Details

analyze1.1s (13.3%)

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
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

18.0ms	256×	body	128	valid
11.0ms	160×	body	128	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify152.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4999	37
1	4999	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: 7.6b

Counts

2 → 2

Compiler

Compiled 79 to 64 computations (19% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
4.3b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
6.9b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
9.4b	(.f64 r (.f64 w w))

rewrite80.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 177

Calls

4 calls:

29.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
12.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
10.0ms	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
8.0ms	(.f64 r (.f64 w w))

series201.0ms (2.4%)

Counts

4 → 12

Calls

4 calls:

72.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
48.0ms	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
47.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
33.0ms	(.f64 r (.f64 w w))

simplify78.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5250	4089

prune343.0ms (4.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	183	6	189
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	185	6	191

Merged error: 3.4b

Counts

191 → 6

Compiler

Compiled 6217 to 3589 computations (42.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 2 (*.f64 r r))
0.4b	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
4.3b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
6.9b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))

rewrite68.0ms (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))))
11.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
9.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
4.0ms	(/.f64 2 (*.f64 r r))

series181.0ms (2.2%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
49.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
45.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
18.0ms	(/.f64 2 (*.f64 r r))

simplify127.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4950	4154
1	4950	4154

prune340.0ms (4.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	184	7	191
Fresh	2	3	5
Picked	1	0	1
Done	0	0	0
Total	187	10	197

Merged error: 0.0b

Counts

197 → 10

Compiler

Compiled 6372 to 3759 computations (41% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))
0.4b	(/.f64 2 (*.f64 r r))
3.2b	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
6.2b	(.f64 (/.f64 (.f64 r w) (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (.f64 v -1/4)))

rewrite92.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

205×	`times-frac_binary64`
170×	`add-sqr-sqrt_binary64`
166×	`*-un-lft-identity_binary64`
112×	`add-cube-cbrt_binary64`
104×	`cbrt-prod_binary64`
34×	`add-exp-log_binary64`
32×	`associate-/r*_binary64` `difference-of-squares_binary64`
27×	`add-cbrt-cube_binary64`
24×	`cbrt-div_binary64`
22×	`associate-l_binary64`
18×	`distribute-lft-out--_binary64`
13×	`pow1_binary64`
12×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64`
11×	`swap-sqr_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
10×	`frac-times_binary64`
9×	`cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64`
7×	`div-inv_binary64`
6×	`associate-r/_binary64` `pow1/3_binary64` `associate-/l_binary64`
5×	`unswap-sqr_binary64` `associate-*l/_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64`
2×	`flip3-+_binary64` `pow-prod-up_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-sqr_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `pow2_binary64`

Counts

4 → 265

Calls

4 calls:

20.0ms	(.f64 (/.f64 (.f64 r w) (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (.f64 v -1/4)))
13.0ms	(*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))
12.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
8.0ms	(/.f64 2 (*.f64 r r))

series321.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

195.0ms	(.f64 (/.f64 (.f64 r w) (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (.f64 v -1/4)))
85.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
24.0ms	(*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))
16.0ms	(/.f64 2 (*.f64 r r))

simplify140.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4925	6518
1	4925	6518

prune850.0ms (10.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	277	0	277
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	277	10	287

Merged error: 0.0b

Counts

287 → 10

Compiler

Compiled 12671 to 8353 computations (34.1% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 w (.f64 r w))
0.4b	(/.f64 2 (*.f64 r r))
4.3b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 1 (-.f64 1 v)) (.f64 r (.f64 w (.f64 r w)))))
5.7b	(.f64 r (.f64 w (*.f64 r w)))

rewrite50.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

101×	`add-exp-log_binary64`
67×	`prod-exp_binary64`
65×	`add-cbrt-cube_binary64`
39×	`cbrt-unprod_binary64`
38×	`pow1_binary64`
24×	`pow-prod-down_binary64`
10×	`div-exp_binary64`
9×	`-un-lft-identity_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64` `add-sqr-sqrt_binary64`
6×	`cbrt-undiv_binary64`
5×	`associate-*l/_binary64`
4×	`add-log-exp_binary64` `1-exp_binary64` `rec-exp_binary64`
3×	`associate-r_binary64` `associate-/l_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`flip3-+_binary64` `flip-+_binary64` `frac-times_binary64`
1×	`associate-/r_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 108

Calls

4 calls:

19.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 1 (-.f64 1 v)) (.f64 r (.f64 w (.f64 r w)))))
7.0ms	(.f64 r (.f64 w (*.f64 r w)))
5.0ms	(.f64 w (.f64 r w))
4.0ms	(/.f64 2 (*.f64 r r))

series123.0ms (1.5%)

Counts

4 → 12

Calls

4 calls:

64.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 1 (-.f64 1 v)) (.f64 r (.f64 w (.f64 r w)))))
24.0ms	(.f64 r (.f64 w (*.f64 r w)))
17.0ms	(/.f64 2 (*.f64 r r))
17.0ms	(.f64 w (.f64 r w))

simplify54.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5129	1974

prune160.0ms (1.9%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	8	8
Picked	0	1	1
Done	0	1	1
Total	120	10	130

Merged error: 0.0b

Counts

130 → 10

Compiler

Compiled 3516 to 2121 computations (39.7% saved)

regimes890.0ms (10.8%)

Compiler: Compiled 14091 to 10847 computations (23% 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%)

sample2.8s (33.6%)

Algorithm

1×

intervals

Results

557.0ms	8000×	body	128	valid
341.0ms	4920×	body	128	invalid

Compiler

Compiled 2210 to 1706 computations (22.8% saved)

Details

analyze1.1s (13.3%)

sample45.0ms (0.5%)

simplify152.0ms (1.8%)

prune8.0ms (0.1%)

localize18.0ms (0.2%)

rewrite80.0ms (1%)

series201.0ms (2.4%)

simplify78.0ms (0.9%)

prune343.0ms (4.2%)

localize16.0ms (0.2%)

rewrite68.0ms (0.8%)

series181.0ms (2.2%)

simplify127.0ms (1.5%)

prune340.0ms (4.1%)

localize21.0ms (0.3%)

rewrite92.0ms (1.1%)

series321.0ms (3.9%)

simplify140.0ms (1.7%)

prune850.0ms (10.3%)

localize17.0ms (0.2%)

rewrite50.0ms (0.6%)

series123.0ms (1.5%)

simplify54.0ms (0.7%)

prune160.0ms (1.9%)

regimes890.0ms (10.8%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.8s (33.6%)

Profiling