Details

sample38.0ms

Algorithm

intervals

Results

6.0ms	21×	body	320	valid
6.0ms	47×	body	1280	valid
6.0ms	255×	body	80	nan
4.0ms	39×	body	640	valid
3.0ms	133×	body	80	valid
1.0ms	16×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune3.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 28.6b

Counts

2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

3.1b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
8×	`*-un-lft-identity` `sqrt-prod`
4×	`difference-of-squares`
3×	`distribute-lft-out--` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out`

Counts

1 → 19

Calls

1 calls:

7.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

series228.0ms

Counts

1 → 3

Calls

1 calls:

228.0ms

(- (sqrt (+ x 1.0)) (sqrt x))

simplify117.0ms

Algorithm

egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 2 (22.0ms)

Iter	Nodes	Cost
0	203	216
1	808	206
2	4153	197
3	5001	197

prune69.0ms

Filtered

22 candidates to 15 candidates (31.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	19	3	22
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	20	3	23

Merged error: 0.1b

Counts

23 → 3

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
31×	`distribute-lft-out`
24×	`times-frac` `sqrt-prod`
14×	`add-sqr-sqrt` `add-cube-cbrt`
6×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow1` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

2 → 64

Calls

2 calls:

7.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
11.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series376.0ms

Counts

2 → 6

Calls

2 calls:

119.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
257.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify59.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	435	698
1	1872	651
2	5001	615

prune208.0ms

Filtered

70 candidates to 44 candidates (37.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	65	5	70
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	66	7	73

Merged error: 0.0b

Counts

73 → 7

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

597×	`*-un-lft-identity`
420×	`sqrt-prod`
256×	`distribute-lft-out`
247×	`times-frac`
130×	`add-sqr-sqrt`
99×	`add-cube-cbrt`
71×	`swap-sqr`
33×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `flip3-+` `pow1/2` `flip-+` `unswap-sqr`
8×	`associate-/l*`
7×	`div-inv`
5×	`sqrt-div` `pow-prod-up`
4×	`associate-/l/` `add-log-exp`
3×	`pow-prod-down` `pow-sqr`
2×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `div-exp` `clear-num`
1×	`pow2` `frac-times` `pow-plus` `sqrt-unprod` `associate-r/` `associate-l/` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 316

Calls

4 calls:

16.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
44.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.5s

Counts

4 → 12

Calls

4 calls:

682.0ms	(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
257.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
257.0ms	(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
310.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify170.0ms

Algorithm

egg-herbie

Counts

328 → 328

Iterations

Useful iterations: 2 (123.0ms)

Iter	Nodes	Cost
0	827	3981
1	4531	3471
2	5001	3422

prune1.5s

Filtered

328 candidates to 151 candidates (54.0%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	323	5	328
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	326	9	335

Merged error: 0b

Counts

335 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (fabs (/ 1 (cbrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (/ (+ 1.0 0) (cbrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
0.2b	(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (fabs (/ 1 (cbrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (/ (+ 1.0 0) (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

138×	`*-un-lft-identity`
115×	`sqrt-prod`
62×	`times-frac`
55×	`distribute-lft-out`
48×	`add-sqr-sqrt`
46×	`associate-r`
38×	`add-cube-cbrt`
37×	`cbrt-prod`
36×	`associate-l`
11×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`cbrt-div`
5×	`sqrt-div`
4×	`flip3-+` `associate-*r/` `pow-prod-down` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `add-log-exp` `unswap-sqr`
2×	`pow1/3` `*-commutative` `div-inv`
1×	`frac-times` `associate-*l/`

Counts

4 → 147

Calls

4 calls:

23.0ms	(* (fabs (/ 1 (cbrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (/ (+ 1.0 0) (cbrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
7.0ms	(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
7.0ms	(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
35.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (fabs (/ 1 (cbrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (/ (+ 1.0 0) (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))))

series2.4s

Counts

4 → 12

Calls

4 calls:

664.0ms	(* (fabs (/ 1 (cbrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (/ (+ 1.0 0) (cbrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
445.0ms	(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
443.0ms	(cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))
811.0ms	(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (fabs (/ 1 (cbrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (/ (+ 1.0 0) (cbrt (+ (sqrt (+ x 1.0)) (sqrt x)))))))

simplify122.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (94.0ms)

Iter	Nodes	Cost
0	1086	3588
1	4450	3328
2	5001	3306

prune1.6s

Filtered

159 candidates to 104 candidates (34.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	159	9	168

Merged error: 0b

Counts

168 → 9

regimes64.0ms

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	12	6
1	16	6
2	16	6

end0.0ms

sample910.0ms

Algorithm

intervals

Results

211.0ms	1739×	body	1280	valid
189.0ms	8028×	body	80	nan
115.0ms	1183×	body	640	valid
104.0ms	4129×	body	80	valid
48.0ms	620×	body	320	valid
17.0ms	329×	body	160	valid

Details

sample38.0ms

simplify4.0ms

prune3.0ms

localize5.0ms

rewrite8.0ms

series228.0ms

simplify117.0ms

prune69.0ms

localize7.0ms

rewrite21.0ms

series376.0ms

simplify59.0ms

prune208.0ms

localize9.0ms

rewrite109.0ms

series1.5s

simplify170.0ms

prune1.5s

localize17.0ms

rewrite80.0ms

series2.4s

simplify122.0ms

prune1.6s

regimes64.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample910.0ms

Profiling