Details

analyze1.0ms

Algorithm

Search

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

sample31.0ms

Algorithm

intervals

Results

11.0ms	70×	body	640	valid
6.0ms	32×	body	1280	valid
5.0ms	134×	body	80	valid
1.0ms	12×	body	320	valid
1.0ms	8×	body	160	valid

simplify27.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	527	11
1	527	11

prune6.0ms

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: 19.2b

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))
2.0b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite47.0ms

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))
33.0ms	(- (/ 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)))
7.0ms	(/ 1.0 (sqrt x))
13.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify55.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5078	1649

prune243.0ms

Filtered

87 candidates to 125 candidates (-43.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	115	10	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	116	10	126

Merged error: 18.7b

Counts

126 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ 1.0 x)))
0.2b	(/ 1.0 (sqrt x))
0.3b	(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ 1.0 x)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
2.2b	(- (/ 1.0 x) (/ 1.0 (+ 1.0 x)))

rewrite84.0ms

Algorithm

rewrite-expression-head

Rules

124×	`*-un-lft-identity`
105×	`times-frac`
65×	`add-sqr-sqrt`
53×	`add-cube-cbrt`
52×	`sqrt-prod`
35×	`distribute-lft-out`
27×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
8×	`distribute-lft-out--`
7×	`associate-/l*`
6×	`add-log-exp`
5×	`associate-/r/`
4×	`pow1` `cbrt-undiv` `div-exp` `difference-of-squares`
3×	`frac-2neg` `associate-*r/` `clear-num` `associate-/l/`
2×	`flip3--` `flip3-+` `sqrt-div` `frac-sub` `flip--` `flip-+`
1×	`sub-neg` `diff-log` `frac-add` `prod-exp` `cbrt-unprod`

Counts

4 → 157

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt (+ 1.0 x)))
4.0ms	(/ 1.0 (sqrt x))
49.0ms	(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ 1.0 x)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
16.0ms	(- (/ 1.0 x) (/ 1.0 (+ 1.0 x)))

series40.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt (+ 1.0 x)))
7.0ms	(/ 1.0 (sqrt x))
23.0ms	(/ (* 1.0 (- (/ 1.0 x) (/ 1.0 (+ 1.0 x)))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
4.0ms	(- (/ 1.0 x) (/ 1.0 (+ 1.0 x)))

simplify36.0ms

Algorithm

egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5125	2718

prune336.0ms

Filtered

112 candidates to 169 candidates (-50.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	164	5	169
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	173	6	179

Merged error: 7.4b

Counts

179 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
36×	`times-frac`
30×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
24×	`sqrt-prod`
17×	`associate-*r/`
15×	`associate-r` `distribute-lft-out`
14×	`flip3-+` `flip-+`
13×	`add-exp-log` `add-cbrt-cube`
12×	`frac-times`
11×	`pow1`
7×	`associate-l`
6×	`distribute-rgt-in` `distribute-lft-in` `frac-add` `associate-/r*` `add-log-exp`
4×	`pow-prod-down` `associate-*l/` `prod-exp` `cbrt-unprod`
3×	`div-inv` `associate-/l*`
2×	`associate--l+` `*-commutative`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `diff-log` `div-exp` `clear-num` `flip--` `unswap-sqr`

Counts

4 → 128

Calls

4 calls:

38.0ms	(* (+ 1.0 x) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
37.0ms	(* x (* (+ 1.0 x) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x))))))
4.0ms	(/ 1.0 (sqrt x))
6.0ms	(- (* 1.0 (+ 1.0 x)) (* x 1.0))

series37.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (+ 1.0 x) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
17.0ms	(* x (* (+ 1.0 x) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x))))))
7.0ms	(/ 1.0 (sqrt x))
1.0ms	(- (* 1.0 (+ 1.0 x)) (* x 1.0))

simplify71.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4941	2105
1	4941	2105

prune295.0ms

Filtered

98 candidates to 140 candidates (-42.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	139	7	146

Merged error: 0.3b

Counts

146 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ 1.0 x) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
0.2b	(* x (* (+ 1.0 x) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x))))))
0.2b	(/ 1.0 (sqrt x))
0.4b	(/ (* 1.0 1.0) (* x (* (+ 1.0 x) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))))

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
37×	`times-frac`
34×	`add-exp-log` `add-cbrt-cube`
31×	`associate-*r/`
30×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
24×	`sqrt-prod`
21×	`flip3-+` `flip-+`
18×	`frac-times`
15×	`associate-r` `distribute-lft-out`
13×	`prod-exp` `cbrt-unprod`
11×	`pow1` `associate-/r/`
9×	`frac-add`
7×	`cbrt-undiv` `div-exp` `associate-l` `associate-/r*`
6×	`associate-*l/`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`pow-prod-down` `div-inv` `associate-/l*` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`unswap-sqr`

Counts

4 → 151

Calls

4 calls:

37.0ms	(* (+ 1.0 x) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
35.0ms	(* x (* (+ 1.0 x) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x))))))
5.0ms	(/ 1.0 (sqrt x))
37.0ms	(/ (* 1.0 1.0) (* x (* (+ 1.0 x) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))))

series69.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(* (+ 1.0 x) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
20.0ms	(* x (* (+ 1.0 x) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x))))))
7.0ms	(/ 1.0 (sqrt x))
30.0ms	(/ (* 1.0 1.0) (* x (* (+ 1.0 x) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))))

simplify40.0ms

Algorithm

egg-herbie

Counts

163 → 163

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5040	3275

prune356.0ms

Filtered

119 candidates to 163 candidates (-37.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	158	5	163
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	162	8	170

Merged error: 0.0b

Counts

170 → 8

regimes55.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	21
1	46	21

end0.0ms

sample857.0ms

Algorithm

intervals

Results

288.0ms	1870×	body	640	valid
207.0ms	1108×	body	1280	valid
173.0ms	4132×	body	80	valid
64.0ms	586×	body	320	valid
23.0ms	304×	body	160	valid

Details

analyze1.0ms

sample31.0ms

simplify27.0ms

prune6.0ms

localize7.0ms

rewrite47.0ms

series26.0ms

simplify55.0ms

prune243.0ms

localize12.0ms

rewrite84.0ms

series40.0ms

simplify36.0ms

prune336.0ms

localize14.0ms

rewrite89.0ms

series37.0ms

simplify71.0ms

prune295.0ms

localize11.0ms

rewrite121.0ms

series69.0ms

simplify40.0ms

prune356.0ms

regimes55.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample857.0ms

Profiling