Details

sample29.0ms

Algorithm

intervals

Results

6.0ms	62×	body	640	valid
5.0ms	229×	body	80	nan
4.0ms	36×	body	1280	valid
3.0ms	135×	body	80	valid
1.0ms	17×	body	320	valid
0.0ms	6×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	6
1	14	6
2	14	6

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: 19.6b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
1.9b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

175×	`associate-/r*`
170×	`*-un-lft-identity`
156×	`frac-sub`
145×	`add-sqr-sqrt`
133×	`sqrt-prod`
115×	`add-cube-cbrt`
81×	`associate-/l*`
69×	`times-frac`
27×	`frac-2neg` `clear-num`
19×	`distribute-lft-out`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube`
5×	`add-log-exp`
4×	`div-inv`
3×	`pow1`
2×	`cbrt-undiv` `sqrt-div` `div-exp` `associate-/r/`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

3 → 272

Calls

3 calls:

6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
44.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series265.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(/ 1.0 (sqrt (+ x 1.0)))
43.0ms	(/ 1.0 (sqrt x))
143.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify64.0ms

Algorithm

egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1369	3756
1	5001	3674

prune462.0ms

Filtered

281 candidates to 170 candidates (39.5%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	264	17	281
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	265	17	282

Merged error: 19.1b

Counts

282 → 17

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt x))
0.3b	(/ 1.0 (sqrt x))
0.5b	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
1.9b	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

rewrite7.9s

Algorithm

rewrite-expression-head

Rules

64220×	`associate-/r*`
57242×	`frac-times`
39833×	`*-un-lft-identity`
34956×	`sqrt-prod`
33490×	`frac-sub`
31548×	`add-sqr-sqrt`
30098×	`associate-/l*`
29840×	`add-cube-cbrt`
10278×	`clear-num`
9910×	`frac-2neg`
4775×	`distribute-lft-out`
4586×	`associate-r/` `associate-l/`
890×	`times-frac`
736×	`un-div-inv`
315×	`unswap-sqr`
289×	`difference-of-squares`
232×	`swap-sqr`
46×	`associate-l`
35×	`*-commutative`
31×	`distribute-lft-out--`
22×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
12×	`div-inv`
11×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`prod-exp` `cbrt-unprod`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `diff-log` `pow-prod-down` `pow-sqr` `pow-prod-up` `flip--`

Counts

4 → 34172

Calls

4 calls:

4.0ms	(/ 1.0 (sqrt x))
4.0ms	(/ 1.0 (sqrt x))
24.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
1.7s	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

series177.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(/ 1.0 (sqrt x))
41.0ms	(/ 1.0 (sqrt x))
28.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x)))
69.0ms	(- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0)))))

simplify11.0s

Algorithm

egg-herbie

Counts

34184 → 34184

Iterations

Useful iterations: 0 (719.0ms)

Iter	Nodes	Cost
0	37878	1229814

prune1.2m

Filtered

34184 candidates to 14979 candidates (56.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	34175	9	34184
Fresh	13	3	16
Picked	1	0	1
Done	0	0	0
Total	34189	12	34201

Merged error: 5.9b

Counts

34201 → 12

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ 1.0 (sqrt x))
0.3b	(/ 1.0 (sqrt x))
0.3b	(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
1.9b	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

rewrite6.8s

Algorithm

rewrite-expression-head

Rules

99528×	`sqrt-div`
51690×	`associate-/r*`
31710×	`*-un-lft-identity`
27943×	`sqrt-prod`
24964×	`frac-times`
24960×	`frac-sub`
24804×	`frac-add`
24077×	`add-sqr-sqrt`
23979×	`add-cube-cbrt`
23931×	`associate-/l*`
7977×	`frac-2neg` `clear-num`
3849×	`distribute-lft-out`
160×	`flip3--` `flip--`
159×	`flip3-+` `flip-+`
158×	`associate-r/` `associate-l/`
122×	`times-frac`
32×	`difference-of-squares`
31×	`associate-r`
24×	`distribute-lft-out--`
15×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube`
8×	`div-inv`
6×	`pow1` `add-log-exp`
3×	`sub-neg`
2×	`cbrt-undiv` `distribute-rgt-in` `distribute-lft-in` `div-exp`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 25616

Calls

4 calls:

4.0ms	(/ 1.0 (sqrt x))
4.0ms	(/ 1.0 (sqrt x))
622.0ms	(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
50.0ms	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

series991.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(/ 1.0 (sqrt x))
42.0ms	(/ 1.0 (sqrt x))
612.0ms	(* (+ (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0))))))
294.0ms	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

simplify9.8s

Algorithm

egg-herbie

Counts

25628 → 25628

Iterations

Useful iterations: 0 (251.0ms)

Iter	Nodes	Cost
0	15780	1273982

prune1.1m

Filtered

25628 candidates to 10846 candidates (57.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	25624	4	25628
Fresh	8	3	11
Picked	1	0	1
Done	0	0	0
Total	25633	7	25640

Merged error: 5.9b

Counts

25640 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sqrt (sqrt x)) (sqrt (/ 1.0 (sqrt (sqrt (+ x 1.0))))))
0.2b	(/ (* (+ (* (sqrt (/ 1.0 (sqrt 1))) (sqrt (sqrt (sqrt (+ x 1.0))))) (* (sqrt (sqrt x)) (sqrt (/ 1.0 (sqrt (sqrt (+ x 1.0))))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))) (* (sqrt (sqrt x)) (sqrt (sqrt (sqrt (+ x 1.0))))))
0.3b	(/ 1.0 (sqrt x))
1.9b	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

rewrite42.8s

Algorithm

rewrite-expression-head

Rules

577658×	`sqrt-div`
205411×	`associate-/r*`
157436×	`frac-times`
148285×	`sqrt-prod`
122042×	`*-un-lft-identity`
101936×	`associate-*r/`
97148×	`associate-/l/`
96936×	`add-sqr-sqrt`
96672×	`frac-add`
95472×	`frac-sub`
93745×	`add-cube-cbrt`
86973×	`associate-/l*`
33233×	`flip3-+` `flip-+`
31138×	`associate-*l/`
28977×	`frac-2neg` `clear-num`
13759×	`distribute-lft-out`
3206×	`times-frac`
1877×	`associate-r`
983×	`associate-l`
656×	`difference-of-squares`
612×	`flip3--` `flip--`
607×	`unswap-sqr`
492×	`distribute-lft-out--`
87×	`*-commutative`
85×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`add-log-exp`
5×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
4×	`associate-/r/`
3×	`pow-prod-down`
2×	`sqrt-pow1` `pow1/2`
1×	`sub-neg` `sqrt-unprod` `diff-log`

Counts

4 → 99335

Calls

4 calls:

57.0ms	(* (sqrt (sqrt x)) (sqrt (/ 1.0 (sqrt (sqrt (+ x 1.0))))))
7.7s	(/ (* (+ (* (sqrt (/ 1.0 (sqrt 1))) (sqrt (sqrt (sqrt (+ x 1.0))))) (* (sqrt (sqrt x)) (sqrt (/ 1.0 (sqrt (sqrt (+ x 1.0))))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))) (* (sqrt (sqrt x)) (sqrt (sqrt (sqrt (+ x 1.0))))))
4.0ms	(/ 1.0 (sqrt x))
48.0ms	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

series1.8s

Counts

4 → 12

Calls

4 calls:

226.0ms	(* (sqrt (sqrt x)) (sqrt (/ 1.0 (sqrt (sqrt (+ x 1.0))))))
1.3s	(/ (* (+ (* (sqrt (/ 1.0 (sqrt 1))) (sqrt (sqrt (sqrt (+ x 1.0))))) (* (sqrt (sqrt x)) (sqrt (/ 1.0 (sqrt (sqrt (+ x 1.0))))))) (- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))) (* (sqrt (sqrt x)) (sqrt (sqrt (sqrt (+ x 1.0))))))
38.0ms	(/ 1.0 (sqrt x))
294.0ms	(- (sqrt (/ 1.0 (sqrt x))) (sqrt (/ 1.0 (sqrt (+ x 1.0)))))

simplify27.7s

Algorithm

egg-herbie

Counts

99347 → 99347

Iterations

Useful iterations: 0 (752.0ms)

Iter	Nodes	Cost
0	33538	3034230

prune5.9m

Filtered: 99347 candidates to 40634 candidates (59.1%)