Details

analyze1.1s (11.4%)

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)

sample46.0ms (0.5%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
13.0ms	152×	body	128	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify145.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4999	37
1	4999	37

prune7.0ms (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: 10.1b

Counts

2 → 2

Compiler

Compiled 79 to 64 computations (19% saved)

localize24.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.2b	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
3.4b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
8.1b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
12.0b	(.f64 r (.f64 w w))

rewrite71.0ms (0.8%)

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:

21.0ms	(.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))

series198.0ms (2.1%)

Counts

4 → 12

Calls

4 calls:

67.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
49.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
42.0ms	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
40.0ms	(.f64 r (.f64 w w))

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5250	4089

prune332.0ms (3.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	182	7	189
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	183	8	191

Merged error: 3.5b

Counts

191 → 8

Compiler

Compiled 6293 to 3644 computations (42.1% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(/.f64 2 (*.f64 r r))
1.2b	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
3.4b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
8.1b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))

rewrite65.0ms (0.7%)

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:

20.0ms	(.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 (1.9%)

Counts

4 → 12

Calls

4 calls:

66.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
54.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
44.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
17.0ms	(/.f64 2 (*.f64 r r))

simplify123.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (79.0ms)

Iter	Nodes	Cost
0	4950	4154
1	4950	4154

prune358.0ms (3.8%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	177	14	191
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	182	17	199

Merged error: 0.0b

Counts

199 → 17

Compiler

Compiled 6667 to 3967 computations (40.5% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))
0.7b	(/.f64 2 (*.f64 r r))
2.1b	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
3.6b	(.f64 (/.f64 (.f64 r w) (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (.f64 v -1/4)))

rewrite90.0ms (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:

19.0ms	(.f64 (/.f64 (.f64 r w) (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (.f64 v -1/4)))
17.0ms	(*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))
11.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
4.0ms	(/.f64 2 (*.f64 r r))

series339.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

204.0ms	(.f64 (/.f64 (.f64 r w) (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (+.f64 3/8 (.f64 v -1/4)))
90.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
26.0ms	(*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))
18.0ms	(/.f64 2 (*.f64 r r))

simplify143.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4925	6518
1	4925	6518

prune854.0ms (9.1%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	276	1	277
Fresh	1	15	16
Picked	0	1	1
Done	0	0	0
Total	277	17	294

Merged error: 0.0b

Counts

294 → 17

Compiler

Compiled 12964 to 8560 computations (34% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.7b	(pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 v))) 6)
0.7b	(/.f64 2 (*.f64 r r))
1.1b	(.f64 (.f64 r w) (/.f64 (+.f64 3/8 (*.f64 v -1/4)) (pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 v))) 6)))
2.1b	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))

rewrite85.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

252×	`times-frac_binary64`
183×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
135×	`add-cube-cbrt_binary64`
132×	`cbrt-prod_binary64`
52×	`associate-r_binary64`
48×	`unpow-prod-down_binary64`
39×	`add-exp-log_binary64`
32×	`associate-/r*_binary64` `difference-of-squares_binary64`
25×	`add-cbrt-cube_binary64`
16×	`distribute-lft-out--_binary64`
13×	`prod-exp_binary64`
11×	`div-exp_binary64`
10×	`pow1_binary64`
7×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `div-inv_binary64`
6×	`associate-/l*_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64`
3×	`pow-to-exp_binary64` `pow-prod-down_binary64` `pow-unpow_binary64` `pow-exp_binary64`
2×	`pow-pow_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`associate-r/_binary64` `pow1/3_binary64` `associate-/r/_binary64` `associate-l_binary64` `-commutative_binary64`

Counts

4 → 266

Calls

4 calls:

21.0ms	(.f64 (.f64 r w) (/.f64 (+.f64 3/8 (*.f64 v -1/4)) (pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 v))) 6)))
13.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
7.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 v))) 6)
4.0ms	(/.f64 2 (*.f64 r r))

series393.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

203.0ms	(.f64 (.f64 r w) (/.f64 (+.f64 3/8 (*.f64 v -1/4)) (pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 v))) 6)))
99.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
73.0ms	(pow.f64 (cbrt.f64 (cbrt.f64 (-.f64 1 v))) 6)
17.0ms	(/.f64 2 (*.f64 r r))

simplify122.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

278 → 278

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4928	6723
1	4928	6723

prune759.0ms (8.1%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	278	0	278
Fresh	0	15	15
Picked	0	1	1
Done	0	1	1
Total	278	17	295

Merged error: 0.0b

Counts

295 → 17

Compiler

Compiled 12257 to 8270 computations (32.5% saved)

regimes976.0ms (10.3%)

Compiler: Compiled 16046 to 12240 computations (23.7% 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%)

sample2.9s (30.8%)

Algorithm

1×

intervals

Results

525.0ms	8000×	body	128	valid
323.0ms	4886×	body	128	invalid

Compiler

Compiled 2532 to 1937 computations (23.5% saved)

Details

analyze1.1s (11.4%)

sample46.0ms (0.5%)

simplify145.0ms (1.5%)

prune7.0ms (0.1%)

localize24.0ms (0.3%)

rewrite71.0ms (0.8%)

series198.0ms (2.1%)

simplify77.0ms (0.8%)

prune332.0ms (3.5%)

localize18.0ms (0.2%)

rewrite65.0ms (0.7%)

series181.0ms (1.9%)

simplify123.0ms (1.3%)

prune358.0ms (3.8%)

localize20.0ms (0.2%)

rewrite90.0ms (1%)

series339.0ms (3.6%)

simplify143.0ms (1.5%)

prune854.0ms (9.1%)

localize21.0ms (0.2%)

rewrite85.0ms (0.9%)

series393.0ms (4.2%)

simplify122.0ms (1.3%)

prune759.0ms (8.1%)

regimes976.0ms (10.3%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.9s (30.8%)

Profiling