Details

analyze1.1s (17.1%)

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)

sample44.0ms (0.7%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
12.0ms	170×	body	128	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify218.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

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: 5.9b

Counts

2 → 2

Compiler

Compiled 79 to 64 computations (19% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 2 (*.f64 r r))
4.8b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
7.0b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
9.2b	(.f64 r (.f64 w w))

rewrite73.0ms (1.2%)

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))

series311.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

113.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
101.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
56.0ms	(.f64 r (.f64 w w))
41.0ms	(/.f64 2 (*.f64 r r))

simplify67.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5259	3748

prune323.0ms (5.1%)

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: 2.0b

Counts

180 → 11

Compiler

Compiled 6037 to 3511 computations (41.8% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
1.0b	(/.f64 2 (*.f64 r r))
4.8b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
7.0b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))

rewrite71.0ms (1.1%)

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:

22.0ms	(.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))

series331.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

120.0ms	(.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)))
79.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
34.0ms	(/.f64 2 (*.f64 r r))

simplify88.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5244	4160

prune329.0ms (5.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	185	6	191
Fresh	4	6	10
Picked	1	0	1
Done	0	0	0
Total	190	12	202

Merged error: 0.0b

Counts

202 → 12

Compiler

Compiled 6484 to 3828 computations (41% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (.f64 r w) w)
1.0b	(/.f64 2 (*.f64 r r))
4.4b	(.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4)))
5.2b	(.f64 (.f64 (/.f64 r (-.f64 1 v)) (+.f64 3/8 (.f64 v -1/4))) (.f64 (*.f64 r w) w))

rewrite55.0ms (0.9%)

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))

series352.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

160.0ms	(.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)
43.0ms	(/.f64 2 (*.f64 r r))

simplify58.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5853	2537

prune213.0ms (3.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	137	2	139
Fresh	2	9	11
Picked	0	1	1
Done	0	0	0
Total	139	12	151

Merged error: 0.0b

Counts

151 → 12

Compiler

Compiled 4553 to 2751 computations (39.6% saved)

localize23.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 2 (*.f64 r r))
2.1b	(.f64 (/.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (-.f64 1 v)) (.f64 (.f64 w (*.f64 r w)) (cbrt.f64 r)))
2.4b	(.f64 (.f64 w (*.f64 r w)) (cbrt.f64 r))
4.8b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (-.f64 1 v)) (.f64 (.f64 w (*.f64 r w)) (cbrt.f64 r))))

rewrite83.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

140×	`add-exp-log_binary64`
103×	`add-cbrt-cube_binary64`
88×	`cbrt-unprod_binary64` `prod-exp_binary64`
47×	`pow1_binary64`
31×	`pow-prod-down_binary64`
18×	`cbrt-undiv_binary64` `div-exp_binary64`
16×	`associate-l_binary64`
14×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
8×	`associate-r_binary64`
6×	`associate-*l/_binary64`
4×	`add-log-exp_binary64`
3×	`associate-/l_binary64` `cbrt-prod_binary64` `-commutative_binary64`
2×	`flip3-+_binary64` `associate-/r/_binary64` `difference-of-squares_binary64` `div-inv_binary64` `flip-+_binary64` `frac-times_binary64`
1×	`associate-/r_binary64` `flip3--_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `distribute-lft-out--_binary64` `flip--_binary64`

Counts

4 → 143

Calls

4 calls:

24.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (-.f64 1 v)) (.f64 (.f64 w (*.f64 r w)) (cbrt.f64 r))))
18.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (-.f64 1 v)) (.f64 (.f64 w (*.f64 r w)) (cbrt.f64 r)))
8.0ms	(.f64 (.f64 w (*.f64 r w)) (cbrt.f64 r))
5.0ms	(/.f64 2 (*.f64 r r))

series464.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

172.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (-.f64 1 v)) (.f64 (.f64 w (*.f64 r w)) (cbrt.f64 r))))
127.0ms	(.f64 (.f64 w (*.f64 r w)) (cbrt.f64 r))
127.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 r) (cbrt.f64 r)) (-.f64 1 v)) (.f64 (.f64 w (*.f64 r w)) (cbrt.f64 r)))
38.0ms	(/.f64 2 (*.f64 r r))

simplify87.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4985	3083
1	4985	3083

prune220.0ms (3.5%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	155	12	167

Merged error: 0.0b

Counts

167 → 12

Compiler

Compiled 5021 to 2584 computations (48.5% saved)

regimes170.0ms (2.7%)

Compiler: Compiled 1549 to 1235 computations (20.3% saved)

bsearch73.0ms (1.2%)

Steps

Iters	Range		Point
5	5.009823315829063e+82	1.2038952150761206e+83	8.120287775346159e+82
10	-8.20959698438519e+140	-1.1526280836232353e+129	-1.962133336738353e+134

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	201	123
1	201	123

end0.0ms (0%)

sample1.5s (23.9%)

Algorithm

1×

intervals

Results

540.0ms	8000×	body	128	valid
333.0ms	4819×	body	128	invalid

Compiler

Compiled 471 to 364 computations (22.7% saved)

Details

analyze1.1s (17.1%)

sample44.0ms (0.7%)

simplify218.0ms (3.5%)

prune8.0ms (0.1%)

localize26.0ms (0.4%)

rewrite73.0ms (1.2%)

series311.0ms (4.9%)

simplify67.0ms (1.1%)

prune323.0ms (5.1%)

localize19.0ms (0.3%)

rewrite71.0ms (1.1%)

series331.0ms (5.2%)

simplify88.0ms (1.4%)

prune329.0ms (5.2%)

localize17.0ms (0.3%)

rewrite55.0ms (0.9%)

series352.0ms (5.6%)

simplify58.0ms (0.9%)

prune213.0ms (3.4%)

localize23.0ms (0.4%)

rewrite83.0ms (1.3%)

series464.0ms (7.4%)

simplify87.0ms (1.4%)

prune220.0ms (3.5%)

regimes170.0ms (2.7%)

bsearch73.0ms (1.2%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.5s (23.9%)

Profiling