Details

analyze12.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample45.0ms (0.7%)

Algorithm

1×

intervals

Results

17.0ms	69×	body	1024	valid
8.0ms	126×	body	128	valid
7.0ms	37×	body	512	valid
2.0ms	19×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify252.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	681	19
1	681	19

prune4.0ms (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

Error

31.6b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize12.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
3.4b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite90.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`*-un-lft-identity_binary64_760`
88×	`times-frac_binary64_766`
85×	`add-sqr-sqrt_binary64_782`
37×	`add-cube-cbrt_binary64_795`
34×	`cancel-sign-sub-inv_binary64_726`
27×	`distribute-lft-out_binary64_711`
22×	`difference-of-squares_binary64_729` `distribute-lft-out--_binary64_712`
11×	`associate-/r*_binary64_704`
9×	`difference-of-sqr-1_binary64_730`
7×	`add-exp-log_binary64_798` `add-cbrt-cube_binary64_796` `associate-/l*_binary64_705`
6×	`associate-/r/_binary64_706`
5×	`add-log-exp_binary64_799`
3×	`div-inv_binary64_757` `pow1_binary64_821` `flip--_binary64_735` `flip3--_binary64_764`
2×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `flip3-+_binary64_763` `associate-/l/_binary64_707` `flip-+_binary64_734` `div-exp_binary64_811` `clear-num_binary64_759`
1×	`diff-log_binary64_852` `frac-sub_binary64_769` `sub-neg_binary64_753`

Counts

3 → 147

Calls

3 calls:

59.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))

series92.0ms (1.5%)

Counts

3 → 9

Calls

3 calls:

49.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
27.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
16.0ms	(/.f64 x (+.f64 x 1))

simplify90.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5658	2774

prune268.0ms (4.4%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	153	3	156
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	154	3	157

Error

0.1b

Counts

157 → 3

Compiler

Compiled 3061 to 2159 computations (29.5% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
0.3b	(/.f64 3 (pow.f64 x 3))
0.5b	(/.f64 -1 (*.f64 x x))
7.4b	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

rewrite152.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

73×	`*-un-lft-identity_binary64_760`
68×	`times-frac_binary64_766`
44×	`add-sqr-sqrt_binary64_782`
40×	`add-cube-cbrt_binary64_795`
14×	`add-exp-log_binary64_798` `unpow3_binary64_826`
13×	`cancel-sign-sub-inv_binary64_726` `associate-/r*_binary64_704`
12×	`cube-prod_binary64_788` `unpow-prod-down_binary64_839`
11×	`distribute-lft-out_binary64_711` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796`
8×	`distribute-rgt-out_binary64_713`
6×	`div-inv_binary64_757` `associate-/l*_binary64_705`
5×	`div-exp_binary64_811`
4×	`cube-mult_binary64_790` `sqr-pow_binary64_732` `pow1_binary64_821`
3×	`cbrt-undiv_binary64_794` `frac-sub_binary64_769`
2×	`diff-log_binary64_852` `frac-2neg_binary64_771` `flip3-+_binary64_763` `distribute-rgt1-in_binary64_716` `frac-add_binary64_768` `difference-of-squares_binary64_729` `flip-+_binary64_734` `distribute-lft-out--_binary64_712` `sum-log_binary64_851` `clear-num_binary64_759`
1×	`prod-exp_binary64_809` `pow-exp_binary64_828` `pow-to-exp_binary64_829` `+-commutative_binary64_690` `associate--r+_binary64_696` `cbrt-unprod_binary64_793` `sub-neg_binary64_753` `flip--_binary64_735` `flip3--_binary64_764`

Counts

4 → 141

Calls

4 calls:

54.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
52.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))
11.0ms	(/.f64 3 (pow.f64 x 3))
9.0ms	(/.f64 -1 (*.f64 x x))

series163.0ms (2.7%)

Counts

4 → 12

Calls

4 calls:

76.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
45.0ms	(/.f64 3 (pow.f64 x 3))
25.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))
17.0ms	(/.f64 -1 (*.f64 x x))

simplify75.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5045	2493

prune266.0ms (4.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	152	4	156

Error

0.1b

Counts

156 → 4

Compiler

Compiled 3229 to 2248 computations (30.4% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 x (-.f64 x 1))
0.0b	(*.f64 (+.f64 x 1) (+.f64 x 1))
0.0b	(/.f64 (-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 -1 (*.f64 x x)))
20.5b	(-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1)))

rewrite493.0ms (8.2%)

Algorithm

1×	rewrite-expression-head

Rules

44×	`associate-*r/_binary64_702`
39×	`*-un-lft-identity_binary64_760`
32×	`frac-sub_binary64_769`
31×	`flip3-+_binary64_763` `flip-+_binary64_734`
30×	`add-sqr-sqrt_binary64_782`
22×	`add-cube-cbrt_binary64_795`
20×	`frac-times_binary64_770`
19×	`flip--_binary64_735` `flip3--_binary64_764`
18×	`associate-/l/_binary64_707`
13×	`cancel-sign-sub-inv_binary64_726` `pow1_binary64_821`
11×	`associate-r_binary64_700`
10×	`associate-*l/_binary64_703` `add-exp-log_binary64_798` `distribute-lft-in_binary64_709` `distribute-rgt-in_binary64_710` `add-cbrt-cube_binary64_796`
9×	`times-frac_binary64_766`
8×	`associate--l+_binary64_697`
7×	`associate-l_binary64_701`
6×	`distribute-lft-out_binary64_711` `add-log-exp_binary64_799` `swap-sqr_binary64_727`
5×	`sub-neg_binary64_753`
3×	`associate-/r_binary64_704` `associate-/l_binary64_705`
2×	`unswap-sqr_binary64_728` `prod-exp_binary64_809` `associate-/r/_binary64_706` `difference-of-squares_binary64_729` `associate--r+_binary64_696` `cbrt-unprod_binary64_793` `pow-prod-down_binary64_831` `*-commutative_binary64_691`
1×	`pow2_binary64_841` `diff-log_binary64_852` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `pow-sqr_binary64_733` `pow-plus_binary64_823` `div-inv_binary64_757` `difference-of-sqr-1_binary64_730` `distribute-lft-out--_binary64_712` `div-sub_binary64_765` `div-exp_binary64_811` `clear-num_binary64_759` `pow-prod-up_binary64_830`

Counts

4 → 158

Calls

4 calls:

26.0ms	(/.f64 (-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 -1 (*.f64 x x)))
21.0ms	(-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1)))
15.0ms	(*.f64 (+.f64 x 1) (+.f64 x 1))
13.0ms	(*.f64 x (-.f64 x 1))

series108.0ms (1.8%)

Counts

4 → 12

Calls

4 calls:

37.0ms	(/.f64 (-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1))) (+.f64 -1 (*.f64 x x)))
34.0ms	(-.f64 (.f64 x (-.f64 x 1)) (.f64 (+.f64 x 1) (+.f64 x 1)))
25.0ms	(*.f64 x (-.f64 x 1))
12.0ms	(*.f64 (+.f64 x 1) (+.f64 x 1))

simplify140.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5078	3890

prune384.0ms (6.3%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	169	1	170
Fresh	2	0	2
Picked	1	0	1
Done	0	1	1
Total	172	2	174

Error

Counts

174 → 2

Compiler

Compiled 5140 to 3405 computations (33.8% saved)

localize13.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 -1 (*.f64 x 3))
16.2b	(/.f64 (-.f64 -1 (.f64 x 3)) (+.f64 -1 (.f64 x x)))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`*-un-lft-identity_binary64_760` `add-cube-cbrt_binary64_795` `add-sqr-sqrt_binary64_782`
9×	`times-frac_binary64_766`
4×	`add-exp-log_binary64_798` `add-log-exp_binary64_799` `add-cbrt-cube_binary64_796`
3×	`associate-/r_binary64_704` `associate-/l_binary64_705`
2×	`associate-/r/_binary64_706` `associate-/l/_binary64_707` `pow1_binary64_821` `flip--_binary64_735` `flip3--_binary64_764`
1×	`diff-log_binary64_852` `frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `flip3-+_binary64_763` `cancel-sign-sub-inv_binary64_726` `div-inv_binary64_757` `flip-+_binary64_734` `div-sub_binary64_765` `div-exp_binary64_811` `clear-num_binary64_759` `sub-neg_binary64_753`

Counts

2 → 44

Calls

2 calls:

17.0ms	(/.f64 (-.f64 -1 (.f64 x 3)) (+.f64 -1 (.f64 x x)))
6.0ms	(-.f64 -1 (*.f64 x 3))

series44.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

22.0ms	(/.f64 (-.f64 -1 (.f64 x 3)) (+.f64 -1 (.f64 x x)))
22.0ms	(-.f64 -1 (*.f64 x 3))

simplify118.0ms (2%)

Algorithm

1×	egg-herbie

Counts

50 → 50

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	4906	987
1	4906	987

prune55.0ms (0.9%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	50	0	50
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	50	2	52

Error

Counts

52 → 2

Compiler

Compiled 919 to 639 computations (30.5% saved)

regimes317.0ms (5.2%)

Accuracy

Total 0.0b remaining (91.7%)

Threshold costs 0.0b (91.7%)

Compiler

Compiled 2568 to 1983 computations (22.8% saved)

bsearch68.0ms (1.1%)

Steps

Iters	Range		Point
9	527586723076.3732	1.4724239656240512e+18	23245692697104.223
6	-3.3537279351463606e+50	-5.270554226181804e+49	-1.3460071312632054e+50

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	79	52
1	79	52

end0.0ms (0%)

sample2.7s (45%)

Algorithm

1×

intervals

Results

390.0ms	1996×	body	1024	valid
229.0ms	4266×	body	128	valid
151.0ms	1043×	body	512	valid
53.0ms	208×	body	2048	valid
48.0ms	487×	body	256	valid

Compiler

Compiled 1248 to 964 computations (22.8% saved)

Details

analyze12.0ms (0.2%)

sample45.0ms (0.7%)

simplify252.0ms (4.2%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

rewrite90.0ms (1.5%)

series92.0ms (1.5%)

simplify90.0ms (1.5%)

prune268.0ms (4.4%)

localize17.0ms (0.3%)

rewrite152.0ms (2.5%)

series163.0ms (2.7%)

simplify75.0ms (1.2%)

prune266.0ms (4.4%)

localize19.0ms (0.3%)

rewrite493.0ms (8.2%)

series108.0ms (1.8%)

simplify140.0ms (2.3%)

prune384.0ms (6.3%)

localize13.0ms (0.2%)

rewrite29.0ms (0.5%)

series44.0ms (0.7%)

simplify118.0ms (2%)

prune55.0ms (0.9%)

regimes317.0ms (5.2%)

bsearch68.0ms (1.1%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample2.7s (45%)

Profiling