Details

analyze217.0ms

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

sample22.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
1.0ms	13×	body	80	invalid

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5043	18

prune6.0ms

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: 0.2b

Counts

2 → 2

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

266×	`*-un-lft-identity_binary64`
223×	`times-frac_binary64`
140×	`add-sqr-sqrt_binary64`
94×	`add-cube-cbrt_binary64`
58×	`distribute-lft-out_binary64`
46×	`associate-r_binary64`
45×	`distribute-rgt-neg-in_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
21×	`associate-/l*_binary64`
18×	`associate-l_binary64`
17×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
12×	`distribute-lft-neg-in_binary64`
11×	`associate-/r*_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`pow1_binary64` `associate-/r/_binary64`
5×	`div-inv_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `neg-mul-1_binary64` `unswap-sqr_binary64` `div-sub_binary64` `prod-exp_binary64`
3×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `neg-sub0_binary64` `distribute-frac-neg_binary64` `flip--_binary64` `flip-+_binary64`
1×	`pow-prod-down_binary64` `associate-+r-_binary64` `associate-r/_binary64` `frac-add_binary64` `frac-times_binary64` `unsub-neg_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

4 → 244

Calls

4 calls:

47.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (+.f64 (/.f64 PI.f64 a) (/.f64 (neg.f64 PI.f64) b)) (-.f64 b a)))
31.0ms	(/.f64 (+.f64 (/.f64 PI.f64 a) (/.f64 (neg.f64 PI.f64) b)) (-.f64 b a))
3.0ms	(/.f64 PI.f64 a)
5.0ms	(/.f64 (neg.f64 PI.f64) b)

series46.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(*.f64 (/.f64 1/2 (+.f64 b a)) (/.f64 (+.f64 (/.f64 PI.f64 a) (/.f64 (neg.f64 PI.f64) b)) (-.f64 b a)))
14.0ms	(/.f64 (+.f64 (/.f64 PI.f64 a) (/.f64 (neg.f64 PI.f64) b)) (-.f64 b a))
5.0ms	(/.f64 PI.f64 a)
6.0ms	(/.f64 (neg.f64 PI.f64) b)

simplify59.0ms

Algorithm

egg-herbie

Counts

256 → 256

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5347	3397

prune160.0ms

Filtered

169 candidates to 256 candidates (-51.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	249	7	256
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	250	8	258

Merged error: 0b

Counts

258 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-sqr-sqrt_binary64`
51×	`*-un-lft-identity_binary64`
46×	`times-frac_binary64`
33×	`add-cube-cbrt_binary64`
22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`associate-r_binary64`
12×	`associate-l_binary64`
11×	`associate-/r*_binary64`
7×	`associate-/l/_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64` `div-exp_binary64`
6×	`pow1_binary64` `difference-of-squares_binary64` `div-inv_binary64` `frac-times_binary64` `associate-*l/_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-/r/_binary64` `prod-exp_binary64` `frac-sub_binary64`
3×	`distribute-lft-out_binary64` `clear-num_binary64` `frac-2neg_binary64`
2×	`associate-*r/_binary64` `unswap-sqr_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 142

Calls

4 calls:

23.0ms	(/.f64 (*.f64 (-.f64 (/.f64 PI.f64 a) (/.f64 PI.f64 b)) (/.f64 1/2 (+.f64 b a))) (-.f64 b a))
3.0ms	(/.f64 PI.f64 a)
24.0ms	(*.f64 (-.f64 (/.f64 PI.f64 a) (/.f64 PI.f64 b)) (/.f64 1/2 (+.f64 b a)))
3.0ms	(/.f64 PI.f64 b)

series33.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(/.f64 (*.f64 (-.f64 (/.f64 PI.f64 a) (/.f64 PI.f64 b)) (/.f64 1/2 (+.f64 b a))) (-.f64 b a))
5.0ms	(/.f64 PI.f64 a)
12.0ms	(*.f64 (-.f64 (/.f64 PI.f64 a) (/.f64 PI.f64 b)) (/.f64 1/2 (+.f64 b a)))
3.0ms	(/.f64 PI.f64 b)

simplify35.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5210	1820

prune85.0ms

Filtered

113 candidates to 154 candidates (-36.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	153	1	154
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	154	8	162

Merged error: 0b

Counts

162 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b	(/.f64 PI.f64 a)
0.3b	(.f64 (/.f64 (sqrt.f64 1/2) 1) (.f64 (/.f64 (-.f64 (/.f64 PI.f64 a) (/.f64 PI.f64 b)) (-.f64 b a)) (/.f64 (sqrt.f64 1/2) (+.f64 b a))))
0.3b	(/.f64 PI.f64 b)
0.4b	(/.f64 (sqrt.f64 1/2) (+.f64 b a))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

69×	`add-exp-log_binary64`
64×	`*-un-lft-identity_binary64`
60×	`times-frac_binary64`
51×	`add-cbrt-cube_binary64`
50×	`add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
27×	`prod-exp_binary64`
25×	`div-exp_binary64`
24×	`sqrt-prod_binary64`
22×	`associate-l_binary64`
18×	`cbrt-unprod_binary64`
16×	`cbrt-undiv_binary64`
12×	`associate-/l*_binary64`
10×	`associate-/r*_binary64`
9×	`pow1_binary64`
7×	`distribute-lft-out_binary64`
5×	`1-exp_binary64` `associate-*r/_binary64` `frac-times_binary64`
4×	`add-log-exp_binary64` `div-inv_binary64`
3×	`pow-prod-down_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-*l/_binary64`
2×	`associate-/r/_binary64`
1×	`flip3-+_binary64` `associate-r_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 167

Calls

4 calls:

5.0ms	(/.f64 PI.f64 a)
33.0ms	(.f64 (/.f64 (sqrt.f64 1/2) 1) (.f64 (/.f64 (-.f64 (/.f64 PI.f64 a) (/.f64 PI.f64 b)) (-.f64 b a)) (/.f64 (sqrt.f64 1/2) (+.f64 b a))))
3.0ms	(/.f64 PI.f64 b)
7.0ms	(/.f64 (sqrt.f64 1/2) (+.f64 b a))

series40.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(/.f64 PI.f64 a)
26.0ms	(.f64 (/.f64 (sqrt.f64 1/2) 1) (.f64 (/.f64 (-.f64 (/.f64 PI.f64 a) (/.f64 PI.f64 b)) (-.f64 b a)) (/.f64 (sqrt.f64 1/2) (+.f64 b a))))
3.0ms	(/.f64 PI.f64 b)
9.0ms	(/.f64 (sqrt.f64 1/2) (+.f64 b a))

simplify52.0ms

Algorithm

egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5022	2081

prune90.0ms

Filtered

109 candidates to 179 candidates (-64.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	179	0	179
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	179	8	187

Merged error: 0b

Counts

187 → 8

localize20.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 b)
0.6b	(cbrt.f64 b)
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`pow1_binary64` `sqrt-prod_binary64` `cbrt-prod_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
2×	`pow1/2_binary64` `pow1/3_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 48

Calls

4 calls:

1.0ms	(cbrt.f64 b)
1.0ms	(cbrt.f64 b)
2.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

series31.0ms

Counts

4 → 8

Calls

4 calls:

15.0ms	(cbrt.f64 b)
17.0ms	(cbrt.f64 b)
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify36.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (31.0ms)

Iter	Nodes	Cost
0	5746	214

prune30.0ms

Filtered

45 candidates to 56 candidates (-24.4%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	56	8	64

Merged error: 0b

Counts

64 → 8

regimes107.0ms

Accuracy

0% (0.3b 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	39	17
1	39	17

end0.0ms

sample603.0ms

Algorithm

intervals

Results

444.0ms	8000×	body	80	valid
21.0ms	346×	body	80	invalid

Details

analyze217.0ms

sample22.0ms

simplify43.0ms

prune6.0ms

localize11.0ms

rewrite103.0ms

series46.0ms

simplify59.0ms

prune160.0ms

localize13.0ms

rewrite59.0ms

series33.0ms

simplify35.0ms

prune85.0ms

localize13.0ms

rewrite55.0ms

series40.0ms

simplify52.0ms

prune90.0ms

localize20.0ms

rewrite7.0ms

series31.0ms

simplify36.0ms

prune30.0ms

regimes107.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample603.0ms

Profiling