Details

analyze76.0ms (1.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
46.8%	53.1%	0.1%	6
70.2%	29.7%	0.1%	7
76.5%	23.4%	0.1%	8
83.5%	16.4%	0.1%	9
87%	12.9%	0.1%	10
91.1%	8.8%	0.1%	11
93.2%	6.7%	0.1%	12
95.4%	4.5%	0.1%	13
96.5%	3.4%	0.1%	14

Compiler

Compiled 18 to 10 computations (44.4% saved)

sample16.0ms (0.3%)

Algorithm

1×

intervals

Results

10.0ms

256×

body

128

valid

Compiler

Compiled 35 to 21 computations (40% saved)

simplify304.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (134.0ms)

Iter	Nodes	Cost
0	4936	25
1	4936	25

prune2.0ms (0%)

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: 21.4b

Counts

2 → 1

Compiler

Compiled 34 to 18 computations (47.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
0.0b	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
21.2b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))

rewrite75.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`frac-times_binary64_9977` `flip3-+_binary64_9970` `flip-+_binary64_9941`
31×	`add-cbrt-cube_binary64_10003` `add-exp-log_binary64_10005`
30×	`associate-*l/_binary64_9910`
27×	`*-un-lft-identity_binary64_9967`
26×	`associate-/r/_binary64_9913`
18×	`associate-*r/_binary64_9909`
15×	`pow1_binary64_10028`
13×	`prod-exp_binary64_10016` `cbrt-unprod_binary64_10000`
11×	`add-sqr-sqrt_binary64_9989`
9×	`distribute-lft-out_binary64_9918` `associate-r_binary64_9907`
8×	`add-cube-cbrt_binary64_10002`
6×	`div-exp_binary64_10018` `cbrt-undiv_binary64_10001` `swap-sqr_binary64_9934`
5×	`associate-l_binary64_9908`
4×	`pow-prod-down_binary64_10038`
3×	`add-log-exp_binary64_10006`
2×	`distribute-lft-in_binary64_9916` `distribute-rgt-in_binary64_9917` `unswap-sqr_binary64_9935` `*-commutative_binary64_9898`
1×	`times-frac_binary64_9973` `associate-/l_binary64_9912` `pow2_binary64_10048` `div-inv_binary64_9964` `pow-plus_binary64_10030` `associate-/r_binary64_9911` `pow-sqr_binary64_9940` `frac-2neg_binary64_9978` `clear-num_binary64_9966` `pow-prod-up_binary64_10037`

Counts

3 → 140

Calls

3 calls:

22.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
20.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
10.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

series311.0ms (5.5%)

Counts

3 → 9

Calls

3 calls:

214.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
71.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
26.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

simplify86.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4957	3602
1	4957	3602

prune182.0ms (3.2%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	140	9	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	141	9	150

Merged error: 7.5b

Counts

150 → 9

Compiler

Compiled 4247 to 1691 computations (60.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (+.f64 x y) 2)
0.1b	(/.f64 (*.f64 y (/.f64 x (pow.f64 (+.f64 x y) 2))) (+.f64 (+.f64 x y) 1))
7.8b	(*.f64 y (/.f64 x (pow.f64 (+.f64 x y) 2)))
20.0b	(/.f64 x (pow.f64 (+.f64 x y) 2))

rewrite62.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`*-un-lft-identity_binary64_9967`
63×	`times-frac_binary64_9973`
55×	`add-sqr-sqrt_binary64_9989`
43×	`add-cube-cbrt_binary64_10002`
36×	`add-exp-log_binary64_10005`
33×	`unpow-prod-down_binary64_10046`
31×	`associate-r_binary64_9907`
20×	`add-cbrt-cube_binary64_10003`
14×	`div-exp_binary64_10018` `distribute-lft-out_binary64_9918` `associate-/r*_binary64_9911`
9×	`unpow2_binary64_10032` `sqr-pow_binary64_9939`
8×	`prod-exp_binary64_10016`
7×	`pow1_binary64_10028`
6×	`cbrt-undiv_binary64_10001`
5×	`unswap-sqr_binary64_9935`
4×	`cbrt-unprod_binary64_10000` `pow-to-exp_binary64_10036` `associate-/l*_binary64_9912` `add-log-exp_binary64_10006` `pow-exp_binary64_10035`
3×	`associate-l_binary64_9908` `pow-unpow_binary64_10044` `div-inv_binary64_9964`
2×	`associate-*r/_binary64_9909` `frac-2neg_binary64_9978` `clear-num_binary64_9966` `associate-/r/_binary64_9913`
1×	`flip3-+_binary64_9970` `associate-/l/_binary64_9914` `flip-+_binary64_9941` `pow-prod-down_binary64_10038` `*-commutative_binary64_9898` `pow-pow_binary64_10039`

Counts

4 → 159

Calls

4 calls:

17.0ms	(/.f64 (*.f64 y (/.f64 x (pow.f64 (+.f64 x y) 2))) (+.f64 (+.f64 x y) 1))
16.0ms	(*.f64 y (/.f64 x (pow.f64 (+.f64 x y) 2)))
8.0ms	(/.f64 x (pow.f64 (+.f64 x y) 2))
5.0ms	(pow.f64 (+.f64 x y) 2)

series639.0ms (11.4%)

Counts

4 → 12

Calls

4 calls:

404.0ms	(/.f64 (*.f64 y (/.f64 x (pow.f64 (+.f64 x y) 2))) (+.f64 (+.f64 x y) 1))
114.0ms	(*.f64 y (/.f64 x (pow.f64 (+.f64 x y) 2)))
94.0ms	(/.f64 x (pow.f64 (+.f64 x y) 2))
27.0ms	(pow.f64 (+.f64 x y) 2)

simplify54.0ms (1%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5274	2666

prune174.0ms (3.1%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	164	7	171
Fresh	6	2	8
Picked	0	1	1
Done	0	0	0
Total	170	10	180

Merged error: 0.0b

Counts

180 → 10

Compiler

Compiled 3638 to 1638 computations (55% saved)

localize8.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (+.f64 x y))
0.0b	(/.f64 y (+.f64 x y))
0.0b	(*.f64 (/.f64 y (+.f64 x y)) (/.f64 x (+.f64 x y)))
0.1b	(/.f64 (*.f64 (/.f64 y (+.f64 x y)) (/.f64 x (+.f64 x y))) (+.f64 (+.f64 x y) 1))

rewrite68.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64_9967`
57×	`times-frac_binary64_9973`
52×	`add-sqr-sqrt_binary64_9989`
40×	`add-cube-cbrt_binary64_10002`
38×	`add-cbrt-cube_binary64_10003` `add-exp-log_binary64_10005`
20×	`distribute-lft-out_binary64_9918`
18×	`associate-l_binary64_9908` `associate-r_binary64_9907`
15×	`div-exp_binary64_10018` `cbrt-undiv_binary64_10001`
13×	`associate-/r*_binary64_9911`
10×	`associate-/r/_binary64_9913`
8×	`prod-exp_binary64_10016` `cbrt-unprod_binary64_10000`
7×	`associate-/l*_binary64_9912`
6×	`pow1_binary64_10028`
5×	`flip3-+_binary64_9970` `flip-+_binary64_9941` `div-inv_binary64_9964`
4×	`add-log-exp_binary64_10006` `unswap-sqr_binary64_9935`
3×	`associate-/l/_binary64_9914` `frac-2neg_binary64_9978` `clear-num_binary64_9966`
2×	`frac-times_binary64_9977` `associate-l/_binary64_9910` `associate-r/_binary64_9909`
1×	`pow-prod-down_binary64_10038` `*-commutative_binary64_9898`

Counts

4 → 162

Calls

4 calls:

21.0ms	(*.f64 (/.f64 y (+.f64 x y)) (/.f64 x (+.f64 x y)))
19.0ms	(/.f64 (*.f64 (/.f64 y (+.f64 x y)) (/.f64 x (+.f64 x y))) (+.f64 (+.f64 x y) 1))
6.0ms	(/.f64 y (+.f64 x y))
6.0ms	(/.f64 x (+.f64 x y))

series453.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(/.f64 (*.f64 (/.f64 y (+.f64 x y)) (/.f64 x (+.f64 x y))) (+.f64 (+.f64 x y) 1))
127.0ms	(*.f64 (/.f64 y (+.f64 x y)) (/.f64 x (+.f64 x y)))
51.0ms	(/.f64 x (+.f64 x y))
51.0ms	(/.f64 y (+.f64 x y))

simplify85.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4973	2987
1	4973	2987

prune151.0ms (2.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	170	4	174
Fresh	3	5	8
Picked	1	0	1
Done	1	0	1
Total	175	9	184

Merged error: 0b

Counts

184 → 9

Compiler

Compiled 4087 to 1137 computations (72.2% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (+.f64 x y))
0.0b	(*.f64 (/.f64 1 (/.f64 (+.f64 y x) y)) (/.f64 x (+.f64 x y)))
0.1b	(/.f64 (*.f64 (/.f64 1 (/.f64 (+.f64 y x) y)) (/.f64 x (+.f64 x y))) (+.f64 (+.f64 x y) 1))
0.4b	(/.f64 1 (/.f64 (+.f64 y x) y))

rewrite118.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

226×	`times-frac_binary64_9973`
183×	`*-un-lft-identity_binary64_9967`
146×	`add-sqr-sqrt_binary64_9989`
123×	`add-exp-log_binary64_10005`
113×	`add-cube-cbrt_binary64_10002`
65×	`div-exp_binary64_10018`
61×	`add-cbrt-cube_binary64_10003`
53×	`associate-l_binary64_9908`
34×	`distribute-lft-out_binary64_9918`
29×	`cbrt-undiv_binary64_10001`
28×	`prod-exp_binary64_10016`
25×	`associate-/r*_binary64_9911`
18×	`associate-r_binary64_9907`
12×	`cbrt-unprod_binary64_10000` `div-inv_binary64_9964`
10×	`1-exp_binary64_10011` `rec-exp_binary64_10017` `unswap-sqr_binary64_9935`
8×	`associate-/r/_binary64_9913`
7×	`associate-/l*_binary64_9912` `pow1_binary64_10028`
4×	`add-log-exp_binary64_10006`
3×	`flip3-+_binary64_9970` `associate-/l/_binary64_9914` `flip-+_binary64_9941` `frac-2neg_binary64_9978` `clear-num_binary64_9966`
2×	`frac-times_binary64_9977` `associate-l/_binary64_9910` `associate-r/_binary64_9909`
1×	`inv-pow_binary64_10052` `pow-prod-down_binary64_10038` `pow-flip_binary64_10041` `*-commutative_binary64_9898`

Counts

4 → 282

Calls

4 calls:

40.0ms	(*.f64 (/.f64 1 (/.f64 (+.f64 y x) y)) (/.f64 x (+.f64 x y)))
25.0ms	(/.f64 (*.f64 (/.f64 1 (/.f64 (+.f64 y x) y)) (/.f64 x (+.f64 x y))) (+.f64 (+.f64 x y) 1))
9.0ms	(/.f64 1 (/.f64 (+.f64 y x) y))
6.0ms	(/.f64 x (+.f64 x y))

series420.0ms (7.5%)

Counts

4 → 12

Calls

4 calls:

201.0ms	(/.f64 (*.f64 (/.f64 1 (/.f64 (+.f64 y x) y)) (/.f64 x (+.f64 x y))) (+.f64 (+.f64 x y) 1))
112.0ms	(*.f64 (/.f64 1 (/.f64 (+.f64 y x) y)) (/.f64 x (+.f64 x y)))
58.0ms	(/.f64 1 (/.f64 (+.f64 y x) y))
48.0ms	(/.f64 x (+.f64 x y))

simplify115.0ms (2%)

Algorithm

1×	egg-herbie

Counts

294 → 294

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4965	5551
1	4965	5551

prune266.0ms (4.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	294	0	294
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	294	9	303

Merged error: 0b

Counts

303 → 9

Compiler

Compiled 7260 to 2127 computations (70.7% saved)

regimes372.0ms (6.6%)

Compiler: Compiled 5064 to 2915 computations (42.4% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	25
1	14	25

end0.0ms (0%)

sample1.6s (27.6%)

Algorithm

1×

intervals

Results

291.0ms

8000×

body

128

valid

Compiler

Compiled 1712 to 986 computations (42.4% saved)

Details

analyze76.0ms (1.3%)

sample16.0ms (0.3%)

simplify304.0ms (5.4%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite75.0ms (1.3%)

series311.0ms (5.5%)

simplify86.0ms (1.5%)

prune182.0ms (3.2%)

localize11.0ms (0.2%)

rewrite62.0ms (1.1%)

series639.0ms (11.4%)

simplify54.0ms (1%)

prune174.0ms (3.1%)

localize8.0ms (0.1%)

rewrite68.0ms (1.2%)

series453.0ms (8.1%)

simplify85.0ms (1.5%)

prune151.0ms (2.7%)

localize10.0ms (0.2%)

rewrite118.0ms (2.1%)

series420.0ms (7.5%)

simplify115.0ms (2%)

prune266.0ms (4.7%)

regimes372.0ms (6.6%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.6s (27.6%)

Profiling