Details

sample32.0ms

Algorithm

intervals

Results

10.0ms	61×	body	1280	valid
4.0ms	252×	body	80	nan
3.0ms	43×	body	640	valid
3.0ms	132×	body	80	valid
1.0ms	13×	body	320	valid
0.0ms	7×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune2.0ms

Filtered

1 candidates to 0 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: 29.4b

Counts

2 → 1

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(sqrt (+ x 1.0))
1.5b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite13.0ms

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 → 35

Calls

2 calls:

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

series122.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(sqrt (+ x 1.0))
87.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify75.0ms

Algorithm

egg-herbie

Counts

41 → 41

Iterations

Useful iterations: 3 (69.0ms)

Iter	Nodes	Cost
0	182	265
1	544	243
2	2020	233
3	5002	230

prune85.0ms

Filtered

41 candidates to 28 candidates (68.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	38	3	41
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	39	3	42

Merged error: 0.1b

Counts

42 → 3

localize7.0ms

Local error

Found 2 expressions with local error:

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

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

44×	`*-un-lft-identity`
20×	`sqrt-prod`
18×	`times-frac`
17×	`distribute-lft-out`
15×	`add-sqr-sqrt`
14×	`add-cube-cbrt`
6×	`associate-/r*`
4×	`add-exp-log` `add-cbrt-cube`
3×	`pow1` `associate-/l*`
2×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `add-log-exp`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv`

Counts

2 → 57

Calls

2 calls:

3.0ms	(sqrt (+ x 1.0))
11.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series212.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(sqrt (+ x 1.0))
170.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify51.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	309	501
1	1128	459
2	5002	430

prune136.0ms

Filtered

63 candidates to 40 candidates (63.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	57	6	63
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	58	8	66

Merged error: 0.0b

Counts

66 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`add-cube-cbrt`
13×	`cbrt-prod`
10×	`associate-r`
9×	`times-frac` `sqrt-prod`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `cbrt-div`
4×	`flip3-+` `flip-+` `add-log-exp`
3×	`associate-l` `associate-/r` `distribute-lft-out` `associate-/l` `unswap-sqr`
2×	`pow1/3` `sqrt-div` `associate-*r/` `associate-/r/`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `div-inv`

Counts

4 → 86

Calls

4 calls:

10.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
8.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
3.0ms	(cbrt (+ x 1.0))
3.0ms	(cbrt (+ x 1.0))

series560.0ms

Counts

4 → 12

Calls

4 calls:

228.0ms	(/ 1.0 (+ (* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0)))) (sqrt x)))
122.0ms	(* (fabs (cbrt (+ x 1.0))) (sqrt (cbrt (+ x 1.0))))
106.0ms	(cbrt (+ x 1.0))
104.0ms	(cbrt (+ x 1.0))

simplify130.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (107.0ms)

Iter	Nodes	Cost
0	850	1475
1	3967	1385
2	5002	1364

prune341.0ms

Filtered

98 candidates to 79 candidates (80.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	96	2	98
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	97	9	106

Merged error: 0.0b

Counts

106 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

297×	`*-un-lft-identity`
274×	`sqrt-prod`
157×	`times-frac`
119×	`add-sqr-sqrt`
116×	`distribute-lft-out`
88×	`add-cube-cbrt`
41×	`swap-sqr`
27×	`associate-r` `associate-l`
20×	`pow1`
14×	`associate-/r/`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
9×	`sqrt-pow1` `pow1/2` `unswap-sqr`
7×	`flip3-+` `flip-+` `div-inv`
6×	`associate-/l*`
5×	`sqrt-div` `pow-prod-up`
4×	`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 → 250

Calls

4 calls:

11.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
11.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
11.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
43.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series951.0ms

Counts

4 → 12

Calls

4 calls:

414.0ms	(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
170.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
168.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
199.0ms	(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify129.0ms

Algorithm

egg-herbie

Counts

262 → 262

Iterations

Useful iterations: 2 (97.0ms)

Iter	Nodes	Cost
0	647	2845
1	3152	2529
2	5002	2489

prune459.0ms

Filtered

262 candidates to 138 candidates (52.7%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	259	3	262
Fresh	2	5	7
Picked	0	1	1
Done	0	1	1
Total	261	10	271

Merged error: 0b

Counts

271 → 10

regimes82.0ms

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	5
1	9	5

end0.0ms

sample713.0ms

Algorithm

intervals

Results

163.0ms	1744×	body	1280	valid
138.0ms	7896×	body	80	nan
96.0ms	1250×	body	640	valid
82.0ms	4077×	body	80	valid
40.0ms	627×	body	320	valid
11.0ms	302×	body	160	valid