Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

sample34.0ms

Algorithm

intervals

Results

12.0ms	55×	body	1280	valid
6.0ms	35×	body	640	valid
6.0ms	136×	body	80	valid
2.0ms	16×	body	320	valid
1.0ms	14×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	71	7
1	71	7

prune2.0ms

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: 28.0b

Counts

2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
2.9b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-log-exp` `difference-of-squares`
3×	`pow1` `add-cube-cbrt` `distribute-lft-out--`
2×	`add-exp-log` `sqrt-div` `add-cbrt-cube` `distribute-lft-out`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `diff-log` `flip--` `flip-+`

Counts

2 → 34

Calls

2 calls:

3.0ms	(sqrt (+ x 1.0))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series13.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(sqrt (+ x 1.0))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify63.0ms

Algorithm

egg-herbie

Counts

40 → 40

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4975	520
1	4975	520

prune71.0ms

Filtered

30 candidates to 40 candidates (-33.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	36	4	40
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	37	4	41

Merged error: 0.1b

Counts

41 → 4

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
24×	`sqrt-prod`
21×	`distribute-lft-out`
18×	`times-frac`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt`
6×	`associate-/r*`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1`
3×	`flip3-+` `flip-+` `associate-/l*`
2×	`sqrt-div` `associate-/r/`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 71

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
7.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series18.0ms

Counts

3 → 9

Calls

3 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify25.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5038	1051

prune137.0ms

Filtered

59 candidates to 80 candidates (-35.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	74	6	80
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	76	8	84

Merged error: 0.0b

Counts

84 → 8

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (sqrt (+ 1.0 x)))
0.1b	(sqrt (sqrt (+ 1.0 x)))
0.2b	(/ 1.0 (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x)))
0.3b	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

106×	`sqrt-prod`
62×	`add-sqr-sqrt`
46×	`*-un-lft-identity`
40×	`sqrt-pow1`
32×	`sqrt-div`
31×	`pow1`
28×	`add-cube-cbrt`
20×	`pow1/2`
18×	`swap-sqr`
10×	`associate-r` `associate-l`
9×	`flip3-+` `times-frac` `pow-prod-up` `flip-+` `unswap-sqr`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
5×	`pow-prod-down` `pow-sqr`
4×	`frac-times` `rem-sqrt-square` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`associate-r/` `associate-l/` `associate-/r/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 161

Calls

4 calls:

4.0ms	(sqrt (sqrt (+ 1.0 x)))
4.0ms	(sqrt (sqrt (+ 1.0 x)))
17.0ms	(/ 1.0 (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x)))
14.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

series25.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (sqrt (+ 1.0 x)))
6.0ms	(sqrt (sqrt (+ 1.0 x)))
9.0ms	(/ 1.0 (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x)))
4.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

simplify62.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4941	1700
1	4941	1700

prune221.0ms

Filtered

91 candidates to 173 candidates (-90.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	172	9	181

Merged error: 0.0b

Counts

181 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x)))
0.1b	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.2b	(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x))))
0.3b	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

437×	`sqrt-prod`
414×	`times-frac`
404×	`*-un-lft-identity`
246×	`add-sqr-sqrt`
215×	`add-cube-cbrt`
106×	`distribute-lft-out`
44×	`sqrt-div`
36×	`associate-/l*`
33×	`sqrt-pow1`
28×	`pow1`
18×	`swap-sqr` `associate-/r/`
17×	`pow1/2`
16×	`flip3-+` `flip-+`
15×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
10×	`associate-r` `associate-l`
9×	`pow-prod-up` `div-inv` `unswap-sqr`
5×	`pow-prod-down` `pow-sqr`
4×	`cbrt-undiv` `frac-times` `div-exp` `add-log-exp`
2×	`frac-2neg` `associate-r/` `associate-l/` `clear-num`
1×	`pow2` `rem-sqrt-square` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `associate-/l/`

Counts

4 → 410

Calls

4 calls:

14.0ms	(sqrt (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x)))
12.0ms	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
33.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x))))
16.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

series42.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x)))
18.0ms	(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
10.0ms	(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x))))
4.0ms	(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

simplify146.0ms

Algorithm

egg-herbie

Counts

422 → 422

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4951	9344
1	4951	9344

prune629.0ms

Filtered

170 candidates to 422 candidates (-148.2%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	418	4	422
Fresh	1	5	6
Picked	0	1	1
Done	1	1	2
Total	420	11	431

Merged error: 0b

Counts

431 → 11

regimes132.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	9
1	9	9

end0.0ms

sample633.0ms

Algorithm

intervals

Results

236.0ms	1751×	body	1280	valid
127.0ms	1203×	body	640	valid
116.0ms	4141×	body	80	valid
49.0ms	590×	body	320	valid
16.0ms	315×	body	160	valid
0.0ms	1×	body	80	nan

Details

analyze4.0ms

sample34.0ms

simplify4.0ms

prune2.0ms

localize5.0ms

rewrite12.0ms

series13.0ms

simplify63.0ms

prune71.0ms

localize6.0ms

rewrite21.0ms

series18.0ms

simplify25.0ms

prune137.0ms

localize8.0ms

rewrite46.0ms

series25.0ms

simplify62.0ms

prune221.0ms

localize13.0ms

rewrite104.0ms

series42.0ms

simplify146.0ms

prune629.0ms

regimes132.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample633.0ms

Profiling