Details

analyze1.0ms

Algorithm

Search

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

sample29.0ms

Algorithm

intervals

Results

9.0ms	64×	body	640	valid
6.0ms	31×	body	1280	valid
5.0ms	128×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	10×	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: 20.4b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
3.5b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

75×	`*-un-lft-identity`
73×	`add-sqr-sqrt`
69×	`times-frac`
50×	`sqrt-prod`
42×	`add-cube-cbrt`
13×	`associate-/r*`
11×	`distribute-lft-out--`
9×	`difference-of-squares`
8×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
6×	`associate-/l*` `add-log-exp`
5×	`pow1`
4×	`sqrt-div` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `associate-/r/` `flip-+`
1×	`sub-neg` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `diff-log` `frac-sub` `flip--`

Counts

4 → 132

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
32.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series33.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (+ x 1.0))
9.0ms	(/ 1.0 (sqrt (+ x 1.0)))
8.0ms	(/ 1.0 (sqrt x))
13.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify32.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5076	1839

prune256.0ms

Filtered

103 candidates to 144 candidates (-39.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	133	11	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	11	145

Merged error: 19.8b

Counts

145 → 11

localize14.0ms

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 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
3.4b	(- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0)))

rewrite345.0ms

Algorithm

rewrite-expression-head

Rules

2937×	`times-frac`
2554×	`*-un-lft-identity`
1354×	`add-sqr-sqrt`
778×	`add-cube-cbrt`
708×	`distribute-lft-out`
508×	`sqrt-prod`
368×	`distribute-lft-out--`
211×	`div-inv`
144×	`difference-of-squares`
64×	`distribute-rgt-out--`
45×	`associate-/l*`
37×	`associate-/r/`
27×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
4×	`pow1`
3×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `associate-/l/`
2×	`flip3--` `flip3-+` `sqrt-div` `frac-sub` `flip--` `flip-+`
1×	`sub-neg` `diff-log` `div-sub` `frac-add`

Counts

4 → 750

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt (+ 1.0 x)))
4.0ms	(/ 1.0 (sqrt x))
126.0ms	(/ (- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
83.0ms	(- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(/ 1.0 (sqrt (+ 1.0 x)))
13.0ms	(/ 1.0 (sqrt x))
43.0ms	(/ (- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
7.0ms	(- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0)))

simplify486.0ms

Algorithm

egg-herbie

Counts

762 → 762

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4983	23232
1	4983	23232

prune1.1s

Filtered

283 candidates to 762 candidates (-169.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	759	3	762
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	766	7	773

Merged error: 4.0b

Counts

773 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ 1.0 x)))
0.2b	(/ 1.0 (sqrt x))
0.2b	(* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x)))))
2.9b	(- (* 1.0 (/ (+ 1.0 x) 1.0)) (* (/ x 1.0) 1.0))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

50×	`*-un-lft-identity`
48×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt`
29×	`add-exp-log` `add-cbrt-cube`
28×	`sqrt-prod`
15×	`associate-*r/`
13×	`frac-times` `associate-l` `associate-/r*`
10×	`prod-exp` `cbrt-unprod`
9×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/l*` `add-log-exp`
5×	`flip3-+` `associate-*l/` `flip-+`
4×	`distribute-rgt-in` `distribute-lft-in` `frac-add` `distribute-lft-out`
3×	`pow-prod-down` `div-inv`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/r/`
1×	`sub-neg` `flip3--` `diff-log` `associate-r` `*-commutative` `frac-sub` `flip--` `sub-div`

Counts

4 → 152

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt (+ 1.0 x)))
4.0ms	(/ 1.0 (sqrt x))
38.0ms	(* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x)))))
7.0ms	(- (* 1.0 (/ (+ 1.0 x) 1.0)) (* (/ x 1.0) 1.0))

series33.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt (+ 1.0 x)))
7.0ms	(/ 1.0 (sqrt x))
19.0ms	(* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x)))))
1.0ms	(- (* 1.0 (/ (+ 1.0 x) 1.0)) (* (/ x 1.0) 1.0))

simplify67.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5003	2533

prune371.0ms

Filtered

112 candidates to 164 candidates (-46.4%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	162	2	164
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	163	8	171

Merged error: 0.6b

Counts

171 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ 1.0 x)))
0.2b	(/ 1.0 (sqrt x))
0.2b	(* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x)))))
0.7b	(/ 1.0 (* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x))))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log` `add-cbrt-cube`
52×	`*-un-lft-identity`
51×	`times-frac`
44×	`add-sqr-sqrt` `add-cube-cbrt`
28×	`sqrt-prod`
26×	`frac-times` `associate-*r/`
20×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
17×	`associate-/r/`
14×	`associate-/r*`
13×	`associate-l`
9×	`pow1` `flip3-+` `flip-+` `associate-/l*`
8×	`frac-add`
6×	`associate-*l/`
4×	`distribute-rgt-in` `distribute-lft-in` `div-inv` `distribute-lft-out` `add-log-exp`
3×	`frac-2neg` `pow-prod-down` `clear-num`
2×	`sqrt-div`
1×	`associate-r` `*-commutative`

Counts

4 → 185

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt (+ 1.0 x)))
4.0ms	(/ 1.0 (sqrt x))
41.0ms	(* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x)))))
42.0ms	(/ 1.0 (* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x))))))

series67.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt (+ 1.0 x)))
8.0ms	(/ 1.0 (sqrt x))
22.0ms	(* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x)))))
31.0ms	(/ 1.0 (* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x))))))

simplify55.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5103	3820

prune348.0ms

Filtered

129 candidates to 197 candidates (-52.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	190	7	197
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	194	11	205

Merged error: 0.0b

Counts

205 → 11

regimes64.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	25
1	21	25

end0.0ms

sample806.0ms

Algorithm

intervals

Results

253.0ms	1785×	body	640	valid
209.0ms	1114×	body	1280	valid
158.0ms	4137×	body	80	valid
68.0ms	654×	body	320	valid
22.0ms	310×	body	160	valid

Details

analyze1.0ms

sample29.0ms

simplify11.0ms

prune5.0ms

localize7.0ms

rewrite49.0ms

series33.0ms

simplify32.0ms

prune256.0ms

localize14.0ms

rewrite345.0ms

series74.0ms

simplify486.0ms

prune1.1s

localize18.0ms

rewrite63.0ms

series33.0ms

simplify67.0ms

prune371.0ms

localize13.0ms

rewrite100.0ms

series67.0ms

simplify55.0ms

prune348.0ms

regimes64.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample806.0ms

Profiling