Details

analyze4.0ms (0%)

Algorithm

1×

Search

True	Other	False	Iter
0%	56.2%	43.8%	0
0%	56.2%	43.8%	1
0%	56.2%	43.8%	2
42.1%	14%	43.8%	3
42.1%	14%	43.8%	4
52.7%	3.5%	43.8%	5
56.2%	0%	43.8%	6

Compiler

Compiled 42 to 29 computations (31% saved)

sample28.0ms (0.2%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
5.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify419.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (254.0ms)

Iter	Nodes	Cost
0	5111	37

prune5.0ms (0%)

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: 0.8b

Counts

2 → 2

Compiler

Compiled 85 to 60 computations (29.4% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
7.3b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
12.2b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite113.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64_2099`
34×	`distribute-lft-out_binary64_2052` `add-cbrt-cube_binary64_2132` `add-exp-log_binary64_2134`
24×	`flip3-+_binary64_2102` `flip-+_binary64_2073`
21×	`add-sqr-sqrt_binary64_2120` `associate-r_binary64_2041`
18×	`associate-/r/_binary64_2047`
16×	`frac-times_binary64_2109`
15×	`add-cube-cbrt_binary64_2131`
14×	`times-frac_binary64_2105`
13×	`pow1_binary64_2157`
11×	`swap-sqr_binary64_2066`
10×	`cbrt-undiv_binary64_2130` `div-exp_binary64_2147` `associate-*l/_binary64_2044` `prod-exp_binary64_2145` `cbrt-unprod_binary64_2129`
9×	`associate-l_binary64_2042`
8×	`associate-*r/_binary64_2043`
7×	`associate-/l/_binary64_2048`
6×	`associate-/r*_binary64_2045`
5×	`associate-/l*_binary64_2046`
4×	`add-log-exp_binary64_2135`
3×	`unswap-sqr_binary64_2067` `div-inv_binary64_2096`
2×	`*-commutative_binary64_2032` `frac-2neg_binary64_2110` `pow-prod-down_binary64_2167` `clear-num_binary64_2098`
1×	`distribute-rgt-in_binary64_2051` `distribute-lft-in_binary64_2050` `pow2_binary64_2177` `pow-plus_binary64_2159` `pow-prod-up_binary64_2166` `pow-sqr_binary64_2072`

Counts

4 → 158

Calls

4 calls:

34.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
26.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
19.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
16.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

series553.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

220.0ms	(/.f64 (.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))) (+.f64 alpha (+.f64 beta 3)))
194.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
105.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
33.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify98.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4939	3959
1	4939	3959

prune285.0ms (2.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	163	7	170
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	165	7	172

Merged error: 0.0b

Counts

172 → 7

Compiler

Compiled 5236 to 3396 computations (35.1% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))
0.0b	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
7.3b	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))

rewrite213.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

826×	`*-un-lft-identity_binary64_2099`
508×	`times-frac_binary64_2105`
374×	`distribute-lft-out_binary64_2052`
191×	`add-sqr-sqrt_binary64_2120`
182×	`add-cube-cbrt_binary64_2131`
136×	`associate-r_binary64_2041`
34×	`add-cbrt-cube_binary64_2132` `add-exp-log_binary64_2134`
31×	`associate-/l*_binary64_2046`
30×	`associate-/r/_binary64_2047`
20×	`flip3-+_binary64_2102` `flip-+_binary64_2073`
15×	`associate-/r*_binary64_2045` `div-inv_binary64_2096`
14×	`cbrt-undiv_binary64_2130` `div-exp_binary64_2147`
8×	`associate-/l/_binary64_2048`
6×	`pow1_binary64_2157` `prod-exp_binary64_2145` `cbrt-unprod_binary64_2129`
4×	`associate-l_binary64_2042` `associate-*l/_binary64_2044` `add-log-exp_binary64_2135` `frac-times_binary64_2109`
3×	`frac-2neg_binary64_2110` `unswap-sqr_binary64_2067` `clear-num_binary64_2098`
2×	`associate-*r/_binary64_2043`
1×	`*-commutative_binary64_2032` `pow-prod-down_binary64_2167`

Counts

4 → 422

Calls

4 calls:

57.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))
44.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
24.0ms	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
11.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))

series597.0ms (4.7%)

Counts

4 → 12

Calls

4 calls:

229.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
210.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2)))
107.0ms	(/.f64 (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)) (+.f64 (+.f64 alpha beta) 2))
50.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))

simplify165.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

434 → 434

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4938	12638
1	4938	12638

prune1.0s (8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	430	4	434
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	435	6	441

Merged error: 0.0b

Counts

441 → 6

Compiler

Compiled 15522 to 9825 computations (36.7% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta))) (+.f64 (+.f64 alpha beta) 2))
0.0b	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta)))
0.1b	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
7.3b	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta))) (+.f64 (+.f64 alpha beta) 2)))

rewrite561.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Rules

2828×	`*-un-lft-identity_binary64_2099`
2522×	`times-frac_binary64_2105`
1137×	`distribute-lft-out_binary64_2052`
890×	`add-sqr-sqrt_binary64_2120`
869×	`add-cube-cbrt_binary64_2131`
421×	`associate-r_binary64_2041`
100×	`add-exp-log_binary64_2134`
92×	`associate-/r/_binary64_2047`
87×	`associate-/l*_binary64_2046`
58×	`div-exp_binary64_2147`
52×	`add-cbrt-cube_binary64_2132` `div-inv_binary64_2096`
44×	`flip3-+_binary64_2102` `flip-+_binary64_2073`
36×	`associate-/r*_binary64_2045`
26×	`cbrt-undiv_binary64_2130`
16×	`prod-exp_binary64_2145`
8×	`1-exp_binary64_2140` `rec-exp_binary64_2146` `cbrt-unprod_binary64_2129`
7×	`pow1_binary64_2157`
6×	`associate-/l/_binary64_2048` `unswap-sqr_binary64_2067`
4×	`associate-l_binary64_2042` `associate-*l/_binary64_2044` `add-log-exp_binary64_2135` `frac-times_binary64_2109`
3×	`frac-2neg_binary64_2110` `clear-num_binary64_2098`
2×	`associate-*r/_binary64_2043`
1×	`pow-flip_binary64_2170` `inv-pow_binary64_2181` `*-commutative_binary64_2032` `pow-prod-down_binary64_2167`

Counts

4 → 1153

Calls

4 calls:

148.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta))) (+.f64 (+.f64 alpha beta) 2)))
72.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
42.0ms	(/.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta))) (+.f64 (+.f64 alpha beta) 2))
15.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta)))

series648.0ms (5.1%)

Counts

4 → 12

Calls

4 calls:

227.0ms	(/.f64 (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta))) (+.f64 (+.f64 alpha beta) 2))) (+.f64 alpha (+.f64 beta 3)))
191.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta))) (+.f64 (+.f64 alpha beta) 2)))
157.0ms	(/.f64 (/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta))) (+.f64 (+.f64 alpha beta) 2))
73.0ms	(/.f64 1 (/.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 1 beta)))

simplify385.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1165 → 1165

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4990	39754
1	4990	39754

prune4.8s (38%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	1165	0	1165
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	1165	6	1171

Merged error: 0.0b

Counts

1171 → 6

Compiler

Compiled 47068 to 31154 computations (33.8% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
0.1b	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
0.2b	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
7.3b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))

rewrite206.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

829×	`*-un-lft-identity_binary64_2099`
394×	`times-frac_binary64_2105`
355×	`distribute-lft-out_binary64_2052`
248×	`sqrt-prod_binary64_2114`
224×	`add-sqr-sqrt_binary64_2120`
149×	`add-cube-cbrt_binary64_2131`
127×	`swap-sqr_binary64_2066`
45×	`associate-l_binary64_2042`
42×	`associate-r_binary64_2041`
38×	`add-cbrt-cube_binary64_2132` `add-exp-log_binary64_2134`
16×	`pow1_binary64_2157`
14×	`associate-/l*_binary64_2046`
13×	`prod-exp_binary64_2145` `cbrt-unprod_binary64_2129`
12×	`flip3-+_binary64_2102` `associate-/r/_binary64_2047` `flip-+_binary64_2073`
10×	`cbrt-undiv_binary64_2130` `div-exp_binary64_2147` `associate-/r*_binary64_2045` `unswap-sqr_binary64_2067` `frac-times_binary64_2109`
7×	`associate-*r/_binary64_2043`
6×	`associate-*l/_binary64_2044` `div-inv_binary64_2096`
4×	`associate-/l/_binary64_2048` `add-log-exp_binary64_2135` `sqrt-div_binary64_2115` `pow-prod-down_binary64_2167`
2×	`*-commutative_binary64_2032` `frac-2neg_binary64_2110` `clear-num_binary64_2098`
1×	`pow2_binary64_2177` `pow-plus_binary64_2159` `pow-prod-up_binary64_2166` `pow-sqr_binary64_2072`

Counts

4 → 405

Calls

4 calls:

55.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
38.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))
17.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
13.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))

series440.0ms (3.5%)

Counts

4 → 12

Calls

4 calls:

199.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))))
102.0ms	(*.f64 (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)) (/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2)))
71.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))
67.0ms	(/.f64 (sqrt.f64 (+.f64 beta 1)) (+.f64 (+.f64 beta alpha) 2))

simplify144.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

417 → 417

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5751	11883

prune993.0ms (7.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	416	1	417
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	418	5	423

Merged error: 0.0b

Counts

423 → 5

Compiler

Compiled 15011 to 10067 computations (32.9% saved)

regimes33.0ms (0.3%)

Compiler: Compiled 272 to 216 computations (20.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	25	40
1	25	40

end0.0ms (0%)

sample926.0ms (7.3%)

Algorithm

1×

intervals

Results

468.0ms	8000×	body	128	valid
145.0ms	8000×	pre	128	true

Compiler

Compiled 203 to 155 computations (23.6% saved)

Details

analyze4.0ms (0%)

sample28.0ms (0.2%)

simplify419.0ms (3.3%)

prune5.0ms (0%)

localize13.0ms (0.1%)

rewrite113.0ms (0.9%)

series553.0ms (4.3%)

simplify98.0ms (0.8%)

prune285.0ms (2.2%)

localize17.0ms (0.1%)

rewrite213.0ms (1.7%)

series597.0ms (4.7%)

simplify165.0ms (1.3%)

prune1.0s (8%)

localize14.0ms (0.1%)

rewrite561.0ms (4.4%)

series648.0ms (5.1%)

simplify385.0ms (3%)

prune4.8s (38%)

localize14.0ms (0.1%)

rewrite206.0ms (1.6%)

series440.0ms (3.5%)

simplify144.0ms (1.1%)

prune993.0ms (7.8%)

regimes33.0ms (0.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample926.0ms (7.3%)

Profiling