Details

analyze78.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	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 12 to 10 computations (16.7% saved)

sample38.0ms (0.1%)

Algorithm

1×

intervals

Results

15.0ms

256×

body

128

valid

Compiler

Compiled 23 to 20 computations (13% saved)

simplify300.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	14	16
1	14	16

prune9.0ms (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: 0.0b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize37.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite301.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`*-un-lft-identity_binary64_760`
41×	`times-frac_binary64_766`
40×	`add-sqr-sqrt_binary64_782`
24×	`add-cube-cbrt_binary64_795`
12×	`distribute-lft-out_binary64_711`
11×	`associate-/r*_binary64_704`
9×	`add-exp-log_binary64_798`
8×	`difference-of-squares_binary64_729`
7×	`add-cbrt-cube_binary64_796`
6×	`associate-/l*_binary64_705` `distribute-lft-out--_binary64_712`
5×	`add-log-exp_binary64_799`
4×	`associate-/r/_binary64_706` `difference-of-sqr-1_binary64_730` `pow1_binary64_821`
3×	`div-inv_binary64_757` `div-exp_binary64_811`
2×	`frac-2neg_binary64_771` `cbrt-undiv_binary64_794` `flip3-+_binary64_763` `flip-+_binary64_734` `clear-num_binary64_759`
1×	`frac-add_binary64_768` `inv-pow_binary64_845` `+-commutative_binary64_690` `sum-log_binary64_851` `rec-exp_binary64_810` `1-exp_binary64_804` `flip--_binary64_735` `pow-flip_binary64_834` `flip3--_binary64_764`

Counts

3 → 100

Calls

3 calls:

214.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
27.0ms	(/.f64 1 (-.f64 x 1))
23.0ms	(/.f64 x (+.f64 x 1))

series182.0ms (0.3%)

Counts

3 → 9

Calls

3 calls:

95.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 x (+.f64 x 1)))
51.0ms	(/.f64 x (+.f64 x 1))
36.0ms	(/.f64 1 (-.f64 x 1))

simplify388.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 0 (291.0ms)

Iter	Nodes	Cost
0	5162	1579

prune1.2s (2%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	80	29	109
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	80	30	110

Merged error: 0b

Counts

110 → 30

Compiler

Compiled 2476 to 1853 computations (25.2% saved)

localize31.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite363.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

129×	`times-frac_binary64_766`
123×	`*-un-lft-identity_binary64_760`
84×	`add-sqr-sqrt_binary64_782`
68×	`add-cube-cbrt_binary64_795`
23×	`associate-/r*_binary64_704`
22×	`distribute-lft-out_binary64_711`
18×	`add-exp-log_binary64_798`
10×	`div-inv_binary64_757` `add-cbrt-cube_binary64_796`
9×	`div-exp_binary64_811`
8×	`difference-of-squares_binary64_729`
7×	`distribute-lft-out--_binary64_712`
6×	`associate-/l*_binary64_705`
5×	`add-log-exp_binary64_799` `pow1_binary64_821`
4×	`cbrt-undiv_binary64_794` `difference-of-sqr-1_binary64_730`
3×	`associate-/r/_binary64_706` `rec-exp_binary64_810` `1-exp_binary64_804`
2×	`frac-2neg_binary64_771` `inv-pow_binary64_845` `clear-num_binary64_759` `pow-flip_binary64_834`
1×	`flip3-+_binary64_763` `frac-add_binary64_768` `flip-+_binary64_734` `+-commutative_binary64_690` `sum-log_binary64_851` `flip--_binary64_735` `flip3--_binary64_764`

Counts

3 → 159

Calls

3 calls:

268.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (/.f64 (+.f64 1 x) x)))
54.0ms	(/.f64 1 (/.f64 (+.f64 1 x) x))
11.0ms	(/.f64 1 (-.f64 x 1))

series97.0ms (0.2%)

Counts

3 → 9

Calls

3 calls:

56.0ms	(+.f64 (/.f64 1 (-.f64 x 1)) (/.f64 1 (/.f64 (+.f64 1 x) x)))
24.0ms	(/.f64 1 (/.f64 (+.f64 1 x) x))
17.0ms	(/.f64 1 (-.f64 x 1))

simplify175.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	5071	2741

prune3.0s (5.1%)

Pruning

46 alts after pruning (44 fresh and 2 done)

	Pruned	Kept	Total
New	139	29	168
Fresh	13	15	28
Picked	0	1	1
Done	0	1	1
Total	152	46	198

Merged error: 0b

Counts

198 → 46

Compiler

Compiled 4259 to 3248 computations (23.7% saved)

localize23.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 1 (/.f64 (+.f64 1 x) x)))
0.1b	(/.f64 1 (/.f64 (+.f64 1 x) x))
0.5b	(/.f64 1 (+.f64 -1 (*.f64 x x)))
16.3b	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))

rewrite125.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`times-frac_binary64_766`
96×	`*-un-lft-identity_binary64_760`
76×	`add-sqr-sqrt_binary64_782`
69×	`add-cube-cbrt_binary64_795`
28×	`add-exp-log_binary64_798`
19×	`associate-/r*_binary64_704`
16×	`add-cbrt-cube_binary64_796`
15×	`associate-l_binary64_701`
13×	`distribute-lft-out_binary64_711`
11×	`div-exp_binary64_811`
8×	`pow1_binary64_821`
7×	`flip3-+_binary64_763` `div-inv_binary64_757` `flip-+_binary64_734`
6×	`add-log-exp_binary64_799` `associate-/l*_binary64_705`
5×	`cbrt-undiv_binary64_794` `associate-/r/_binary64_706` `frac-add_binary64_768`
4×	`prod-exp_binary64_809` `frac-times_binary64_770` `associate-r_binary64_700` `associate-*r/_binary64_702` `rec-exp_binary64_810` `1-exp_binary64_804`
3×	`unswap-sqr_binary64_728`
2×	`frac-2neg_binary64_771` `associate-*l/_binary64_703` `distribute-lft-in_binary64_709` `associate-+l+_binary64_693` `inv-pow_binary64_845` `distribute-rgt-in_binary64_710` `cbrt-unprod_binary64_793` `clear-num_binary64_759` `pow-flip_binary64_834`
1×	`+-commutative_binary64_690` `sum-log_binary64_851` `pow-prod-down_binary64_831` `*-commutative_binary64_691`

Counts

4 → 183

Calls

4 calls:

43.0ms	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 1 (/.f64 (+.f64 1 x) x)))
28.0ms	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))
15.0ms	(/.f64 1 (/.f64 (+.f64 1 x) x))
9.0ms	(/.f64 1 (+.f64 -1 (*.f64 x x)))

series170.0ms (0.3%)

Counts

4 → 12

Calls

4 calls:

95.0ms	(+.f64 (.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1)) (/.f64 1 (/.f64 (+.f64 1 x) x)))
29.0ms	(/.f64 1 (+.f64 -1 (*.f64 x x)))
23.0ms	(.f64 (/.f64 1 (+.f64 -1 (.f64 x x))) (+.f64 x 1))
21.0ms	(/.f64 1 (/.f64 (+.f64 1 x) x))

simplify172.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

195 → 195

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	5839	3350

prune5.1s (8.6%)

Pruning

63 alts after pruning (60 fresh and 3 done)

	Pruned	Kept	Total
New	157	38	195
Fresh	21	22	43
Picked	0	1	1
Done	0	2	2
Total	178	63	241

Merged error: 0b

Counts

241 → 63

Compiler

Compiled 6452 to 4576 computations (29.1% saved)

localize29.0ms (0%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (+.f64 1 x))
0.5b	(/.f64 1 (+.f64 -1 (*.f64 x x)))
0.5b	(/.f64 1 (+.f64 -1 (*.f64 x x)))
16.3b	(.f64 x (/.f64 1 (+.f64 -1 (.f64 x x))))

rewrite93.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64_760`
44×	`add-sqr-sqrt_binary64_782`
41×	`times-frac_binary64_766`
37×	`add-cube-cbrt_binary64_795`
23×	`add-exp-log_binary64_798`
15×	`add-cbrt-cube_binary64_796` `associate-r_binary64_700`
10×	`associate-/r*_binary64_704`
9×	`associate-/l*_binary64_705`
8×	`associate-/r/_binary64_706` `pow1_binary64_821`
7×	`div-exp_binary64_811`
4×	`cbrt-undiv_binary64_794` `distribute-lft-out_binary64_711` `prod-exp_binary64_809` `flip3-+_binary64_763` `add-log-exp_binary64_799` `div-inv_binary64_757` `flip-+_binary64_734`
3×	`unswap-sqr_binary64_728` `frac-2neg_binary64_771` `associate-l_binary64_701` `rec-exp_binary64_810` `clear-num_binary64_759` `1-exp_binary64_804`
2×	`inv-pow_binary64_845` `cbrt-unprod_binary64_793` `pow-flip_binary64_834`
1×	`associate-r/_binary64_702` `pow-prod-down_binary64_831` `un-div-inv_binary64_758` `-commutative_binary64_691`

Counts

4 → 137

Calls

4 calls:

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

series148.0ms (0.2%)

Counts

4 → 12

Calls

4 calls:

51.0ms	(.f64 x (/.f64 1 (+.f64 -1 (.f64 x x))))
38.0ms	(/.f64 1 (+.f64 -1 (*.f64 x x)))
38.0ms	(/.f64 1 (+.f64 -1 (*.f64 x x)))
21.0ms	(/.f64 x (+.f64 1 x))

simplify164.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	5190	2140

prune3.7s (6.3%)

Pruning

64 alts after pruning (60 fresh and 4 done)

	Pruned	Kept	Total
New	123	26	149
Fresh	25	34	59
Picked	0	1	1
Done	0	3	3
Total	148	64	212

Merged error: 0b

Counts

212 → 64

Compiler

Compiled 4316 to 2704 computations (37.3% saved)

regimes4.0s (6.7%)

Compiler: Compiled 17730 to 13492 computations (23.9% saved)

bsearch15.7s (26.3%)

simplify21.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	36
1	20	36

end0.0ms (0%)

sample23.9s (40.1%)

Algorithm

1×

intervals

Results

483.0ms

8000×

body

128

valid

Compiler

Compiled 9078 to 6904 computations (23.9% saved)

Pareto

0.08918224438860337

Details

analyze78.0ms (0.1%)

sample38.0ms (0.1%)

simplify300.0ms (0.5%)

prune9.0ms (0%)

localize37.0ms (0.1%)

rewrite301.0ms (0.5%)

series182.0ms (0.3%)

simplify388.0ms (0.7%)

prune1.2s (2%)

localize31.0ms (0.1%)

rewrite363.0ms (0.6%)

series97.0ms (0.2%)

simplify175.0ms (0.3%)

prune3.0s (5.1%)

localize23.0ms (0%)

rewrite125.0ms (0.2%)

series170.0ms (0.3%)

simplify172.0ms (0.3%)

prune5.1s (8.6%)

localize29.0ms (0%)

rewrite93.0ms (0.2%)

series148.0ms (0.2%)

simplify164.0ms (0.3%)

prune3.7s (6.3%)

regimes4.0s (6.7%)

bsearch15.7s (26.3%)

simplify21.0ms (0%)

end0.0ms (0%)

sample23.9s (40.1%)

Profiling