Details

analyze1.1s (11.6%)

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
0%	96.7%	3.3%	9
16.4%	74.9%	8.7%	10
17.6%	71.8%	10.7%	11
26.3%	59.5%	14.2%	12
30.7%	45.7%	23.5%	13
31.7%	43.5%	24.7%	14

Compiler

Compiled 30 to 25 computations (16.7% saved)

sample45.0ms (0.5%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
8.0ms	112×	body	128	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify210.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4971	37
1	4971	37

prune8.0ms (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

Merged error: 7.9b

Counts

2 → 2

Compiler

Compiled 79 to 64 computations (19% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 2 (*.f64 r r))
5.2b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
5.9b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
8.6b	(.f64 r (.f64 w w))

rewrite70.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

106×	`times-frac_binary64`
71×	`add-sqr-sqrt_binary64`
65×	`*-un-lft-identity_binary64`
48×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
44×	`add-cube-cbrt_binary64`
36×	`associate-r_binary64`
16×	`cbrt-undiv_binary64` `div-exp_binary64`
15×	`cbrt-unprod_binary64` `prod-exp_binary64`
14×	`difference-of-squares_binary64`
11×	`associate-/r*_binary64` `pow1_binary64`
10×	`div-inv_binary64`
7×	`distribute-lft-out--_binary64`
6×	`associate-l_binary64` `associate-/l*_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64`
3×	`unswap-sqr_binary64`
2×	`flip3-+_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64` `frac-times_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`associate-*r/_binary64`

Counts

4 → 166

Calls

4 calls:

23.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
13.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
8.0ms	(.f64 r (.f64 w w))
5.0ms	(/.f64 2 (*.f64 r r))

series294.0ms (3.2%)

Counts

4 → 12

Calls

4 calls:

114.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
86.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
61.0ms	(.f64 r (.f64 w w))
33.0ms	(/.f64 2 (*.f64 r r))

simplify65.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5259	3748

prune330.0ms (3.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	167	11	178
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	169	11	180

Merged error: 2.5b

Counts

180 → 11

Compiler

Compiled 6014 to 3499 computations (41.8% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
0.5b	(/.f64 2 (*.f64 r r))
5.2b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
5.9b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))

rewrite77.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`times-frac_binary64`
77×	`add-sqr-sqrt_binary64`
72×	`*-un-lft-identity_binary64`
52×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
45×	`add-cube-cbrt_binary64`
35×	`associate-r_binary64`
19×	`cbrt-undiv_binary64` `div-exp_binary64`
18×	`difference-of-squares_binary64`
15×	`cbrt-unprod_binary64` `prod-exp_binary64`
12×	`associate-/r_binary64` `associate-/l_binary64`
11×	`div-inv_binary64`
9×	`distribute-lft-out--_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64`
3×	`associate-l_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `flip-+_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3--_binary64` `associate-r/_binary64` `div-sub_binary64` `flip--_binary64` `-commutative_binary64`

Counts

4 → 179

Calls

4 calls:

24.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
12.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
10.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
5.0ms	(/.f64 2 (*.f64 r r))

series329.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

119.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
97.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
77.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
36.0ms	(/.f64 2 (*.f64 r r))

simplify85.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5244	4160

prune363.0ms (3.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	183	8	191
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	190	12	202

Merged error: 0.0b

Counts

202 → 12

Compiler

Compiled 6446 to 3806 computations (41% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (-.f64 1 v))
0.5b	(/.f64 2 (*.f64 r r))
3.4b	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
5.5b	(.f64 (/.f64 (.f64 r w) (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (.f64 v -1/4)))

rewrite81.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

205×	`times-frac_binary64`
146×	`add-sqr-sqrt_binary64`
144×	`*-un-lft-identity_binary64`
105×	`add-cube-cbrt_binary64`
78×	`cbrt-prod_binary64`
32×	`associate-/r*_binary64` `add-exp-log_binary64`
27×	`add-cbrt-cube_binary64`
26×	`difference-of-squares_binary64`
14×	`cbrt-div_binary64`
13×	`associate-l_binary64` `distribute-lft-out--_binary64`
10×	`cbrt-unprod_binary64` `prod-exp_binary64`
9×	`cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64`
7×	`flip3--_binary64` `div-inv_binary64` `flip--_binary64`
6×	`pow1_binary64` `associate-/l*_binary64` `frac-times_binary64`
4×	`add-log-exp_binary64` `associate-*r/_binary64`
3×	`associate-r_binary64` `associate-*l/_binary64`
2×	`flip3-+_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `pow1/3_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `*-commutative_binary64`

Counts

4 → 222

Calls

4 calls:

21.0ms	(.f64 (/.f64 (.f64 r w) (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (.f64 v -1/4)))
15.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
5.0ms	(/.f64 2 (*.f64 r r))
4.0ms	(cbrt.f64 (-.f64 1 v))

series678.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

415.0ms	(.f64 (/.f64 (.f64 r w) (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (.f64 v -1/4)))
172.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
50.0ms	(cbrt.f64 (-.f64 1 v))
41.0ms	(/.f64 2 (*.f64 r r))

simplify95.0ms (1%)

Algorithm

1×	egg-herbie

Counts

234 → 234

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5119	5789

prune694.0ms (7.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	234	0	234
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	234	12	246

Merged error: 0.0b

Counts

246 → 12

Compiler

Compiled 11011 to 7216 computations (34.5% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 r w) w)
0.5b	(/.f64 2 (*.f64 r r))
3.6b	(.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4)))
5.0b	(.f64 (.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4))) (.f64 (*.f64 r w) w))

rewrite55.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
32×	`pow1_binary64` `add-sqr-sqrt_binary64`
30×	`cbrt-unprod_binary64` `prod-exp_binary64`
27×	`*-un-lft-identity_binary64`
26×	`associate-l_binary64`
22×	`times-frac_binary64`
19×	`pow-prod-down_binary64`
18×	`add-cube-cbrt_binary64`
7×	`associate-r_binary64` `associate-*l/_binary64`
6×	`cbrt-undiv_binary64` `difference-of-squares_binary64` `div-exp_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `associate-*r/_binary64` `flip-+_binary64` `frac-times_binary64`
3×	`associate-/l_binary64` `distribute-lft-out--_binary64` `-commutative_binary64`
2×	`associate-/r/_binary64` `unswap-sqr_binary64` `div-inv_binary64`
1×	`associate-/r*_binary64` `flip3--_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64`

Counts

4 → 127

Calls

4 calls:

17.0ms	(.f64 (.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4))) (.f64 (*.f64 r w) w))
13.0ms	(.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4)))
5.0ms	(.f64 (.f64 r w) w)
5.0ms	(/.f64 2 (*.f64 r r))

series331.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

148.0ms	(.f64 (.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4))) (.f64 (*.f64 r w) w))
93.0ms	(.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4)))
55.0ms	(.f64 (.f64 r w) w)
34.0ms	(/.f64 2 (*.f64 r r))

simplify56.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5853	2537

prune197.0ms (2.1%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	141	10	151

Merged error: 0.0b

Counts

151 → 10

Compiler

Compiled 4220 to 2490 computations (41% saved)

regimes1.1s (11.8%)

Compiler: Compiled 16761 to 12868 computations (23.2% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	130	55
1	130	55

end0.0ms (0%)

sample3.0s (32.2%)

Algorithm

1×

intervals

Results

562.0ms	8000×	body	128	valid
329.0ms	4708×	body	128	invalid

Compiler

Compiled 2618 to 2014 computations (23.1% saved)

Details

analyze1.1s (11.6%)

sample45.0ms (0.5%)

simplify210.0ms (2.3%)

prune8.0ms (0.1%)

localize24.0ms (0.3%)

rewrite70.0ms (0.7%)

series294.0ms (3.2%)

simplify65.0ms (0.7%)

prune330.0ms (3.5%)

localize16.0ms (0.2%)

rewrite77.0ms (0.8%)

series329.0ms (3.5%)

simplify85.0ms (0.9%)

prune363.0ms (3.9%)

localize19.0ms (0.2%)

rewrite81.0ms (0.9%)

series678.0ms (7.3%)

simplify95.0ms (1%)

prune694.0ms (7.4%)

localize16.0ms (0.2%)

rewrite55.0ms (0.6%)

series331.0ms (3.5%)

simplify56.0ms (0.6%)

prune197.0ms (2.1%)

regimes1.1s (11.8%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample3.0s (32.2%)

Profiling