Details

analyze10.0ms (0.1%)

Algorithm

1×

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

Compiler

Compiled 16 to 14 computations (12.5% saved)

sample40.0ms (0.3%)

Algorithm

1×

intervals

Results

9.0ms	141×	body	128	valid
9.0ms	36×	body	1024	valid
7.0ms	42×	body	512	valid
5.0ms	37×	body	256	valid

Compiler

Compiled 31 to 28 computations (9.7% saved)

simplify165.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	192	22
1	192	22

prune5.0ms (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

Error

10.1b

Counts

2 → 1

Compiler

Compiled 30 to 26 computations (13.3% saved)

localize18.0ms (0.2%)

Local error

Found 8 expressions with local error:

3.2b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
0.0b	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
0.0b	(/.f64 1 (+.f64 x 1))
0.0b	(/.f64 1 (-.f64 x 1))
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))
3.2b	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))

rewrite171.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`*-un-lft-identity_binary64_1070`
74×	`times-frac_binary64_1076`
72×	`add-sqr-sqrt_binary64_1092`
39×	`add-cube-cbrt_binary64_1105`
26×	`cancel-sign-sub-inv_binary64_1036`
18×	`distribute-lft-out--_binary64_1022`
17×	`distribute-lft-out_binary64_1021`
14×	`difference-of-squares_binary64_1039` `associate-+l+_binary64_1003`
12×	`add-exp-log_binary64_1108`
11×	`associate-/r*_binary64_1014` `add-log-exp_binary64_1109`
10×	`div-inv_binary64_1067`
8×	`add-cbrt-cube_binary64_1106`
6×	`pow1_binary64_1131` `associate-/l*_binary64_1015`
4×	`associate-/r/_binary64_1016` `difference-of-sqr-1_binary64_1040` `div-exp_binary64_1121`
3×	`flip--_binary64_1045` `flip3--_binary64_1074` `frac-add_binary64_1078`
2×	`inv-pow_binary64_1155` `frac-2neg_binary64_1081` `frac-sub_binary64_1079` `cbrt-undiv_binary64_1104` `flip-+_binary64_1044` `clear-num_binary64_1069` `rec-exp_binary64_1120` `1-exp_binary64_1114` `flip3-+_binary64_1073` `pow-flip_binary64_1144` `sub-neg_binary64_1063` `diff-log_binary64_1162` `sum-log_binary64_1161`
1×	`+-commutative_binary64_1000` `associate-+l-_binary64_1005`

Counts

4 → 161

Calls

8 calls:

81.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
36.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
11.0ms	(/.f64 1 (-.f64 x 1))
10.0ms	(/.f64 1 (+.f64 x 1))
0.0ms	(/.f64 1 (-.f64 x 1))

series325.0ms (2.8%)

Counts

4 → 47

Calls

4 calls:

155.0ms	(+.f64 (-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x)) (/.f64 1 (-.f64 x 1)))
64.0ms	(-.f64 (/.f64 1 (+.f64 x 1)) (/.f64 2 x))
54.0ms	(/.f64 1 (-.f64 x 1))
51.0ms	(/.f64 1 (+.f64 x 1))

Compiler

Compiled 880 to 759 computations (13.8% saved)

simplify180.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

208 → 208

Iterations

Useful iterations: 0 (116.0ms)

Iter	Nodes	Cost
0	4938	3281
1	4938	3281

prune493.0ms (4.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	205	3	208
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	206	3	209

Error

0.1b

Counts

209 → 3

Compiler

Compiled 4179 to 3320 computations (20.6% saved)

localize25.0ms (0.2%)

Local error

Found 8 expressions with local error:

16.0b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))
0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
0.0b	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
0.0b	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
0.0b	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
0.0b	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
0.0b	(-.f64 x (*.f64 (+.f64 1 x) 2))
16.0b	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

rewrite123.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64_1092`
42×	`associate-*r/_binary64_1012`
35×	`*-un-lft-identity_binary64_1070`
32×	`flip--_binary64_1045` `flip3--_binary64_1074` `frac-add_binary64_1078`
27×	`times-frac_binary64_1076`
20×	`frac-times_binary64_1080` `add-cube-cbrt_binary64_1105`
18×	`flip-+_binary64_1044` `associate-/l/_binary64_1017` `difference-of-squares_binary64_1039` `flip3-+_binary64_1073`
10×	`associate-*l/_binary64_1013`
9×	`associate-/r*_binary64_1014`
8×	`add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108` `add-log-exp_binary64_1109`
7×	`associate-l_binary64_1011`
6×	`pow1_binary64_1131`
5×	`cancel-sign-sub-inv_binary64_1036` `distribute-lft-out--_binary64_1022` `distribute-rgt-in_binary64_1020` `sub-neg_binary64_1063` `distribute-lft-in_binary64_1019`
4×	`cube-prod_binary64_1098` `sqr-pow_binary64_1042` `distribute-rgt-out--_binary64_1024` `unpow3_binary64_1136` `unpow-prod-down_binary64_1149` `associate-+l+_binary64_1003`
3×	`associate-r_binary64_1010` `associate-/l*_binary64_1015`
2×	`associate-/r/_binary64_1016` `associate-+r+_binary64_1002`
1×	`frac-2neg_binary64_1081` `cbrt-undiv_binary64_1104` `cbrt-unprod_binary64_1103` `*-commutative_binary64_1001` `difference-of-sqr-1_binary64_1040` `prod-exp_binary64_1119` `clear-num_binary64_1069` `+-commutative_binary64_1000` `unswap-sqr_binary64_1038` `div-exp_binary64_1121` `pow-prod-down_binary64_1141` `diff-log_binary64_1162` `sum-log_binary64_1161` `div-inv_binary64_1067`

Counts

4 → 150

Calls

8 calls:

34.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
23.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))
17.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
6.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
0.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))

series288.0ms (2.5%)

Counts

4 → 29

Calls

4 calls:

115.0ms	(.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2)))
113.0ms	(/.f64 (+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x))) (-.f64 (pow.f64 x 3) x))
46.0ms	(-.f64 x (*.f64 (+.f64 1 x) 2))
15.0ms	(+.f64 (.f64 (-.f64 x 1) (-.f64 x (.f64 (+.f64 1 x) 2))) (*.f64 x (+.f64 1 x)))

Compiler

Compiled 628 to 505 computations (19.6% saved)

simplify203.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	5090	6862

prune574.0ms (4.9%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	181	1	182

Error

0.1b

Counts

182 → 1

Compiler

Compiled 7134 to 4964 computations (30.4% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(/.f64 2 (-.f64 (pow.f64 x 3) x))
0.1b	(/.f64 2 (-.f64 (pow.f64 x 3) x))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64_1092`
27×	`times-frac_binary64_1076` `*-un-lft-identity_binary64_1070`
16×	`difference-of-squares_binary64_1039`
15×	`add-cube-cbrt_binary64_1105`
9×	`associate-/r*_binary64_1014`
4×	`cube-prod_binary64_1098` `sqr-pow_binary64_1042` `distribute-rgt-out--_binary64_1024` `distribute-lft-out--_binary64_1022` `unpow3_binary64_1136` `unpow-prod-down_binary64_1149`
3×	`add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108` `associate-/l*_binary64_1015`
2×	`associate-/r/_binary64_1016`
1×	`frac-2neg_binary64_1081` `flip--_binary64_1045` `cbrt-undiv_binary64_1104` `flip3--_binary64_1074` `clear-num_binary64_1069` `div-exp_binary64_1121` `add-log-exp_binary64_1109` `pow1_binary64_1131` `div-inv_binary64_1067`

Counts

1 → 53

Calls

2 calls:

15.0ms	(/.f64 2 (-.f64 (pow.f64 x 3) x))
0.0ms	(/.f64 2 (-.f64 (pow.f64 x 3) x))

series106.0ms (0.9%)

Counts

1 → 11

Calls

1 calls:

106.0ms

(/.f64 2 (-.f64 (pow.f64 x 3) x))

Compiler

Compiled 199 to 181 computations (9% saved)

simplify107.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4925	1199
1	4925	1199

prune133.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	61	3	64
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	61	4	65

Error

0.0b

Counts

65 → 4

Compiler

Compiled 988 to 736 computations (25.5% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.1b	(/.f64 (/.f64 2 x) (-.f64 (*.f64 x x) 1))
0.1b	(/.f64 (/.f64 2 x) (-.f64 (*.f64 x x) 1))

rewrite40.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`times-frac_binary64_1076`
78×	`add-sqr-sqrt_binary64_1092` `*-un-lft-identity_binary64_1070`
64×	`add-cube-cbrt_binary64_1105`
28×	`difference-of-squares_binary64_1039`
14×	`difference-of-sqr-1_binary64_1040`
13×	`associate-/l*_binary64_1015`
8×	`div-inv_binary64_1067`
6×	`add-cbrt-cube_binary64_1106` `add-exp-log_binary64_1108` `associate-/r*_binary64_1014`
3×	`cbrt-undiv_binary64_1104` `div-exp_binary64_1121`
2×	`associate-/r/_binary64_1016`
1×	`frac-2neg_binary64_1081` `flip--_binary64_1045` `flip3--_binary64_1074` `associate-/l/_binary64_1017` `clear-num_binary64_1069` `add-log-exp_binary64_1109` `pow1_binary64_1131`

Counts

1 → 114

Calls

2 calls:

18.0ms	(/.f64 (/.f64 2 x) (-.f64 (*.f64 x x) 1))
0.0ms	(/.f64 (/.f64 2 x) (-.f64 (*.f64 x x) 1))

series105.0ms (0.9%)

Counts

1 → 11

Calls

1 calls:

105.0ms

(/.f64 (/.f64 2 x) (-.f64 (*.f64 x x) 1))

Compiler

Compiled 199 to 181 computations (9% saved)

simplify127.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	5121	3044

prune218.0ms (1.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	124	5	129

Error

0.0b

Counts

129 → 5

Compiler

Compiled 2256 to 1512 computations (33% saved)

simplify40.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	349	1500
1	349	1500

regimes172.0ms (1.5%)

Accuracy

Total 0.1b remaining (97.4%)

Threshold costs 0.1b (97.4%)

Compiler

Compiled 998 to 831 computations (16.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	16
1	20	16

end0.0ms (0%)

sample7.9s (68.1%)

Algorithm

1×

intervals

Results

366.0ms	1285×	body	1024	valid
324.0ms	4414×	body	128	valid
316.0ms	1497×	body	512	valid
113.0ms	804×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 3013 to 2509 computations (16.7% saved)

Pareto

0.06963029484056187

Details

analyze10.0ms (0.1%)

sample40.0ms (0.3%)

simplify165.0ms (1.4%)

prune5.0ms (0%)

localize18.0ms (0.2%)

rewrite171.0ms (1.5%)

series325.0ms (2.8%)

simplify180.0ms (1.5%)

prune493.0ms (4.2%)

localize25.0ms (0.2%)

rewrite123.0ms (1.1%)

series288.0ms (2.5%)

simplify203.0ms (1.7%)

prune574.0ms (4.9%)

localize9.0ms (0.1%)

rewrite24.0ms (0.2%)

series106.0ms (0.9%)

simplify107.0ms (0.9%)

prune133.0ms (1.1%)

localize10.0ms (0.1%)

rewrite40.0ms (0.3%)

series105.0ms (0.9%)

simplify127.0ms (1.1%)

prune218.0ms (1.9%)

simplify40.0ms (0.3%)

regimes172.0ms (1.5%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample7.9s (68.1%)

Profiling