Details

analyze1.0ms

Algorithm: search

sample217.0ms

Algorithm

intervals

Results

197.0ms	49×	body	640	valid
7.0ms	36×	body	1280	valid
5.0ms	141×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	12×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune4.0ms

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: 18.6b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
2.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

71×	`*-un-lft-identity`
70×	`add-sqr-sqrt`
69×	`times-frac`
46×	`sqrt-prod`
40×	`add-cube-cbrt`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/l*`
5×	`add-log-exp`
4×	`div-inv`
3×	`pow1`
2×	`cbrt-undiv` `frac-2neg` `sqrt-div` `div-exp` `clear-num` `associate-/r/`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `frac-sub` `flip--` `flip-+`

Counts

3 → 117

Calls

3 calls:

6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
30.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series28.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ 1.0 (sqrt x))
15.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify57.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	541	1048
1	2015	1014
2	5002	983

prune235.0ms

Filtered

85 candidates to 126 candidates (-48.2%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	111	15	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	15	127

Merged error: 18.0b

Counts

127 → 15

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
2.6b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`sqrt-prod`
17×	`add-exp-log` `add-cbrt-cube`
16×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt` `associate-r`
6×	`associate-r/` `associate-l*`
5×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `difference-of-squares` `unswap-sqr`
3×	`pow-prod-down` `distribute-lft-out--`
2×	`flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip--` `flip-+` `associate-/l/` `distribute-lft-out`
1×	`sub-neg` `frac-2neg` `times-frac` `sqrt-unprod` `diff-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

3 → 77

Calls

3 calls:

16.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
10.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series46.0ms

Counts

3 → 9

Calls

3 calls:

31.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
6.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify94.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	785	930
1	4068	833
2	5002	827

prune192.0ms

Filtered

61 candidates to 86 candidates (-41.0%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	82	4	86
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	86	15	101

Merged error: 17.4b

Counts

101 → 15

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
1.9b	(+ x (- 1.0 x))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

105×	`*-un-lft-identity`
41×	`distribute-lft-out`
35×	`sqrt-prod`
31×	`times-frac`
29×	`add-exp-log` `add-sqr-sqrt` `add-cbrt-cube`
21×	`add-cube-cbrt`
9×	`cbrt-undiv` `div-exp` `add-log-exp`
8×	`pow1` `prod-exp` `cbrt-unprod` `distribute-lft-out--`
7×	`associate-r` `associate-/r*`
6×	`associate-l` `associate-/l*`
5×	`flip3-+` `associate-*r/` `flip-+`
4×	`sqrt-div` `associate-/r/` `unswap-sqr`
3×	`pow-prod-down` `associate-/l/`
2×	`associate-+r-` `associate-+r+` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `sum-log` `div-inv`
1×	`+-commutative` `sub-neg` `sqrt-unprod` `diff-log` `div-sub` `*-commutative`

Counts

4 → 136

Calls

4 calls:

14.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
22.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
9.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
6.0ms	(+ x (- 1.0 x))

series51.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
35.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
6.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(+ x (- 1.0 x))

simplify41.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	938	1674
1	5002	1471

prune253.0ms

Filtered

91 candidates to 148 candidates (-62.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	8	6	14
Picked	1	0	1
Done	0	0	0
Total	154	9	163

Merged error: 0.2b

Counts

163 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
31×	`sqrt-prod`
29×	`add-exp-log` `add-cbrt-cube`
27×	`add-sqr-sqrt`
21×	`distribute-lft-out`
19×	`add-cube-cbrt` `times-frac`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`associate-r` `associate-/r*`
6×	`associate-l` `add-log-exp`
5×	`associate-*r/`
4×	`flip3-+` `sqrt-div` `associate-/r/` `flip-+` `associate-/l*` `unswap-sqr`
3×	`pow-prod-down`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv`
1×	`+-commutative` `sqrt-unprod` `sum-log` `*-commutative` `associate-/l/`

Counts

4 → 116

Calls

4 calls:

7.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
18.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

series55.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
6.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
34.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

simplify38.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	935	1360
1	5001	1197

prune236.0ms

Filtered

89 candidates to 128 candidates (-43.8%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	116	12	128
Fresh	4	4	8
Picked	1	0	1
Done	0	0	0
Total	121	16	137

Merged error: 0.0b

Counts

137 → 16

regimes86.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	10
1	14	10

end0.0ms

analyze1.0ms

Algorithm: search

sample831.0ms

Algorithm

intervals

Results

271.0ms	1829×	body	640	valid
213.0ms	1143×	body	1280	valid
162.0ms	4098×	body	80	valid
68.0ms	632×	body	320	valid
21.0ms	298×	body	160	valid

Details

analyze1.0ms

sample217.0ms

simplify4.0ms

prune4.0ms

localize7.0ms

rewrite45.0ms

series28.0ms

simplify57.0ms

prune235.0ms

localize8.0ms

rewrite36.0ms

series46.0ms

simplify94.0ms

prune192.0ms

localize11.0ms

rewrite57.0ms

series51.0ms

simplify41.0ms

prune253.0ms

localize10.0ms

rewrite46.0ms

series55.0ms

simplify38.0ms

prune236.0ms

regimes86.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.0ms

sample831.0ms

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