Details

analyze42.0ms

Algorithm

Search

True	Other	False	Iter
0%	6.2%	93.8%	0
0%	6.2%	93.8%	1
0%	6.2%	93.8%	2
1.6%	3.1%	95.3%	3
1.6%	3.1%	95.3%	4
2.3%	1.6%	96.1%	5
2.3%	1.6%	96.1%	6
2.7%	0.8%	96.5%	7
2.7%	0.8%	96.5%	8
2.9%	0.4%	96.7%	9
2.9%	0.4%	96.7%	10
3%	0.2%	96.8%	11
3%	0.2%	96.8%	12
3.1%	0.1%	96.8%	13
3.1%	0.1%	96.8%	14

sample20.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
4.0ms	256×	pre	80	true
0.0ms	4×	pre	80	false

simplify66.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5165	11

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 12.6b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (.f64 a a) (.f64 b b))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
12.2b	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`add-sqr-sqrt_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
5×	`add-log-exp_binary64`
4×	`pow1_binary64` `associate-/l*_binary64` `times-frac_binary64`
3×	`difference-of-squares_binary64` `sqrt-prod_binary64`
2×	`associate-/l/_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64`
1×	`associate-/r*_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

3 → 51

Calls

3 calls:

4.0ms	(-.f64 (.f64 a a) (.f64 b b))
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
8.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

series34.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(-.f64 (.f64 a a) (.f64 b b))
16.0ms	(sqrt.f64 (fabs.f64 (/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))))
10.0ms	(/.f64 (-.f64 (.f64 a a) (.f64 b b)) (*.f64 a a))

simplify65.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4948	663
1	4948	663

prune56.0ms

Filtered

43 candidates to 60 candidates (-39.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	58	2	60
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	2	61

Merged error: 0.0b

Counts

61 → 2

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))))
0.0b	(/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))
0.0b	(/.f64 a (/.f64 (-.f64 a b) a))
0.0b	(/.f64 (-.f64 a b) a)

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

890×	`times-frac_binary64`
617×	`*-un-lft-identity_binary64`
492×	`add-sqr-sqrt_binary64`
369×	`add-cube-cbrt_binary64`
84×	`associate-/r*_binary64`
63×	`distribute-lft-out_binary64`
61×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
27×	`div-inv_binary64`
20×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`associate-/l*_binary64`
10×	`cbrt-undiv_binary64` `div-exp_binary64`
7×	`associate-/r/_binary64`
5×	`pow1_binary64`
4×	`associate-/l/_binary64` `add-log-exp_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-prod_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `flip--_binary64` `flip-+_binary64`

Counts

4 → 478

Calls

4 calls:

4.0ms	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))))
21.0ms	(/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))
9.0ms	(/.f64 a (/.f64 (-.f64 a b) a))
6.0ms	(/.f64 (-.f64 a b) a)

series42.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(sqrt.f64 (fabs.f64 (/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))))
11.0ms	(/.f64 (+.f64 a b) (/.f64 a (/.f64 (-.f64 a b) a)))
7.0ms	(/.f64 a (/.f64 (-.f64 a b) a))
6.0ms	(/.f64 (-.f64 a b) a)

simplify103.0ms

Algorithm

egg-herbie

Counts

490 → 490

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5010	9101

prune272.0ms

Filtered

283 candidates to 490 candidates (-73.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	489	1	490
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	489	3	492

Merged error: 0b

Counts

492 → 3

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))
0.0b	(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
0.4b	(*.f64 (/.f64 b a) (/.f64 b a))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
40×	`times-frac_binary64`
33×	`*-un-lft-identity_binary64`
32×	`add-cube-cbrt_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
13×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64`
11×	`pow1_binary64`
5×	`add-log-exp_binary64`
4×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
3×	`sqrt-prod_binary64`
2×	`difference-of-squares_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `flip3--_binary64` `diff-log_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-plus_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `pow-sqr_binary64` `flip--_binary64` `frac-times_binary64` `pow2_binary64` `associate-l/_binary64` `*-commutative_binary64`

Counts

3 → 93

Calls

3 calls:

4.0ms	(-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))
1.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
10.0ms	(*.f64 (/.f64 b a) (/.f64 b a))

series25.0ms

Counts

3 → 9

Calls

3 calls:

8.0ms	(-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))
10.0ms	(sqrt.f64 (fabs.f64 (-.f64 1 (*.f64 (/.f64 b a) (/.f64 b a)))))
7.0ms	(*.f64 (/.f64 b a) (/.f64 b a))

simplify44.0ms

Algorithm

egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5046	860

prune84.0ms

Filtered

67 candidates to 102 candidates (-52.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	102	3	105

Merged error: 0b

Counts

105 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(/.f64 a (-.f64 a (/.f64 (*.f64 b b) a)))
0.0b	(sqrt.f64 (fabs.f64 (/.f64 1 (/.f64 a (-.f64 a (/.f64 (*.f64 b b) a))))))
0.0b	(/.f64 1 (/.f64 a (-.f64 a (/.f64 (*.f64 b b) a))))
15.5b	(/.f64 (*.f64 b b) a)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

181×	`times-frac_binary64`
148×	`add-sqr-sqrt_binary64`
115×	`*-un-lft-identity_binary64`
83×	`add-cube-cbrt_binary64`
33×	`associate-/r*_binary64`
32×	`difference-of-squares_binary64`
22×	`add-exp-log_binary64`
16×	`add-cbrt-cube_binary64` `distribute-lft-out--_binary64`
11×	`associate-/r/_binary64`
10×	`div-exp_binary64`
7×	`associate-/l*_binary64` `div-inv_binary64`
6×	`pow1_binary64` `cbrt-undiv_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`add-log-exp_binary64`
3×	`clear-num_binary64` `frac-2neg_binary64` `sqrt-prod_binary64`
2×	`1-exp_binary64` `rec-exp_binary64`
1×	`pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `inv-pow_binary64` `prod-exp_binary64` `pow-flip_binary64`

Counts

4 → 195

Calls

4 calls:

8.0ms	(/.f64 a (-.f64 a (/.f64 (*.f64 b b) a)))
1.0ms	(sqrt.f64 (fabs.f64 (/.f64 1 (/.f64 a (-.f64 a (/.f64 (*.f64 b b) a))))))
12.0ms	(/.f64 1 (/.f64 a (-.f64 a (/.f64 (*.f64 b b) a))))
5.0ms	(/.f64 (*.f64 b b) a)

series38.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/.f64 a (-.f64 a (/.f64 (*.f64 b b) a)))
10.0ms	(sqrt.f64 (fabs.f64 (/.f64 1 (/.f64 a (-.f64 a (/.f64 (*.f64 b b) a))))))
15.0ms	(/.f64 1 (/.f64 a (-.f64 a (/.f64 (*.f64 b b) a))))
4.0ms	(/.f64 (*.f64 b b) a)

simplify62.0ms

Algorithm

egg-herbie

Counts

207 → 207

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4961	3099
1	4961	3099

prune130.0ms

Filtered

131 candidates to 207 candidates (-58.0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	207	0	207
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	207	3	210

Merged error: 0b

Counts

210 → 3

regimes97.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	11
1	33	11

end0.0ms

sample553.0ms

Algorithm

intervals

Results

265.0ms	8000×	body	80	valid
146.0ms	8000×	pre	80	true
2.0ms	126×	pre	80	false

Details

analyze42.0ms

sample20.0ms

simplify66.0ms

prune6.0ms

localize7.0ms

rewrite15.0ms

series34.0ms

simplify65.0ms

prune56.0ms

localize8.0ms

rewrite75.0ms

series42.0ms

simplify103.0ms

prune272.0ms

localize6.0ms

rewrite19.0ms

series25.0ms

simplify44.0ms

prune84.0ms

localize8.0ms

rewrite35.0ms

series38.0ms

simplify62.0ms

prune130.0ms

regimes97.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample553.0ms

Profiling