Details

analyze218.0ms

Algorithm

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
15.6%	84.3%	0.1%	6
37.5%	62.4%	0.1%	7
46.8%	53.1%	0.1%	8
57.8%	39.8%	2.4%	9
64.6%	30.4%	5%	10
71.8%	20.3%	7.9%	11
74.1%	16.2%	9.7%	12
77.4%	10.7%	12%	13
78.6%	8.4%	13%	14

sample21.0ms

Algorithm

intervals

Results

14.0ms	256×	body	128	valid
0.0ms	7×	body	128	invalid

simplify51.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5005	29

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 15.8b

Counts

2 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.9b	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
5.0b	(-.f64 (.f64 b b) (.f64 a a))
9.3b	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

224×	`times-frac_binary64`
157×	`add-sqr-sqrt_binary64`
132×	`*-un-lft-identity_binary64`
100×	`add-cube-cbrt_binary64`
58×	`associate-l_binary64`
46×	`difference-of-squares_binary64`
19×	`associate-r_binary64` `div-inv_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`distribute-lft-out--_binary64`
13×	`associate-/l*_binary64`
8×	`add-log-exp_binary64`
6×	`pow1_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
4×	`associate-/r*_binary64` `sub-neg_binary64` `associate-/r/_binary64`
3×	`cbrt-unprod_binary64` `associate-*r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `frac-sub_binary64` `frac-times_binary64`
2×	`diff-log_binary64`
1×	`pow-prod-down_binary64` `associate-/l/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 230

Calls

4 calls:

18.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
9.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
4.0ms	(-.f64 (.f64 b b) (.f64 a a))
44.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
64.0ms	(/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (.f64 a a)))
45.0ms	(-.f64 (.f64 b b) (.f64 a a))
93.0ms	(.f64 (/.f64 (/.f64 PI.f64 2) (-.f64 (.f64 b b) (*.f64 a a))) (-.f64 (/.f64 1 a) (/.f64 1 b)))

simplify85.0ms

Algorithm

egg-herbie

Counts

242 → 242

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5172	6697

prune284.0ms

Filtered

194 candidates to 242 candidates (-24.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	234	8	242
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	236	8	244

Merged error: 0.0b

Counts

244 → 8

localize8.0ms

Local error

Found 2 expressions with local error:

0.2b	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
0.3b	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

98×	`times-frac_binary64`
79×	`*-un-lft-identity_binary64`
51×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
39×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
17×	`cbrt-undiv_binary64` `div-exp_binary64`
14×	`distribute-lft-out_binary64` `associate-/l*_binary64`
10×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`div-inv_binary64`
5×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-/r/_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `flip-+_binary64` `associate-*l/_binary64`

Counts

2 → 116

Calls

2 calls:

18.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
9.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

series141.0ms

Counts

2 → 6

Calls

2 calls:

82.0ms	(/.f64 (.f64 (/.f64 (/.f64 PI.f64 2) (+.f64 b a)) 1) (.f64 a b))
59.0ms	(/.f64 (/.f64 PI.f64 2) (+.f64 b a))

simplify63.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5120	2501

prune103.0ms

Filtered

78 candidates to 122 candidates (-56.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	116	6	122
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	122	8	130

Merged error: 0b

Counts

130 → 8

localize9.0ms

Local error

Found 3 expressions with local error:

0.2b	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
0.3b	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))
0.3b	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

621×	`times-frac_binary64`
410×	`*-un-lft-identity_binary64`
278×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
95×	`add-exp-log_binary64`
71×	`associate-/r*_binary64`
66×	`distribute-lft-out_binary64`
62×	`add-cbrt-cube_binary64`
46×	`div-exp_binary64`
31×	`cbrt-undiv_binary64`
28×	`div-inv_binary64`
22×	`prod-exp_binary64`
13×	`cbrt-unprod_binary64`
9×	`rec-exp_binary64`
8×	`associate-/l*_binary64`
6×	`associate-/r/_binary64`
4×	`pow1_binary64`
3×	`associate-/l/_binary64` `add-log-exp_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `inv-pow_binary64` `pow-flip_binary64` `flip-+_binary64` `associate-*l/_binary64`

Counts

3 → 379

Calls

3 calls:

29.0ms	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
9.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))
18.0ms	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))

series219.0ms

Counts

3 → 9

Calls

3 calls:

85.0ms	(/.f64 (.f64 (/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2))) 1) (.f64 a b))
80.0ms	(/.f64 (+.f64 b a) (/.f64 PI.f64 2))
55.0ms	(/.f64 1 (/.f64 (+.f64 b a) (/.f64 PI.f64 2)))

simplify162.0ms

Algorithm

egg-herbie

Counts

388 → 388

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4969	9510
1	4969	9510

prune244.0ms

Filtered

204 candidates to 388 candidates (-90.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	387	1	388
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	389	7	396

Merged error: 0b

Counts

396 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 1 a) (/.f64 1 b))
0.2b	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
0.3b	(/.f64 PI.f64 (+.f64 b a))
0.3b	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

94×	`add-sqr-sqrt_binary64`
87×	`*-un-lft-identity_binary64`
76×	`times-frac_binary64`
37×	`associate-l_binary64`
35×	`add-cube-cbrt_binary64`
32×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
22×	`associate-r_binary64`
21×	`difference-of-squares_binary64`
17×	`distribute-lft-out--_binary64`
16×	`frac-times_binary64`
12×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`pow1_binary64` `div-inv_binary64`
10×	`associate-r/_binary64` `associate-l/_binary64`
8×	`flip3--_binary64` `flip--_binary64`
7×	`distribute-lft-out_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `frac-sub_binary64`
6×	`add-log-exp_binary64` `associate-/r/_binary64`
4×	`pow-prod-down_binary64` `associate-/r*_binary64`
3×	`associate-/l*_binary64`
2×	`flip3-+_binary64` `unswap-sqr_binary64` `flip-+_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64`

Counts

4 → 179

Calls

4 calls:

15.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
31.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
6.0ms	(/.f64 PI.f64 (+.f64 b a))
35.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(-.f64 (/.f64 1 a) (/.f64 1 b))
97.0ms	(.f64 (/.f64 PI.f64 (+.f64 b a)) (.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a))))
45.0ms	(/.f64 PI.f64 (+.f64 b a))
63.0ms	(*.f64 (-.f64 (/.f64 1 a) (/.f64 1 b)) (/.f64 1/2 (-.f64 b a)))

simplify68.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4956	4157
1	4956	4157

prune156.0ms

Filtered

132 candidates to 191 candidates (-44.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	190	1	191
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	191	7	198

Merged error: 0b

Counts

198 → 7

regimes32.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	16	20
1	16	20

end0.0ms

sample638.0ms

Algorithm

intervals

Results

462.0ms	8000×	body	128	valid
21.0ms	331×	body	128	invalid

Details

analyze218.0ms

sample21.0ms

simplify51.0ms

prune4.0ms

localize14.0ms

rewrite106.0ms

series224.0ms

simplify85.0ms

prune284.0ms

localize8.0ms

rewrite40.0ms

series141.0ms

simplify63.0ms

prune103.0ms

localize9.0ms

rewrite116.0ms

series219.0ms

simplify162.0ms

prune244.0ms

localize12.0ms

rewrite109.0ms

series226.0ms

simplify68.0ms

prune156.0ms

regimes32.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample638.0ms

Profiling