Details

sample41.0ms

Algorithm

intervals

Results

8.0ms	59×	body	640	valid
8.0ms	245×	body	80	nan
7.0ms	38×	body	1280	valid
5.0ms	134×	body	80	valid
2.0ms	22×	body	320	valid
0.0ms	3×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	11
1	14	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: 20.0b

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)))
0.3b	(/ 1.0 (sqrt x))
1.7b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite48.0ms

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 → 133

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
31.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series30.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify33.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5072	1846

prune252.0ms

Filtered

103 candidates to 145 candidates (-40.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	135	10	145
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	136	10	146

Merged error: 19.4b

Counts

146 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite344.0ms

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 → 751

Calls

4 calls:

10.0ms	(/ 1.0 (sqrt (+ 1.0 x)))
4.0ms	(/ 1.0 (sqrt x))
124.0ms	(/ (- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
84.0ms	(- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0)))

series36.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt (+ 1.0 x)))
7.0ms	(/ 1.0 (sqrt x))
19.0ms	(/ (- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
4.0ms	(- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0)))

simplify199.0ms

Algorithm

egg-herbie

Counts

763 → 763

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5115	23514

prune1.4s

Filtered

283 candidates to 763 candidates (-169.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	758	5	763
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	766	7	773

Merged error: 5.3b

Counts

773 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x))))
0.2b	(* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x)))))
0.3b	(/ 1.0 (sqrt x))
1.4b	(- (* 1.0 (/ (+ 1.0 x) 1.0)) (* (/ x 1.0) 1.0))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
58×	`times-frac`
46×	`add-sqr-sqrt`
41×	`add-cube-cbrt`
32×	`add-exp-log` `add-cbrt-cube`
29×	`associate-l`
24×	`sqrt-prod`
18×	`associate-*r/`
17×	`distribute-lft-out`
16×	`frac-times`
15×	`associate-r`
12×	`prod-exp` `cbrt-unprod`
11×	`pow1`
7×	`cbrt-undiv` `div-exp`
6×	`flip3-+` `associate-l/` `frac-add` `associate-/r` `flip-+` `add-log-exp`
5×	`distribute-rgt-in` `distribute-lft-in` `div-inv`
4×	`pow-prod-down`
3×	`associate-/l*`
2×	`*-commutative` `unswap-sqr`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `clear-num` `frac-sub` `flip--` `sub-div`

Counts

4 → 162

Calls

4 calls:

39.0ms	(* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x))))
38.0ms	(* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x)))))
4.0ms	(/ 1.0 (sqrt x))
8.0ms	(- (* 1.0 (/ (+ 1.0 x) 1.0)) (* (/ x 1.0) 1.0))

series42.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x))))
18.0ms	(* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x)))))
8.0ms	(/ 1.0 (sqrt x))
1.0ms	(- (* 1.0 (/ (+ 1.0 x) 1.0)) (* (/ x 1.0) 1.0))

simplify73.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4973	3046
1	4973	3046

prune399.0ms

Filtered

122 candidates to 174 candidates (-42.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	0	6	6
Picked	1	0	1
Done	0	0	0
Total	174	7	181

Merged error: 0.7b

Counts

181 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x))))
0.2b	(* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x)))))
0.3b	(/ 1.0 (sqrt x))
0.9b	(/ 1.0 (* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x))))))

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

72×	`*-un-lft-identity`
61×	`add-exp-log` `times-frac` `add-cbrt-cube`
48×	`add-sqr-sqrt`
43×	`add-cube-cbrt`
29×	`frac-times` `associate-r/` `associate-l*`
24×	`sqrt-prod`
22×	`prod-exp` `cbrt-unprod`
19×	`cbrt-undiv` `div-exp`
17×	`distribute-lft-out`
15×	`associate-r` `associate-/r/`
11×	`pow1`
10×	`flip3-+` `frac-add` `flip-+`
7×	`associate-l/` `associate-/r`
6×	`div-inv` `associate-/l*`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`pow-prod-down` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative` `unswap-sqr`

Counts

4 → 194

Calls

4 calls:

37.0ms	(* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x))))
40.0ms	(* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x)))))
4.0ms	(/ 1.0 (sqrt x))
41.0ms	(/ 1.0 (* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x))))))

series254.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x))))
18.0ms	(* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x)))))
7.0ms	(/ 1.0 (sqrt x))
216.0ms	(/ 1.0 (* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x))))))

simplify64.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5286	4367

prune407.0ms

Filtered

145 candidates to 206 candidates (-42.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	201	5	206
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	205	8	213

Merged error: 0.0b

Counts

213 → 8

regimes55.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	23
1	17	23

end0.0ms

sample1.2s

Algorithm

intervals

Results

275.0ms	1902×	body	640	valid
252.0ms	8097×	body	80	nan
210.0ms	1135×	body	1280	valid
152.0ms	4008×	body	80	valid
67.0ms	632×	body	320	valid
23.0ms	323×	body	160	valid

Details

sample41.0ms

simplify3.0ms

prune5.0ms

localize7.0ms

rewrite48.0ms

series30.0ms

simplify33.0ms

prune252.0ms

localize13.0ms

rewrite344.0ms

series36.0ms

simplify199.0ms

prune1.4s

localize16.0ms

rewrite95.0ms

series42.0ms

simplify73.0ms

prune399.0ms

localize12.0ms

rewrite129.0ms

series254.0ms

simplify64.0ms

prune407.0ms

regimes55.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.2s

Profiling