Details

analyze1.1s (10.7%)

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 (0.4%)

Algorithm

1×

intervals

Results

18.0ms	256×	body	128	valid
11.0ms	150×	body	128	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify220.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4993	37
1	4993	37

prune11.0ms (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: 9.6b

Counts

2 → 2

Compiler

Compiled 133 to 108 computations (18.8% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
5.2b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
7.7b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
10.8b	(.f64 r (.f64 w w))

rewrite87.0ms (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:

27.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
15.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
12.0ms	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
9.0ms	(.f64 r (.f64 w w))

series359.0ms (3.4%)

Counts

4 → 12

Calls

4 calls:

115.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
96.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
83.0ms	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
65.0ms	(.f64 r (.f64 w w))

simplify76.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5468	4089

prune695.0ms (6.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	181	8	189
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	182	9	191

Merged error: 4.5b

Counts

191 → 9

Compiler

Compiled 14087 to 9394 computations (33.3% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 2 (*.f64 r r))
0.5b	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
5.2b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
7.7b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))

rewrite80.0ms (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:

25.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
13.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
11.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
5.0ms	(/.f64 2 (*.f64 r r))

series343.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

125.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
96.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
86.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
36.0ms	(/.f64 2 (*.f64 r r))

simplify91.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5248	4160

prune1.2s (11.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	180	11	191
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	187	13	200

Merged error: 0.0b

Counts

200 → 13

Compiler

Compiled 23724 to 17070 computations (28% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
0.4b	(/.f64 2 (*.f64 r r))
2.0b	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
5.2b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))))

rewrite212.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

384×	`times-frac_binary64`
260×	`add-sqr-sqrt_binary64`
247×	`*-un-lft-identity_binary64`
184×	`add-cube-cbrt_binary64`
169×	`add-exp-log_binary64`
134×	`add-cbrt-cube_binary64`
127×	`cbrt-prod_binary64`
99×	`associate-r_binary64`
71×	`cbrt-unprod_binary64` `prod-exp_binary64`
59×	`cbrt-undiv_binary64` `div-exp_binary64`
42×	`difference-of-squares_binary64`
32×	`associate-/r*_binary64`
21×	`distribute-lft-out--_binary64`
16×	`associate-l_binary64`
14×	`frac-times_binary64`
12×	`cbrt-div_binary64`
11×	`pow1_binary64` `div-inv_binary64`
10×	`associate-/r/_binary64`
9×	`associate-*r/_binary64`
8×	`associate-*l/_binary64`
6×	`flip3--_binary64` `associate-/l*_binary64` `flip--_binary64`
4×	`pow-prod-down_binary64` `flip3-+_binary64` `add-log-exp_binary64` `unswap-sqr_binary64` `flip-+_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

4 → 377

Calls

4 calls:

71.0ms	(.f64 (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
41.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))))
14.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
5.0ms	(/.f64 2 (*.f64 r r))

series453.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

164.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
142.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))))
111.0ms	(.f64 (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
34.0ms	(/.f64 2 (*.f64 r r))

simplify131.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

389 → 389

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5044	11932

prune1.4s (13.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	388	1	389
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	389	13	402

Merged error: 0.0b

Counts

402 → 13

Compiler

Compiled 19287 to 12555 computations (34.9% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (-.f64 1 v))
0.3b	(.f64 (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
2.0b	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
5.2b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))))

rewrite212.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

381×	`times-frac_binary64`
262×	`add-sqr-sqrt_binary64`
249×	`*-un-lft-identity_binary64`
183×	`add-cube-cbrt_binary64`
164×	`add-exp-log_binary64`
133×	`cbrt-prod_binary64`
129×	`add-cbrt-cube_binary64`
99×	`associate-r_binary64`
70×	`cbrt-unprod_binary64` `prod-exp_binary64`
57×	`cbrt-undiv_binary64` `div-exp_binary64`
44×	`difference-of-squares_binary64`
31×	`associate-/r*_binary64`
22×	`distribute-lft-out--_binary64`
16×	`associate-l_binary64`
14×	`cbrt-div_binary64` `frac-times_binary64`
11×	`pow1_binary64`
10×	`associate-/r/_binary64` `div-inv_binary64`
9×	`associate-*r/_binary64`
8×	`associate-*l/_binary64`
7×	`flip3--_binary64` `flip--_binary64`
4×	`pow-prod-down_binary64` `flip3-+_binary64` `add-log-exp_binary64` `unswap-sqr_binary64` `flip-+_binary64`
3×	`associate-/l*_binary64`
2×	`*-commutative_binary64`
1×	`pow1/3_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 372

Calls

4 calls:

71.0ms	(.f64 (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
41.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))))
14.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
4.0ms	(cbrt.f64 (-.f64 1 v))

series453.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

152.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
129.0ms	(.f64 (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
127.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (.f64 (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))))
44.0ms	(cbrt.f64 (-.f64 1 v))

simplify127.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

384 → 384

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5026	11997

prune1.4s (13.1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	384	0	384
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	384	13	397

Merged error: 0.0b

Counts

397 → 13

Compiler

Compiled 17933 to 11862 computations (33.9% saved)

regimes145.0ms (1.4%)

Compiler: Compiled 1660 to 1343 computations (19.1% 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%)

sample1.6s (15%)

Algorithm

1×

intervals

Results

556.0ms	8000×	body	128	valid
329.0ms	4686×	body	128	invalid

Compiler

Compiled 460 to 371 computations (19.3% saved)

Details

analyze1.1s (10.7%)

sample44.0ms (0.4%)

simplify220.0ms (2.1%)

prune11.0ms (0.1%)

localize26.0ms (0.2%)

rewrite87.0ms (0.8%)

series359.0ms (3.4%)

simplify76.0ms (0.7%)

prune695.0ms (6.7%)

localize17.0ms (0.2%)

rewrite80.0ms (0.8%)

series343.0ms (3.3%)

simplify91.0ms (0.9%)

prune1.2s (11.1%)

localize21.0ms (0.2%)

rewrite212.0ms (2%)

series453.0ms (4.3%)

simplify131.0ms (1.3%)

prune1.4s (13.2%)

localize21.0ms (0.2%)

rewrite212.0ms (2%)

series453.0ms (4.3%)

simplify127.0ms (1.2%)

prune1.4s (13.1%)

regimes145.0ms (1.4%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.6s (15%)

Profiling