Details

analyze1.1s (13.6%)

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)

sample48.0ms (0.6%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
10.0ms	147×	body	128	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify219.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4993	37
1	4993	37

prune17.0ms (0.2%)

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: 7.7b

Counts

2 → 2

Compiler

Compiled 133 to 108 computations (18.8% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.1b	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
4.5b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
9.2b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
10.5b	(.f64 r (.f64 w w))

rewrite87.0ms (1.1%)

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:

24.0ms	(.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))))
11.0ms	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
8.0ms	(.f64 r (.f64 w w))

series360.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

117.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
98.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
87.0ms	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
57.0ms	(.f64 r (.f64 w w))

simplify75.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5468	4089

prune692.0ms (8.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	182	7	189
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	184	7	191

Merged error: 3.3b

Counts

191 → 7

Compiler

Compiled 14001 to 9443 computations (32.6% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 2 (*.f64 r r))
1.1b	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
4.5b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
9.2b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))

rewrite79.0ms (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:

27.0ms	(.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)))
11.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
5.0ms	(/.f64 2 (*.f64 r r))

series340.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
94.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
91.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
37.0ms	(/.f64 2 (*.f64 r r))

simplify91.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	5248	4160

prune900.0ms (11%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	182	9	191
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	188	10	198

Merged error: 0.0b

Counts

198 → 10

Compiler

Compiled 18370 to 12880 computations (29.9% 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))
2.9b	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
4.5b	(.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))))

rewrite123.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

204×	`times-frac_binary64`
167×	`add-sqr-sqrt_binary64`
165×	`*-un-lft-identity_binary64`
111×	`add-cube-cbrt_binary64`
104×	`cbrt-prod_binary64`
102×	`add-exp-log_binary64`
82×	`add-cbrt-cube_binary64`
45×	`cbrt-unprod_binary64` `prod-exp_binary64`
32×	`associate-/r*_binary64` `cbrt-undiv_binary64` `difference-of-squares_binary64` `div-exp_binary64`
18×	`distribute-lft-out--_binary64`
16×	`pow1_binary64`
13×	`frac-times_binary64`
12×	`cbrt-div_binary64` `associate-l_binary64`
11×	`swap-sqr_binary64`
10×	`associate-r_binary64`
8×	`associate-*r/_binary64`
7×	`associate-*l/_binary64`
6×	`flip3--_binary64` `pow1/3_binary64` `associate-/l*_binary64` `div-inv_binary64` `flip--_binary64`
5×	`pow-prod-down_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `unswap-sqr_binary64` `flip-+_binary64`
2×	`pow-prod-up_binary64` `clear-num_binary64` `frac-2neg_binary64` `pow-sqr_binary64` `*-commutative_binary64`
1×	`associate-/r/_binary64` `pow-plus_binary64` `pow2_binary64`

Counts

4 → 279

Calls

4 calls:

37.0ms	(.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))))
15.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
14.0ms	(*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))
5.0ms	(/.f64 2 (*.f64 r r))

series395.0ms (4.8%)

Counts

4 → 12

Calls

4 calls:

166.0ms	(/.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))))
49.0ms	(*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))
37.0ms	(/.f64 2 (*.f64 r r))

simplify142.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

291 → 291

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4931	7033
1	4931	7033

prune922.0ms (11.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	289	2	291
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	290	11	301

Merged error: 0.0b

Counts

301 → 11

Compiler

Compiled 16369 to 11025 computations (32.6% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(cbrt.f64 (-.f64 1 v))
0.3b	(*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))
0.4b	(/.f64 2 (*.f64 r r))
4.5b	(.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 (/.f64 r (cbrt.f64 (-.f64 1 v))) w)))

rewrite85.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`add-exp-log_binary64`
78×	`add-cbrt-cube_binary64`
55×	`cbrt-unprod_binary64` `prod-exp_binary64`
39×	`add-sqr-sqrt_binary64`
38×	`cbrt-prod_binary64`
37×	`*-un-lft-identity_binary64`
20×	`pow1_binary64`
19×	`cbrt-undiv_binary64` `div-exp_binary64`
16×	`add-cube-cbrt_binary64`
14×	`cbrt-div_binary64`
13×	`frac-times_binary64` `associate-*l/_binary64`
12×	`associate-l_binary64`
11×	`swap-sqr_binary64`
10×	`associate-r_binary64` `difference-of-squares_binary64`
8×	`pow-prod-down_binary64` `associate-*r/_binary64`
7×	`flip3--_binary64` `pow1/3_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `unswap-sqr_binary64` `flip-+_binary64`
3×	`associate-/l*_binary64` `times-frac_binary64`
2×	`pow-prod-up_binary64` `pow-sqr_binary64` `*-commutative_binary64`
1×	`associate-/r*_binary64` `pow-plus_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `pow2_binary64`

Counts

4 → 154

Calls

4 calls:

33.0ms	(.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 (/.f64 r (cbrt.f64 (-.f64 1 v))) w)))
14.0ms	(*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))
5.0ms	(/.f64 2 (*.f64 r r))
4.0ms	(cbrt.f64 (-.f64 1 v))

series273.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

141.0ms	(.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 (/.f64 r (cbrt.f64 (-.f64 1 v))) w)))
48.0ms	(*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))
46.0ms	(cbrt.f64 (-.f64 1 v))
37.0ms	(/.f64 2 (*.f64 r r))

simplify89.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4933	3381
1	4933	3381

prune397.0ms (4.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	166	11	177

Merged error: 0.0b

Counts

177 → 11

Compiler

Compiled 7146 to 4845 computations (32.2% saved)

regimes125.0ms (1.5%)

Compiler: Compiled 1580 to 1246 computations (21.1% saved)

bsearch0.0ms (0%)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	141	55
1	141	55

end0.0ms (0%)

sample1.5s (18.9%)

Algorithm

1×

intervals

Results

553.0ms	8000×	body	128	valid
336.0ms	4782×	body	128	invalid

Compiler

Compiled 458 to 362 computations (21% saved)

Details

analyze1.1s (13.6%)

sample48.0ms (0.6%)

simplify219.0ms (2.7%)

prune17.0ms (0.2%)

localize19.0ms (0.2%)

rewrite87.0ms (1.1%)

series360.0ms (4.4%)

simplify75.0ms (0.9%)

prune692.0ms (8.4%)

localize17.0ms (0.2%)

rewrite79.0ms (1%)

series340.0ms (4.1%)

simplify91.0ms (1.1%)

prune900.0ms (11%)

localize21.0ms (0.3%)

rewrite123.0ms (1.5%)

series395.0ms (4.8%)

simplify142.0ms (1.7%)

prune922.0ms (11.2%)

localize21.0ms (0.3%)

rewrite85.0ms (1%)

series273.0ms (3.3%)

simplify89.0ms (1.1%)

prune397.0ms (4.8%)

regimes125.0ms (1.5%)

bsearch0.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.5s (18.9%)

Profiling