Details

analyze5.0ms (0.1%)

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)

sample27.0ms (0.3%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
4.0ms	256×	pre	128	true

Compiler

Compiled 77 to 55 computations (28.6% saved)

simplify259.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (253.0ms)

Iter	Nodes	Cost
0	5110	37

prune5.0ms (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: 1.4b

Counts

2 → 2

Compiler

Compiled 85 to 60 computations (29.4% saved)

localize17.0ms (0.2%)

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)))
6.5b	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
10.5b	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))

rewrite115.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`*-un-lft-identity_binary64`
34×	`distribute-lft-out_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
24×	`flip3-+_binary64` `flip-+_binary64`
21×	`associate-r_binary64` `add-sqr-sqrt_binary64`
18×	`associate-/r/_binary64`
16×	`frac-times_binary64`
15×	`add-cube-cbrt_binary64`
14×	`times-frac_binary64`
13×	`pow1_binary64`
11×	`swap-sqr_binary64`
10×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64` `associate-*l/_binary64`
9×	`associate-l_binary64`
8×	`associate-*r/_binary64`
7×	`associate-/l/_binary64`
6×	`associate-/r*_binary64`
5×	`associate-/l*_binary64`
4×	`add-log-exp_binary64`
3×	`unswap-sqr_binary64` `div-inv_binary64`
2×	`pow-prod-down_binary64` `clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`pow-prod-up_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `pow-plus_binary64` `pow-sqr_binary64` `pow2_binary64`

Counts

4 → 158

Calls

4 calls:

29.0ms	(/.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))))
18.0ms	(/.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))

series531.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

219.0ms	(/.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)))
180.0ms	(.f64 (+.f64 alpha 1) (/.f64 (+.f64 beta 1) (.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))))
100.0ms	(/.f64 (+.f64 beta 1) (*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2)))
32.0ms	(*.f64 (+.f64 (+.f64 alpha beta) 2) (+.f64 (+.f64 alpha beta) 2))

simplify97.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

170 → 170

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4938	3959
1	4938	3959

prune300.0ms (3.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	163	7	170
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	164	8	172

Merged error: 0.0b

Counts

172 → 8

Compiler

Compiled 5264 to 3408 computations (35.3% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))
0.1b	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))) (+.f64 alpha (+.f64 beta 3)))
0.1b	(*.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))
6.5b	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))))

rewrite139.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

133×	`*-un-lft-identity_binary64`
82×	`add-exp-log_binary64`
67×	`times-frac_binary64`
61×	`add-cbrt-cube_binary64`
54×	`distribute-lft-out_binary64` `add-sqr-sqrt_binary64`
37×	`add-cube-cbrt_binary64`
32×	`prod-exp_binary64`
27×	`associate-r_binary64`
25×	`associate-l_binary64`
24×	`div-exp_binary64`
22×	`cbrt-unprod_binary64`
19×	`cbrt-undiv_binary64` `frac-times_binary64`
13×	`flip3-+_binary64` `associate-/l/_binary64` `associate-*r/_binary64` `flip-+_binary64`
11×	`pow1_binary64` `associate-*l/_binary64`
10×	`associate-/r*_binary64`
8×	`associate-/r/_binary64`
6×	`unswap-sqr_binary64` `rec-exp_binary64`
5×	`associate-/l*_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64` `div-inv_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

4 → 206

Calls

4 calls:

40.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))) (+.f64 alpha (+.f64 beta 3)))
32.0ms	(*.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))
26.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))))
11.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))

series688.0ms (7.8%)

Counts

4 → 12

Calls

4 calls:

343.0ms	(/.f64 (.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))) (+.f64 alpha (+.f64 beta 3)))
200.0ms	(.f64 (+.f64 alpha 1) (.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))))
96.0ms	(*.f64 (/.f64 1 (+.f64 (+.f64 beta alpha) 2)) (/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2)))
48.0ms	(/.f64 (+.f64 beta 1) (+.f64 (+.f64 beta alpha) 2))

simplify114.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

218 → 218

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4962	5666
1	4962	5666

prune382.0ms (4.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	213	5	218
Fresh	5	1	6
Picked	1	0	1
Done	1	0	1
Total	220	6	226

Merged error: 0b

Counts

226 → 6

Compiler

Compiled 7114 to 4614 computations (35.1% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1)))) (+.f64 alpha (+.f64 beta 3)))
2.5b	(*.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1)))
3.9b	(.f64 (sqrt.f64 (+.f64 alpha 1)) (.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1))))

rewrite274.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

783×	`*-un-lft-identity_binary64`
491×	`times-frac_binary64`
354×	`distribute-lft-out_binary64`
192×	`add-sqr-sqrt_binary64`
174×	`add-cube-cbrt_binary64`
143×	`associate-l_binary64`
52×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
40×	`flip3-+_binary64` `flip-+_binary64`
34×	`frac-times_binary64`
28×	`associate-/r/_binary64`
27×	`associate-/l*_binary64`
24×	`associate-*r/_binary64`
18×	`associate-/l/_binary64`
17×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
14×	`div-inv_binary64`
11×	`pow1_binary64` `sqrt-prod_binary64` `associate-*l/_binary64`
10×	`associate-/r*_binary64`
8×	`associate-r_binary64`
6×	`unswap-sqr_binary64`
4×	`pow-prod-down_binary64` `add-log-exp_binary64`
2×	`clear-num_binary64` `frac-2neg_binary64` `*-commutative_binary64`

Counts

4 → 440

Calls

4 calls:

59.0ms	(*.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1)))
48.0ms	(/.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1)))) (+.f64 alpha (+.f64 beta 3)))
46.0ms	(.f64 (sqrt.f64 (+.f64 alpha 1)) (.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1))))
27.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))

series708.0ms (8.1%)

Counts

4 → 12

Calls

4 calls:

230.0ms	(/.f64 (.f64 (sqrt.f64 (+.f64 alpha 1)) (.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1)))) (+.f64 alpha (+.f64 beta 3)))
201.0ms	(.f64 (sqrt.f64 (+.f64 alpha 1)) (.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1))))
176.0ms	(*.f64 (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)) (sqrt.f64 (+.f64 alpha 1)))
101.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))

simplify203.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

452 → 452

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4957	15248
1	4957	15248

prune1.5s (16.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	452	0	452
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	452	6	458

Merged error: 0b

Counts

458 → 6

Compiler

Compiled 19002 to 12696 computations (33.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))
0.1b	(/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))))
0.5b	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))))
6.5b	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))

rewrite261.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

821×	`*-un-lft-identity_binary64`
550×	`times-frac_binary64`
365×	`distribute-lft-out_binary64`
203×	`add-sqr-sqrt_binary64`
194×	`add-cube-cbrt_binary64`
136×	`associate-r_binary64`
67×	`add-exp-log_binary64`
52×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
34×	`associate-/l*_binary64`
32×	`div-exp_binary64`
26×	`flip3-+_binary64` `flip-+_binary64`
25×	`cbrt-undiv_binary64`
20×	`associate-/r*_binary64`
19×	`div-inv_binary64`
12×	`prod-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
9×	`cbrt-unprod_binary64`
7×	`pow1_binary64`
6×	`associate-*r/_binary64`
5×	`rec-exp_binary64`
4×	`add-log-exp_binary64` `associate-l_binary64`
3×	`associate-/l/_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`pow-prod-down_binary64` `inv-pow_binary64` `pow-flip_binary64` `*-commutative_binary64`

Counts

4 → 464

Calls

4 calls:

61.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))
42.0ms	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))))
39.0ms	(/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))))
26.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))

series705.0ms (8%)

Counts

4 → 12

Calls

4 calls:

224.0ms	(/.f64 1 (/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))))
196.0ms	(*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2)))
190.0ms	(/.f64 (+.f64 alpha (+.f64 beta 3)) (*.f64 (+.f64 alpha 1) (/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))))
95.0ms	(/.f64 (/.f64 (+.f64 1 beta) (+.f64 (+.f64 alpha beta) 2)) (+.f64 (+.f64 alpha beta) 2))

simplify179.0ms (2%)

Algorithm

1×	egg-herbie

Counts

476 → 476

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	5163	15643

prune1.2s (14.1%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	476	0	476
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	476	6	482

Merged error: 0b

Counts

482 → 6

Compiler

Compiled 17601 to 11458 computations (34.9% saved)

regimes39.0ms (0.4%)

Compiler: Compiled 386 to 298 computations (22.8% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	47
1	26	47

end0.0ms (0%)

sample973.0ms (11.1%)

Algorithm

1×

intervals

Results

483.0ms	8000×	body	128	valid
141.0ms	8000×	pre	128	true

Compiler

Compiled 264 to 199 computations (24.6% saved)

Details

analyze5.0ms (0.1%)

sample27.0ms (0.3%)

simplify259.0ms (3%)

prune5.0ms (0.1%)

localize17.0ms (0.2%)

rewrite115.0ms (1.3%)

series531.0ms (6.1%)

simplify97.0ms (1.1%)

prune300.0ms (3.4%)

localize16.0ms (0.2%)

rewrite139.0ms (1.6%)

series688.0ms (7.8%)

simplify114.0ms (1.3%)

prune382.0ms (4.4%)

localize15.0ms (0.2%)

rewrite274.0ms (3.1%)

series708.0ms (8.1%)

simplify203.0ms (2.3%)

prune1.5s (16.7%)

localize13.0ms (0.2%)

rewrite261.0ms (3%)

series705.0ms (8%)

simplify179.0ms (2%)

prune1.2s (14.1%)

regimes39.0ms (0.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample973.0ms (11.1%)

Profiling