Details

analyze1.0ms

Algorithm

Search

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

sample30.0ms

Algorithm

intervals

Results

8.0ms	61×	body	640	valid
8.0ms	43×	body	1280	valid
4.0ms	115×	body	80	valid
2.0ms	23×	body	320	valid
1.0ms	14×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (10.0ms)

Iter	Nodes	Cost
0	265	11
1	265	11

prune10.0ms

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: 21.6b

Counts

2 → 1

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
4.3b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite46.0ms

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))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
29.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series31.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ 1.0 (sqrt x))
14.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify33.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5076	1839

prune264.0ms

Filtered

103 candidates to 144 candidates (-39.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	130	14	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	131	14	145

Merged error: 20.9b

Counts

145 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1.0 (sqrt (+ 1.0 x)))
0.2b	(/ (- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ 1.0 x)))))
0.3b	(/ 1.0 (sqrt x))
4.2b	(- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0)))

rewrite364.0ms

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)))
126.0ms	(/ (- (/ 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 (sqrt x))
88.0ms	(- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0)))

series37.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(/ 1.0 (sqrt (+ 1.0 x)))
20.0ms	(/ (- (/ 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 (sqrt x))
4.0ms	(- (/ 1.0 (/ x 1.0)) (/ 1.0 (/ (+ 1.0 x) 1.0)))

simplify233.0ms

Algorithm

egg-herbie

Counts

762 → 762

Iterations

Useful iterations: 0 (101.0ms)

Iter	Nodes	Cost
0	4983	23232
1	4983	23232

prune1.5s

Filtered

283 candidates to 762 candidates (-169.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	757	5	762
Fresh	9	4	13
Picked	1	0	1
Done	0	0	0
Total	767	9	776

Merged error: 5.3b

Counts

776 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x)))))
0.2b	(* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x))))
0.3b	(/ 1.0 (sqrt x))
3.4b	(- (* 1.0 (/ (+ 1.0 x) 1.0)) (* (/ x 1.0) 1.0))

rewrite101.0ms

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 → 161

Calls

4 calls:

42.0ms	(* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x)))))
41.0ms	(* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x))))
4.0ms	(/ 1.0 (sqrt x))
7.0ms	(- (* 1.0 (/ (+ 1.0 x) 1.0)) (* (/ x 1.0) 1.0))

series39.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify79.0ms

Algorithm

egg-herbie

Counts

173 → 173

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4970	3042
1	4970	3042

prune392.0ms

Filtered

122 candidates to 173 candidates (-41.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	171	2	173
Fresh	0	8	8
Picked	1	0	1
Done	0	0	0
Total	172	10	182

Merged error: 0.4b

Counts

182 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x)))))
0.2b	(* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x))))
0.3b	(/ 1.0 (sqrt x))
0.6b	(/ 1.0 (* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x))))))

rewrite134.0ms

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:

38.0ms	(* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x)))))
41.0ms	(* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x))))
4.0ms	(/ 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))))))

series71.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x)))))
13.0ms	(* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x))))
7.0ms	(/ 1.0 (sqrt x))
33.0ms	(/ 1.0 (* (/ x 1.0) (* (/ (+ 1.0 x) 1.0) (+ (/ 1.0 (sqrt (+ 1.0 x))) (/ 1.0 (sqrt x))))))

simplify61.0ms

Algorithm

egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5010	4367

prune409.0ms

Filtered

145 candidates to 206 candidates (-42.1%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	198	8	206
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	206	10	216

Merged error: 0.0b

Counts

216 → 10

regimes57.0ms

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	17	23
1	17	23

end0.0ms

sample811.0ms

Algorithm

intervals

Results

260.0ms	1816×	body	640	valid
211.0ms	1168×	body	1280	valid
154.0ms	4073×	body	80	valid
67.0ms	624×	body	320	valid
22.0ms	319×	body	160	valid

Details

analyze1.0ms

sample30.0ms

simplify12.0ms

prune10.0ms

localize7.0ms

rewrite46.0ms

series31.0ms

simplify33.0ms

prune264.0ms

localize13.0ms

rewrite364.0ms

series37.0ms

simplify233.0ms

prune1.5s

localize15.0ms

rewrite101.0ms

series39.0ms

simplify79.0ms

prune392.0ms

localize12.0ms

rewrite134.0ms

series71.0ms

simplify61.0ms

prune409.0ms

regimes57.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample811.0ms

Profiling