Details

analyze5.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	0%	50%	2

sample30.0ms

Algorithm

intervals

Results

9.0ms	62×	body	640	valid
7.0ms	36×	body	1280	valid
5.0ms	126×	body	80	valid
3.0ms	24×	body	320	valid
1.0ms	8×	body	160	valid

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	265	11
1	265	11

prune5.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 22.3b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
1.7b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite49.0ms

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 → 116

Calls

3 calls:

6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
34.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series26.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
8.0ms	(/ 1.0 (sqrt x))
13.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify30.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5082	1654

prune235.0ms

Filtered

87 candidates to 125 candidates (-43.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	111	14	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	112	14	126

Merged error: 21.8b

Counts

126 → 14

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
0.3b	(* (sqrt x) (sqrt (+ 1.0 x)))
1.7b	(- (sqrt (+ 1.0 x)) (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 → 76

Calls

3 calls:

17.0ms	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
8.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))
8.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

series48.0ms

Counts

3 → 9

Calls

3 calls:

32.0ms	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
6.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))
10.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

simplify34.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4987	1388
1	4987	1388

prune160.0ms

Filtered

61 candidates to 85 candidates (-39.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	8	5	13
Picked	1	0	1
Done	0	0	0
Total	92	7	99

Merged error: 0.3b

Counts

99 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ 1.0 x)) (sqrt x))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.2b	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
0.3b	(* (sqrt x) (sqrt (+ 1.0 x)))

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 125

Calls

4 calls:

7.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
15.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
20.0ms	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
8.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))

series54.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
33.0ms	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
6.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))

simplify62.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5523	2087

prune254.0ms

Filtered

91 candidates to 137 candidates (-50.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	129	8	137
Fresh	4	2	6
Picked	0	1	1
Done	0	0	0
Total	133	11	144

Merged error: 0.0b

Counts

144 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* (sqrt x) (sqrt (+ x 1.0))))
0.1b	(/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0)))))
0.1b	(/ (/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ 1.0 x)))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

106×	`times-frac`
72×	`*-un-lft-identity`
67×	`add-sqr-sqrt`
55×	`sqrt-prod`
48×	`add-cube-cbrt`
23×	`distribute-lft-out`
20×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
12×	`flip3-+` `flip-+`
11×	`associate-/r` `associate-/l`
10×	`div-inv`
8×	`pow1`
7×	`cbrt-undiv` `div-exp` `associate-r`
6×	`associate-l` `add-log-exp`
4×	`sqrt-div` `unswap-sqr`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `associate-*r/` `clear-num`
1×	`+-commutative` `sqrt-unprod` `sum-log` `*-commutative` `associate-/l/`

Counts

4 → 176

Calls

4 calls:

3.0ms	(+ x (* (sqrt x) (sqrt (+ x 1.0))))
6.0ms	(/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0)))))
12.0ms	(/ (/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ 1.0 x)))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

series50.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ x (* (sqrt x) (sqrt (+ x 1.0))))
10.0ms	(/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0)))))
28.0ms	(/ (/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ 1.0 x)))
6.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

simplify84.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4975	4295
1	4975	4295

prune333.0ms

Filtered

127 candidates to 188 candidates (-48.0%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	184	4	188
Fresh	3	6	9
Picked	0	1	1
Done	0	1	1
Total	187	12	199

Merged error: 0.0b

Counts

199 → 12

regimes66.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	18
1	13	18

end0.0ms

sample1.0s

Algorithm

intervals

Results

353.0ms	4127×	body	80	valid
273.0ms	1810×	body	640	valid
214.0ms	1127×	body	1280	valid
70.0ms	619×	body	320	valid
23.0ms	317×	body	160	valid

Details

analyze5.0ms

sample30.0ms

simplify11.0ms

prune5.0ms

localize7.0ms

rewrite49.0ms

series26.0ms

simplify30.0ms

prune235.0ms

localize8.0ms

rewrite36.0ms

series48.0ms

simplify34.0ms

prune160.0ms

localize10.0ms

rewrite55.0ms

series54.0ms

simplify62.0ms

prune254.0ms

localize11.0ms

rewrite36.0ms

series50.0ms

simplify84.0ms

prune333.0ms

regimes66.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.0s

Profiling