Details

analyze80.0ms (3.2%)

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

sample16.0ms (0.7%)

Algorithm

1×

intervals

Results

9.0ms

256×

body

valid

simplify59.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5284	17

prune5.0ms (0.2%)

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: 15.2b

Counts

2 → 1

localize8.0ms (0.3%)

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) 1.0))
15.1b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1.0)))

rewrite59.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`flip3-+_binary64` `flip-+_binary64` `frac-times_binary64`
31×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
30×	`associate-*l/_binary64`
27×	`*-un-lft-identity_binary64`
26×	`associate-/r/_binary64`
18×	`associate-*r/_binary64`
15×	`pow1_binary64`
13×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`distribute-lft-out_binary64` `associate-r_binary64`
8×	`add-cube-cbrt_binary64`
6×	`swap-sqr_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
5×	`associate-l_binary64`
4×	`pow-prod-down_binary64`
3×	`add-log-exp_binary64`
2×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `pow-prod-up_binary64` `pow-plus_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

3 → 140

Calls

3 calls:

23.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1.0)))
19.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1.0))
9.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

series47.0ms (1.9%)

Counts

3 → 9

Calls

3 calls:

27.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1.0)))
12.0ms	(.f64 (.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1.0))
8.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

simplify67.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5000	2686

prune234.0ms (9.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	137	12	149
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	138	12	150

Merged error: 8.2b

Counts

150 → 12

localize10.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 x (+.f64 x y))
0.1b	(.f64 (+.f64 (.f64 x (+.f64 x y)) (*.f64 y (+.f64 x y))) (+.f64 (+.f64 x y) 1.0))
2.6b	(+.f64 (.f64 x (+.f64 x y)) (.f64 y (+.f64 x y)))
15.1b	(/.f64 (.f64 x y) (.f64 (+.f64 (.f64 x (+.f64 x y)) (.f64 y (+.f64 x y))) (+.f64 (+.f64 x y) 1.0)))

rewrite61.0ms (2.4%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`associate-*r/_binary64`
50×	`flip3-+_binary64` `flip-+_binary64`
28×	`frac-add_binary64`
24×	`frac-times_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/r/_binary64`
15×	`*-un-lft-identity_binary64`
13×	`add-sqr-sqrt_binary64`
12×	`associate-*l/_binary64`
9×	`associate-r_binary64`
8×	`pow1_binary64` `add-cube-cbrt_binary64`
7×	`associate-l_binary64`
6×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
4×	`distribute-lft-out_binary64` `cbrt-undiv_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `div-exp_binary64`
3×	`distribute-rgt-out_binary64` `unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `associate-+l+_binary64` `associate-+r+_binary64` `*-commutative_binary64`
1×	`associate-/r_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `times-frac_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 128

Calls

4 calls:

19.0ms	(/.f64 (.f64 x y) (.f64 (+.f64 (.f64 x (+.f64 x y)) (.f64 y (+.f64 x y))) (+.f64 (+.f64 x y) 1.0)))
17.0ms	(.f64 (+.f64 (.f64 x (+.f64 x y)) (*.f64 y (+.f64 x y))) (+.f64 (+.f64 x y) 1.0))
11.0ms	(+.f64 (.f64 x (+.f64 x y)) (.f64 y (+.f64 x y)))
7.0ms	(*.f64 x (+.f64 x y))

series62.0ms (2.5%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(/.f64 (.f64 x y) (.f64 (+.f64 (.f64 x (+.f64 x y)) (.f64 y (+.f64 x y))) (+.f64 (+.f64 x y) 1.0)))
15.0ms	(.f64 (+.f64 (.f64 x (+.f64 x y)) (*.f64 y (+.f64 x y))) (+.f64 (+.f64 x y) 1.0))
9.0ms	(*.f64 x (+.f64 x y))
8.0ms	(+.f64 (.f64 x (+.f64 x y)) (.f64 y (+.f64 x y)))

simplify52.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4991	2925
1	4991	2925

prune198.0ms (7.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	135	5	140
Fresh	4	7	11
Picked	1	0	1
Done	0	0	0
Total	140	12	152

Merged error: 5.9b

Counts

152 → 12

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 y (+.f64 (+.f64 x y) 1.0))
0.0b	(*.f64 (+.f64 x y) (+.f64 x y))
0.1b	(.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) (/.f64 y (+.f64 (+.f64 x y) 1.0)))
19.2b	(/.f64 x (*.f64 (+.f64 x y) (+.f64 x y)))

rewrite63.0ms (2.5%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`*-un-lft-identity_binary64`
43×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
34×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
31×	`add-cube-cbrt_binary64`
27×	`distribute-lft-out_binary64`
25×	`associate-r_binary64`
20×	`flip3-+_binary64` `associate-/r/_binary64` `flip-+_binary64`
19×	`associate-l_binary64`
13×	`pow1_binary64` `frac-times_binary64`
10×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
7×	`associate-r/_binary64` `associate-l/_binary64`
6×	`associate-/r_binary64` `swap-sqr_binary64` `associate-/l_binary64`
5×	`unswap-sqr_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64`
2×	`pow-prod-down_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`pow-prod-up_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

4 → 170

Calls

4 calls:

25.0ms	(.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) (/.f64 y (+.f64 (+.f64 x y) 1.0)))
12.0ms	(/.f64 x (*.f64 (+.f64 x y) (+.f64 x y)))
10.0ms	(*.f64 (+.f64 x y) (+.f64 x y))
8.0ms	(/.f64 y (+.f64 (+.f64 x y) 1.0))

series56.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

30.0ms	(.f64 (/.f64 x (.f64 (+.f64 x y) (+.f64 x y))) (/.f64 y (+.f64 (+.f64 x y) 1.0)))
12.0ms	(/.f64 x (*.f64 (+.f64 x y) (+.f64 x y)))
8.0ms	(/.f64 y (+.f64 (+.f64 x y) 1.0))
5.0ms	(*.f64 (+.f64 x y) (+.f64 x y))

simplify81.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4978	2143
1	4978	2143

prune236.0ms (9.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	176	6	182
Fresh	9	2	11
Picked	1	0	1
Done	0	0	0
Total	186	8	194

Merged error: 0.0b

Counts

194 → 8

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 y (+.f64 (+.f64 x y) 1.0))
0.0b	(/.f64 x (+.f64 x y))
0.1b	(/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))
0.1b	(*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1.0)))

rewrite101.0ms (4%)

Algorithm

1×	rewrite-expression-head

Rules

313×	`*-un-lft-identity_binary64`
303×	`times-frac_binary64`
163×	`add-sqr-sqrt_binary64`
142×	`add-cube-cbrt_binary64`
89×	`distribute-lft-out_binary64`
78×	`associate-l_binary64`
34×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
28×	`associate-/r/_binary64`
24×	`associate-/l*_binary64`
21×	`associate-r_binary64`
14×	`flip3-+_binary64` `cbrt-undiv_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`
13×	`associate-/r*_binary64`
6×	`pow1_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64`
4×	`add-log-exp_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `associate-r/_binary64` `frac-times_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 310

Calls

4 calls:

50.0ms	(*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1.0)))
12.0ms	(/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))
8.0ms	(/.f64 y (+.f64 (+.f64 x y) 1.0))
6.0ms	(/.f64 x (+.f64 x y))

series55.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

27.0ms	(*.f64 (/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y)) (/.f64 y (+.f64 (+.f64 x y) 1.0)))
12.0ms	(/.f64 (/.f64 x (+.f64 x y)) (+.f64 x y))
8.0ms	(/.f64 y (+.f64 (+.f64 x y) 1.0))
7.0ms	(/.f64 x (+.f64 x y))

simplify64.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

322 → 322

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5095	4843

prune354.0ms (14.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	316	6	322
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	323	7	330

Merged error: 0b

Counts

330 → 7

regimes100.0ms (4%)

Accuracy

Total 0.1b remaining (76.5%)

Threshold costs 0.1b (76.5%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	17
1	12	17

end0.0ms (0%)

sample423.0ms (16.9%)

Algorithm

1×

intervals

Results

290.0ms

8000×

body

valid

Details

analyze80.0ms (3.2%)

sample16.0ms (0.7%)

simplify59.0ms (2.4%)

prune5.0ms (0.2%)

localize8.0ms (0.3%)

rewrite59.0ms (2.4%)

series47.0ms (1.9%)

simplify67.0ms (2.7%)

prune234.0ms (9.3%)

localize10.0ms (0.4%)

rewrite61.0ms (2.4%)

series62.0ms (2.5%)

simplify52.0ms (2.1%)

prune198.0ms (7.9%)

localize9.0ms (0.3%)

rewrite63.0ms (2.5%)

series56.0ms (2.2%)

simplify81.0ms (3.2%)

prune236.0ms (9.4%)

localize8.0ms (0.3%)

rewrite101.0ms (4%)

series55.0ms (2.2%)

simplify64.0ms (2.5%)

prune354.0ms (14.1%)

regimes100.0ms (4%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample423.0ms (16.9%)

Profiling