Details

analyze158.0ms (2%)

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)

sample30.0ms (0.4%)

Algorithm

1×

intervals

Results

17.0ms

256×

body

128

valid

Compiler

Compiled 35 to 21 computations (40% saved)

simplify430.0ms (5.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (251.0ms)

Iter	Nodes	Cost
0	4953	25
1	4953	25

prune4.0ms (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: 22.8b

Counts

2 → 1

Compiler

Compiled 34 to 18 computations (47.1% saved)

localize15.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
0.1b	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
22.6b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))

rewrite117.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`frac-times_binary64_13387` `flip-+_binary64_13351` `flip3-+_binary64_13380`
31×	`add-exp-log_binary64_13415` `add-cbrt-cube_binary64_13413`
30×	`associate-*l/_binary64_13320`
27×	`*-un-lft-identity_binary64_13377`
26×	`associate-/r/_binary64_13323`
18×	`associate-*r/_binary64_13319`
15×	`pow1_binary64_13438`
13×	`prod-exp_binary64_13426` `cbrt-unprod_binary64_13410`
11×	`add-sqr-sqrt_binary64_13399`
9×	`associate-r_binary64_13317` `distribute-lft-out_binary64_13328`
8×	`add-cube-cbrt_binary64_13412`
6×	`swap-sqr_binary64_13344` `div-exp_binary64_13428` `cbrt-undiv_binary64_13411`
5×	`associate-l_binary64_13318`
4×	`pow-prod-down_binary64_13448`
3×	`add-log-exp_binary64_13416`
2×	`distribute-rgt-in_binary64_13327` `distribute-lft-in_binary64_13326` `unswap-sqr_binary64_13345` `*-commutative_binary64_13308`
1×	`div-inv_binary64_13374` `clear-num_binary64_13376` `associate-/r_binary64_13321` `times-frac_binary64_13383` `pow-plus_binary64_13440` `pow-sqr_binary64_13350` `pow-prod-up_binary64_13447` `pow2_binary64_13458` `frac-2neg_binary64_13388` `associate-/l_binary64_13322`

Counts

3 → 140

Calls

3 calls:

33.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
31.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
16.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

series255.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

175.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))
56.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1))
24.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

simplify163.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	5027	3629

prune307.0ms (4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	144	5	149
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	144	6	150

Merged error: 7.6b

Counts

150 → 6

Compiler

Compiled 4108 to 1600 computations (61.1% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (+.f64 x y) 2)
0.0b	(/.f64 (*.f64 y (/.f64 x (pow.f64 (+.f64 x y) 2))) (+.f64 (+.f64 x y) 1))
8.2b	(*.f64 y (/.f64 x (pow.f64 (+.f64 x y) 2)))
19.8b	(/.f64 x (pow.f64 (+.f64 x y) 2))

rewrite98.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

69×	`*-un-lft-identity_binary64_13377`
63×	`times-frac_binary64_13383`
55×	`add-sqr-sqrt_binary64_13399`
43×	`add-cube-cbrt_binary64_13412`
36×	`add-exp-log_binary64_13415`
33×	`unpow-prod-down_binary64_13456`
31×	`associate-r_binary64_13317`
20×	`add-cbrt-cube_binary64_13413`
14×	`associate-/r*_binary64_13321` `distribute-lft-out_binary64_13328` `div-exp_binary64_13428`
9×	`unpow2_binary64_13442` `sqr-pow_binary64_13349`
8×	`prod-exp_binary64_13426`
7×	`pow1_binary64_13438`
6×	`cbrt-undiv_binary64_13411`
5×	`unswap-sqr_binary64_13345`
4×	`cbrt-unprod_binary64_13410` `pow-to-exp_binary64_13446` `pow-exp_binary64_13445` `add-log-exp_binary64_13416` `associate-/l*_binary64_13322`
3×	`div-inv_binary64_13374` `pow-unpow_binary64_13454` `associate-l_binary64_13318`
2×	`clear-num_binary64_13376` `associate-*r/_binary64_13319` `associate-/r/_binary64_13323` `frac-2neg_binary64_13388`
1×	`associate-/l/_binary64_13324` `pow-pow_binary64_13449` `pow-prod-down_binary64_13448` `*-commutative_binary64_13308` `flip-+_binary64_13351` `flip3-+_binary64_13380`

Counts

4 → 159

Calls

4 calls:

27.0ms	(/.f64 (*.f64 y (/.f64 x (pow.f64 (+.f64 x y) 2))) (+.f64 (+.f64 x y) 1))
25.0ms	(*.f64 y (/.f64 x (pow.f64 (+.f64 x y) 2)))
12.0ms	(/.f64 x (pow.f64 (+.f64 x y) 2))
8.0ms	(pow.f64 (+.f64 x y) 2)

series410.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

186.0ms	(/.f64 (*.f64 y (/.f64 x (pow.f64 (+.f64 x y) 2))) (+.f64 (+.f64 x y) 1))
106.0ms	(*.f64 y (/.f64 x (pow.f64 (+.f64 x y) 2)))
92.0ms	(/.f64 x (pow.f64 (+.f64 x y) 2))
24.0ms	(pow.f64 (+.f64 x y) 2)

simplify152.0ms (2%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4966	2666
1	4966	2666

prune313.0ms (4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	166	5	171
Fresh	3	1	4
Picked	1	0	1
Done	0	1	1
Total	170	7	177

Merged error: 0.0b

Counts

177 → 7

Compiler

Compiled 3565 to 1597 computations (55.2% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite120.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`*-un-lft-identity_binary64_13377`
57×	`times-frac_binary64_13383`
52×	`add-sqr-sqrt_binary64_13399`
40×	`add-cube-cbrt_binary64_13412`
38×	`add-exp-log_binary64_13415` `add-cbrt-cube_binary64_13413`
20×	`distribute-lft-out_binary64_13328`
18×	`associate-r_binary64_13317` `associate-l_binary64_13318`
15×	`div-exp_binary64_13428` `cbrt-undiv_binary64_13411`
13×	`associate-/r*_binary64_13321`
10×	`associate-/r/_binary64_13323`
8×	`prod-exp_binary64_13426` `cbrt-unprod_binary64_13410`
7×	`associate-/l*_binary64_13322`
6×	`pow1_binary64_13438`
5×	`div-inv_binary64_13374` `flip-+_binary64_13351` `flip3-+_binary64_13380`
4×	`unswap-sqr_binary64_13345` `add-log-exp_binary64_13416`
3×	`associate-/l/_binary64_13324` `clear-num_binary64_13376` `frac-2neg_binary64_13388`
2×	`associate-l/_binary64_13320` `frac-times_binary64_13387` `associate-r/_binary64_13319`
1×	`pow-prod-down_binary64_13448` `*-commutative_binary64_13308`

Counts

4 → 162

Calls

4 calls:

41.0ms	(*.f64 (/.f64 y (+.f64 x y)) (/.f64 x (+.f64 x y)))
30.0ms	(/.f64 (*.f64 (/.f64 y (+.f64 x y)) (/.f64 x (+.f64 x y))) (+.f64 (+.f64 x y) 1))
10.0ms	(/.f64 y (+.f64 x y))
9.0ms	(/.f64 x (+.f64 x y))

series359.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

165.0ms	(/.f64 (*.f64 (/.f64 y (+.f64 x y)) (/.f64 x (+.f64 x y))) (+.f64 (+.f64 x y) 1))
96.0ms	(*.f64 (/.f64 y (+.f64 x y)) (/.f64 x (+.f64 x y)))
56.0ms	(/.f64 y (+.f64 x y))
41.0ms	(/.f64 x (+.f64 x y))

simplify156.0ms (2%)

Algorithm

1×	egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	4981	2987
1	4981	2987

prune265.0ms (3.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	170	4	174
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	173	8	181

Merged error: 0.0b

Counts

181 → 8

Compiler

Compiled 4047 to 1104 computations (72.7% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

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

rewrite244.0ms (3.2%)

Algorithm

1×	rewrite-expression-head

Rules

429×	`*-un-lft-identity_binary64_13377`
357×	`times-frac_binary64_13383`
177×	`add-sqr-sqrt_binary64_13399`
156×	`add-cube-cbrt_binary64_13412`
155×	`distribute-lft-out_binary64_13328`
96×	`associate-r_binary64_13317`
34×	`add-exp-log_binary64_13415` `add-cbrt-cube_binary64_13413`
32×	`associate-/r/_binary64_13323`
24×	`associate-/l*_binary64_13322`
18×	`associate-l_binary64_13318`
16×	`div-inv_binary64_13374` `flip-+_binary64_13351` `flip3-+_binary64_13380`
14×	`div-exp_binary64_13428` `cbrt-undiv_binary64_13411`
13×	`associate-/r*_binary64_13321`
6×	`prod-exp_binary64_13426` `cbrt-unprod_binary64_13410` `unswap-sqr_binary64_13345` `pow1_binary64_13438`
4×	`add-log-exp_binary64_13416`
3×	`clear-num_binary64_13376` `frac-2neg_binary64_13388`
1×	`associate-/l/_binary64_13324` `associate-l/_binary64_13320` `pow-prod-down_binary64_13448` `-commutative_binary64_13308` `frac-times_binary64_13387` `associate-*r/_binary64_13319`

Counts

4 → 340

Calls

4 calls:

107.0ms	(*.f64 (/.f64 y (+.f64 y x)) (/.f64 (/.f64 x (+.f64 y x)) (+.f64 (+.f64 y x) 1)))
34.0ms	(/.f64 (/.f64 x (+.f64 y x)) (+.f64 (+.f64 y x) 1))
10.0ms	(/.f64 x (+.f64 y x))
10.0ms	(/.f64 y (+.f64 y x))

series363.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

175.0ms	(*.f64 (/.f64 y (+.f64 y x)) (/.f64 (/.f64 x (+.f64 y x)) (+.f64 (+.f64 y x) 1)))
91.0ms	(/.f64 (/.f64 x (+.f64 y x)) (+.f64 (+.f64 y x) 1))
53.0ms	(/.f64 y (+.f64 y x))
43.0ms	(/.f64 x (+.f64 y x))

simplify233.0ms (3%)

Algorithm

1×	egg-herbie

Counts

352 → 352

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	5028	8623

prune554.0ms (7.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	350	2	352
Fresh	2	3	5
Picked	1	0	1
Done	0	2	2
Total	353	7	360

Merged error: 0b

Counts

360 → 7

Compiler

Compiled 9373 to 2647 computations (71.8% saved)

regimes489.0ms (6.3%)

Compiler: Compiled 3624 to 2075 computations (42.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	25
1	14	25

end0.0ms (0%)

sample2.4s (31.6%)

Algorithm

1×

intervals

Results

533.0ms

8000×

body

128

valid

Compiler

Compiled 1232 to 706 computations (42.7% saved)

Details

analyze158.0ms (2%)

sample30.0ms (0.4%)

simplify430.0ms (5.6%)

prune4.0ms (0%)

localize15.0ms (0.2%)

rewrite117.0ms (1.5%)

series255.0ms (3.3%)

simplify163.0ms (2.1%)

prune307.0ms (4%)

localize16.0ms (0.2%)

rewrite98.0ms (1.3%)

series410.0ms (5.3%)

simplify152.0ms (2%)

prune313.0ms (4%)

localize16.0ms (0.2%)

rewrite120.0ms (1.6%)

series359.0ms (4.6%)

simplify156.0ms (2%)

prune265.0ms (3.4%)

localize20.0ms (0.3%)

rewrite244.0ms (3.2%)

series363.0ms (4.7%)

simplify233.0ms (3%)

prune554.0ms (7.2%)

regimes489.0ms (6.3%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.4s (31.6%)

Profiling