Details

analyze1.1s (6.6%)

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)

sample50.0ms (0.3%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
12.0ms	166×	body	128	invalid

Compiler

Compiled 59 to 52 computations (11.9% saved)

simplify146.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4999	37
1	4999	37

prune17.0ms (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

Error

9.3b

Counts

2 → 2

Compiler

Compiled 79 to 64 computations (19% saved)

localize19.0ms (0.1%)

Local error

Found 8 expressions with local error:

6.1b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
0.7b	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
0.5b	(/.f64 2 (*.f64 r r))
0.0b	(+.f64 (/.f64 2 (*.f64 r r)) -3/2)
0.7b	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
6.1b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
6.4b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
9.9b	(.f64 r (.f64 w w))

rewrite83.0ms (0.5%)

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

8 calls:

24.0ms	(.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))
0.0ms	(+.f64 (/.f64 2 (*.f64 r r)) -3/2)

series711.0ms (4.3%)

Counts

4 → 42

Calls

4 calls:

271.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))))
193.0ms	(/.f64 (-.f64 1 v) (.f64 r (.f64 w w)))
177.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 r (.f64 w w))))
70.0ms	(.f64 r (.f64 w w))

Compiler

Compiled 2039 to 1737 computations (14.8% saved)

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

219 → 219

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5473	4451

prune425.0ms (2.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	210	9	219
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	212	9	221

Error

3.4b

Counts

221 → 9

Compiler

Compiled 7003 to 4049 computations (42.2% saved)

localize17.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.7b	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
0.5b	(/.f64 2 (*.f64 r r))
0.2b	(.f64 (.f64 r w) w)
0.0b	(+.f64 (/.f64 2 (*.f64 r r)) -3/2)
0.5b	(/.f64 2 (*.f64 r r))
0.7b	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
6.1b	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
6.4b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))

rewrite72.0ms (0.4%)

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

8 calls:

23.0ms	(.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)))
9.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
5.0ms	(/.f64 2 (*.f64 r r))
0.0ms	(+.f64 (/.f64 2 (*.f64 r r)) -3/2)

series657.0ms (4%)

Counts

4 → 39

Calls

4 calls:

258.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))))
192.0ms	(/.f64 (-.f64 1 v) (.f64 (.f64 r w) w))
181.0ms	(/.f64 r (/.f64 (-.f64 1 v) (.f64 (.f64 r w) w)))
27.0ms	(/.f64 2 (*.f64 r r))

Compiler

Compiled 1889 to 1611 computations (14.7% saved)

simplify115.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4941	4555
1	4941	4555

prune471.0ms (2.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	206	12	218
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	214	13	227

Error

0.0b

Counts

227 → 13

Compiler

Compiled 7159 to 4188 computations (41.5% saved)

localize21.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(cbrt.f64 (-.f64 1 v))
0.1b	(/.f64 (.f64 r w) (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))))
0.1b	(/.f64 (cbrt.f64 (-.f64 1 v)) w)
0.0b	(+.f64 (/.f64 2 (*.f64 r r)) -3/2)
0.3b	(.f64 (.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
0.5b	(/.f64 2 (*.f64 r r))
2.6b	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
3.9b	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 (.f64 r w) (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))))

rewrite153.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

379×	`times-frac_binary64`
249×	`add-sqr-sqrt_binary64`
247×	`*-un-lft-identity_binary64`
184×	`add-cube-cbrt_binary64`
126×	`cbrt-prod_binary64`
125×	`add-exp-log_binary64`
111×	`associate-r_binary64`
102×	`add-cbrt-cube_binary64`
55×	`cbrt-unprod_binary64` `prod-exp_binary64`
42×	`difference-of-squares_binary64`
39×	`cbrt-undiv_binary64` `div-exp_binary64`
32×	`associate-/r*_binary64`
21×	`distribute-lft-out--_binary64`
15×	`frac-times_binary64`
13×	`associate-*l/_binary64`
12×	`cbrt-div_binary64`
11×	`pow1_binary64` `div-inv_binary64`
10×	`associate-/r/_binary64`
6×	`flip3-+_binary64` `flip3--_binary64` `associate-r/_binary64` `associate-/l_binary64` `flip--_binary64` `flip-+_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `associate-l_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`unswap-sqr_binary64`

Counts

4 → 360

Calls

8 calls:

46.0ms	(.f64 (.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
23.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 (.f64 r w) (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))))
12.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
5.0ms	(/.f64 2 (*.f64 r r))
0.0ms	(+.f64 (/.f64 2 (*.f64 r r)) -3/2)

series1.4s (8.3%)

Counts

4 → 38

Calls

4 calls:

689.0ms	(.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 (.f64 r w) (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v)))))
377.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
273.0ms	(.f64 (.f64 (+.f64 3/8 (.f64 v -1/4)) (/.f64 (.f64 r w) (*.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))))) (/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w)))
31.0ms	(/.f64 2 (*.f64 r r))

Compiler

Compiled 2471 to 2037 computations (17.6% saved)

simplify136.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

398 → 398

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5020	13362

prune1.4s (8.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	396	2	398
Fresh	2	10	12
Picked	0	1	1
Done	0	0	0
Total	398	13	411

Error

0.0b

Counts

411 → 13

Compiler

Compiled 18287 to 11832 computations (35.3% saved)

localize22.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(cbrt.f64 (-.f64 1 v))
0.1b	(/.f64 (.f64 r w) (.f64 (cbrt.f64 (-.f64 1 v)) (cbrt.f64 (-.f64 1 v))))
0.1b	(/.f64 (cbrt.f64 (-.f64 1 v)) w)
0.0b	(+.f64 (/.f64 2 (*.f64 r r)) -3/2)
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)))
0.5b	(/.f64 2 (*.f64 r r))
2.6b	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
6.4b	(.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))))

rewrite189.0ms (1.1%)

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

8 calls:

63.0ms	(.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)))
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))))
12.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
5.0ms	(/.f64 2 (*.f64 r r))
0.0ms	(+.f64 (/.f64 2 (*.f64 r r)) -3/2)

series859.0ms (5.2%)

Counts

4 → 37

Calls

4 calls:

371.0ms	(/.f64 r (/.f64 (cbrt.f64 (-.f64 1 v)) w))
267.0ms	(.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))))
190.0ms	(.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)))
30.0ms	(/.f64 2 (*.f64 r r))

Compiler

Compiled 2174 to 1832 computations (15.7% saved)

simplify134.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

414 → 414

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4990	12188
1	4990	12188

prune1.4s (8.4%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	414	0	414
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	414	13	427

Error

0.0b

Counts

427 → 13

Compiler

Compiled 17792 to 11242 computations (36.8% saved)

simplify164.0ms (1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (112.0ms)

Iter	Nodes	Cost
0	5045	4245

regimes784.0ms (4.7%)

Compiler: Compiled 11848 to 9184 computations (22.5% saved)

bsearch0.0ms (0%)

regimes570.0ms (3.5%)

Compiler: Compiled 8220 to 6512 computations (20.8% saved)

bsearch0.0ms (0%)

regimes576.0ms (3.5%)

Compiler: Compiled 8076 to 6396 computations (20.8% saved)

bsearch5.0ms (0%)

Compiler: Compiled 3 to 4 computations (-33.3% saved)

regimes267.0ms (1.6%)

Compiler: Compiled 2255 to 1867 computations (17.2% saved)

bsearch90.0ms (0.5%)

Steps

Iters	Range		Point
7	3.768188042942504e+40	2.699491949893235e+42	3.2366970952931783e+41
10	-6.07471160654164e+29	-1.1765057823338115e+19	-3.806672820169377e+23

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes181.0ms (1.1%)

Compiler: Compiled 1255 to 1071 computations (14.7% saved)

bsearch86.0ms (0.5%)

Steps

Iters	Range		Point
10	1.6814889473710594e-09	206311.1983157708	0.9608221583659738
8	-109303372001.62778	-12176299.174611766	-12391569.29492999

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes122.0ms (0.7%)

Compiler: Compiled 407 to 398 computations (2.2% saved)

bsearch91.0ms (0.5%)

Steps

Iters	Range		Point
10	1.6814889473710594e-09	206311.1983157708	0.7324601245828686
8	-109303372001.62778	-12176299.174611766	-12391569.29492999

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes127.0ms (0.8%)

Compiler: Compiled 339 to 346 computations (-2.1% saved)

bsearch83.0ms (0.5%)

Steps

Iters	Range		Point
10	1.6814889473710594e-09	206311.1983157708	1.0129891302451897
8	-109303372001.62778	-12176299.174611766	-12391569.29492999

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes123.0ms (0.7%)

Compiler: Compiled 271 to 290 computations (-7% saved)

bsearch87.0ms (0.5%)

Steps

Iters	Range		Point
10	1.6814889473710594e-09	206311.1983157708	9.315081571616325
9	-1.1765057823338115e+19	-2162934412163.3599	-110201753769437.28

Compiler

Compiled 1 to 3 computations (-200% saved)

regimes30.0ms (0.2%)

Compiler: Compiled 66 to 96 computations (-45.5% saved)

bsearch0.0ms (0%)

regimes23.0ms (0.1%)

Compiler: Compiled 15 to 54 computations (-260% saved)

bsearch0.0ms (0%)

regimes23.0ms (0.1%)

Accuracy

Total 0.2b remaining (92.2%)

Threshold costs 0.2b (92.2%)

Compiler

Compiled 12 to 42 computations (-250% saved)

bsearch20.0ms (0.1%)

Compiler: Compiled 450 to 299 computations (33.6% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	438	552
1	438	552

end0.0ms (0%)

sample3.5s (20.9%)

Algorithm

1×

intervals

Results

536.0ms	8000×	body	128	valid
328.0ms	4936×	body	128	invalid

Compiler

Compiled 3108 to 2394 computations (23% saved)

Pareto

0.9312455742070787

Details

analyze1.1s (6.6%)

sample50.0ms (0.3%)

simplify146.0ms (0.9%)

prune17.0ms (0.1%)

localize19.0ms (0.1%)

rewrite83.0ms (0.5%)

series711.0ms (4.3%)

simplify80.0ms (0.5%)

prune425.0ms (2.6%)

localize17.0ms (0.1%)

rewrite72.0ms (0.4%)

series657.0ms (4%)

simplify115.0ms (0.7%)

prune471.0ms (2.9%)

localize21.0ms (0.1%)

rewrite153.0ms (0.9%)

series1.4s (8.3%)

simplify136.0ms (0.8%)

prune1.4s (8.3%)

localize22.0ms (0.1%)

rewrite189.0ms (1.1%)

series859.0ms (5.2%)

simplify134.0ms (0.8%)

prune1.4s (8.4%)

simplify164.0ms (1%)

regimes784.0ms (4.7%)

bsearch0.0ms (0%)

regimes570.0ms (3.5%)

bsearch0.0ms (0%)

regimes576.0ms (3.5%)

bsearch5.0ms (0%)

regimes267.0ms (1.6%)

bsearch90.0ms (0.5%)

regimes181.0ms (1.1%)

bsearch86.0ms (0.5%)

regimes122.0ms (0.7%)

bsearch91.0ms (0.5%)

regimes127.0ms (0.8%)

bsearch83.0ms (0.5%)

regimes123.0ms (0.7%)

bsearch87.0ms (0.5%)

regimes30.0ms (0.2%)

bsearch0.0ms (0%)

regimes23.0ms (0.1%)

bsearch0.0ms (0%)

regimes23.0ms (0.1%)

bsearch20.0ms (0.1%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample3.5s (20.9%)

Profiling