64_1147` `sqrt-div_binary64_1128` `difference-of-squares_binary64_1080` `add-exp-log_binary64_1149`
1×	`pow1/2_binary64_1191` `rem-sqrt-square_binary64_1124` `flip-+_binary64_1085` `flip3--_binary64_1115` `flip3-+_binary64_1114` `+-commutative_binary64_1041` `difference-of-sqr-1_binary64_1081` `distribute-lft-out_binary64_1062` `sqrt-pow1_binary64_1129` `sum-log_binary64_1202` `flip--_binary64_1086`

Counts

2 → 30

Calls

2 calls:

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

series98.0ms (2.8%)

Counts

2 → 6

Calls

2 calls:

57.0ms	(+.f64 x (sqrt.f64 (-.f64 (*.f64 x x) 1)))
41.0ms	(sqrt.f64 (-.f64 (*.f64 x x) 1))

simplify50.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	4922	536
1	4922	536

prune42.0ms (1.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	34	2	36
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	35	2	37

Merged error: 0b

Counts

37 → 2

Compiler

Compiled 637 to 428 computations (32.8% saved)

localize9.0ms (0.3%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))
0.5b	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))

rewrite23.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_1133`
15×	`sqrt-prod_binary64_1127`
12×	`sqrt-div_binary64_1128`
11×	`*-un-lft-identity_binary64_1111`
10×	`associate-r_binary64_1051`
7×	`associate-l_binary64_1052`
6×	`add-cube-cbrt_binary64_1146` `pow1_binary64_1172`
4×	`add-cbrt-cube_binary64_1147` `flip-+_binary64_1085` `frac-times_binary64_1121` `flip3-+_binary64_1114` `unswap-sqr_binary64_1079` `add-log-exp_binary64_1150` `add-exp-log_binary64_1149`
3×	`flip3--_binary64_1115` `pow-prod-down_binary64_1182` `flip--_binary64_1086`
2×	`pow1/2_binary64_1191` `associate-l/_binary64_1054` `difference-of-squares_binary64_1080` `sqrt-pow1_binary64_1129` `associate-r/_binary64_1053`
1×	`*-commutative_binary64_1042` `prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `+-commutative_binary64_1041` `difference-of-sqr-1_binary64_1081` `distribute-lft-out_binary64_1062` `sqrt-unprod_binary64_1131` `sum-log_binary64_1202` `distribute-lft-out--_binary64_1063`

Counts

2 → 54

Calls

2 calls:

14.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
3.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

series128.0ms (3.7%)

Counts

2 → 6

Calls

2 calls:

75.0ms	(*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1)))
53.0ms	(+.f64 x (*.f64 (sqrt.f64 (+.f64 x 1)) (sqrt.f64 (-.f64 x 1))))

simplify61.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4960	1195
1	4960	1195

prune69.0ms (2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	61	1	62

Merged error: 0b

Counts

62 → 1

Compiler

Compiled 1225 to 926 computations (24.4% saved)

localize13.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

rewrite69.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`sqrt-div_binary64_1128`
62×	`sqrt-prod_binary64_1127`
36×	`add-sqr-sqrt_binary64_1133`
32×	`frac-times_binary64_1121`
27×	`*-un-lft-identity_binary64_1111`
23×	`flip-+_binary64_1085` `flip3-+_binary64_1114`
20×	`associate-l_binary64_1052` `pow1_binary64_1172`
16×	`add-cube-cbrt_binary64_1146` `associate-*r/_binary64_1053`
13×	`sqrt-pow1_binary64_1129`
12×	`flip3--_binary64_1115` `flip--_binary64_1086`
11×	`add-cbrt-cube_binary64_1147` `associate-r_binary64_1051` `add-exp-log_binary64_1149`
10×	`associate-*l/_binary64_1054` `pow-prod-down_binary64_1182`
9×	`pow1/2_binary64_1191`
6×	`unswap-sqr_binary64_1079`
4×	`prod-exp_binary64_1160` `cbrt-unprod_binary64_1144` `rem-sqrt-square_binary64_1124` `add-log-exp_binary64_1150` `distribute-lft-out_binary64_1062`
3×	`sqrt-unprod_binary64_1131`
2×	`*-commutative_binary64_1042` `difference-of-squares_binary64_1080`
1×	`difference-of-sqr-1_binary64_1081` `distribute-lft-out--_binary64_1063`

Counts

4 → 146

Calls

4 calls:

23.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 (sqrt.f64 (+.f64 x 1)))))
17.0ms	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x 1)))
5.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x 1)))

series275.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

122.0ms	(*.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 (sqrt.f64 (+.f64 x 1))))
72.0ms	(.f64 (sqrt.f64 (sqrt.f64 (+.f64 x 1))) (.f64 (sqrt.f64 (-.f64 x 1)) (sqrt.f64 (sqrt.f64 (+.f64 x 1)))))
41.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x 1)))
39.0ms	(sqrt.f64 (sqrt.f64 (+.f64 x 1)))

simplify106.0ms (3%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4912	3529
1	4912	3529

prune253.0ms (7.2%)

Pruning

1 alts after pruning (0 fresh and 1 done)

	Pruned	Kept	Total
New	158	0	158
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	158	1	159

Merged error: 0b

Counts

159 → 1

Compiler

Compiled 4211 to 3274 computations (22.3% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	31
1	26	31

end0.0ms (0%)

sample1.7s (48.4%)

Algorithm

1×

intervals

Results

625.0ms	3996×	body	2048	nan
352.0ms	8000×	body	128	valid
256.0ms	2082×	body	1024	nan
94.0ms	1016×	body	512	nan
32.0ms	514×	body	256	nan
17.0ms	520×	body	128	nan
2.0ms	12×	body	4096	nan

Compiler

Compiled 48 to 41 computations (14.6% saved)

Details

analyze263.0ms (7.5%)

sample52.0ms (1.5%)

simplify273.0ms (7.8%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite15.0ms (0.4%)

series98.0ms (2.8%)

simplify50.0ms (1.4%)

prune42.0ms (1.2%)

localize9.0ms (0.3%)

rewrite23.0ms (0.7%)

series128.0ms (3.7%)

simplify61.0ms (1.7%)

prune69.0ms (2%)

localize13.0ms (0.4%)

rewrite69.0ms (2%)

series275.0ms (7.8%)

simplify106.0ms (3%)

prune253.0ms (7.2%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.7s (48.4%)

Profiling