Details

sample21.0ms

Algorithm

intervals

Results

6.0ms	60×	body	640	valid
4.0ms	131×	body	80	valid
3.0ms	43×	body	320	valid
1.0ms	22×	body	160	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	15	5
2	15	5

prune2.0ms

Filtered

1 candidates to 0 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 17.4b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1.0 (- x 1.0))
0.0b	(/ 1.0 (+ x 1.0))
2.1b	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

84×	`*-un-lft-identity`
55×	`times-frac`
50×	`add-sqr-sqrt`
30×	`add-cube-cbrt`
25×	`distribute-lft-out--`
10×	`distribute-lft-out`
9×	`associate-/r*`
8×	`difference-of-squares`
7×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r/` `associate-/l*`
5×	`add-log-exp`
4×	`div-inv`
3×	`pow1` `flip--`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip-+`
1×	`sub-neg` `flip3-+` `diff-log` `frac-sub`

Counts

3 → 102

Calls

3 calls:

5.0ms	(/ 1.0 (- x 1.0))
5.0ms	(/ 1.0 (+ x 1.0))
22.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

series14.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(/ 1.0 (- x 1.0))
2.0ms	(/ 1.0 (+ x 1.0))
10.0ms	(- (/ 1.0 (+ x 1.0)) (/ 1.0 (- x 1.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	387	679
1	1331	648
2	5001	642

prune160.0ms

Filtered

111 candidates to 78 candidates (29.7%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	109	2	111
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	110	2	112

Merged error: 0.7b

Counts

112 → 2

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (/ 1.0 (+ x 1.0)))
0.0b	(sqrt (/ 1.0 (+ x 1.0)))
0.2b	(* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0))))
10.5b	(- (* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0)))) (/ 1.0 (- x 1.0)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

134×	`sqrt-prod`
114×	`*-un-lft-identity`
97×	`add-sqr-sqrt`
93×	`times-frac`
60×	`add-cube-cbrt`
29×	`swap-sqr`
24×	`distribute-lft-out`
21×	`pow1` `associate-r` `associate-l`
12×	`associate-/r/`
10×	`sqrt-pow1` `pow1/2` `sqrt-div`
9×	`unswap-sqr`
6×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+` `div-inv` `add-log-exp`
5×	`pow-prod-up`
4×	`rem-sqrt-square`
3×	`pow-prod-down` `pow-sqr` `frac-sub`
2×	`frac-times` `associate-r/` `associate-l/` `difference-of-squares`
1×	`pow2` `sub-neg` `flip3--` `pow-plus` `sqrt-unprod` `diff-log` `prod-exp` `rem-square-sqrt` `*-commutative` `flip--` `cbrt-unprod`

Counts

4 → 185

Calls

4 calls:

5.0ms	(sqrt (/ 1.0 (+ x 1.0)))
5.0ms	(sqrt (/ 1.0 (+ x 1.0)))
22.0ms	(* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0))))
18.0ms	(- (* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0)))) (/ 1.0 (- x 1.0)))

series28.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(sqrt (/ 1.0 (+ x 1.0)))
8.0ms	(sqrt (/ 1.0 (+ x 1.0)))
5.0ms	(* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0))))
8.0ms	(- (* (sqrt (/ 1.0 (+ x 1.0))) (sqrt (/ 1.0 (+ x 1.0)))) (/ 1.0 (- x 1.0)))

simplify91.0ms

Algorithm

egg-herbie

Counts

197 → 197

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	550	1597
1	2816	1442
2	5002	1411

prune313.0ms

Filtered

197 candidates to 127 candidates (35.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	196	1	197
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	196	3	199

Merged error: 0.7b

Counts

199 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))
0.2b	(/ -1 (pow x 6))
0.3b	(/ 1 (pow x 4))
0.8b	(/ 1 (pow x 2))

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

72×	`times-frac`
65×	`*-un-lft-identity`
55×	`add-sqr-sqrt` `add-cube-cbrt`
36×	`unpow-prod-down`
27×	`add-exp-log`
22×	`associate-/r*`
15×	`div-exp`
12×	`sqr-pow`
10×	`add-cbrt-cube`
9×	`associate-/l*`
7×	`pow-to-exp` `pow-exp` `div-inv` `distribute-lft-out`
6×	`rec-exp` `1-exp` `add-log-exp`
4×	`pow1` `unpow2`
3×	`cbrt-undiv` `frac-2neg` `clear-num`
2×	`pow-flip` `inv-pow`
1×	`+-commutative` `flip3-+` `frac-add` `sum-log` `flip-+`

Counts

4 → 174

Calls

4 calls:

32.0ms	(+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))
4.0ms	(/ -1 (pow x 6))
5.0ms	(/ 1 (pow x 4))
5.0ms	(/ 1 (pow x 2))

series15.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (/ 1 (pow x 2)) (/ 1 (pow x 4)))
4.0ms	(/ -1 (pow x 6))
3.0ms	(/ 1 (pow x 4))
2.0ms	(/ 1 (pow x 2))

simplify72.0ms

Algorithm

egg-herbie

Counts

186 → 186

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	471	870
1	2229	692
2	5001	624

prune189.0ms

Filtered

186 candidates to 81 candidates (56.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	184	2	186
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	185	4	189

Merged error: 0.0b

Counts

189 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (- (/ -1 (pow x 6)) (+ (pow x -2) (/ 1 (pow x 4)))))
0.0b	(+ (pow x -2) (/ 1 (pow x 4)))
0.2b	(/ -1 (pow x 6))
0.3b	(/ 1 (pow x 4))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
48×	`*-un-lft-identity`
45×	`times-frac`
38×	`add-cube-cbrt`
25×	`unpow-prod-down`
20×	`add-exp-log`
14×	`associate-/r*`
10×	`associate-r` `add-cbrt-cube`
9×	`div-exp` `sqr-pow`
6×	`pow1` `associate-/l*` `add-log-exp`
4×	`pow-to-exp` `associate-*r/` `pow-exp` `div-inv` `distribute-lft-out` `difference-of-squares`
3×	`rec-exp` `1-exp` `associate-l` `distribute-lft-out--`
2×	`cbrt-undiv` `distribute-rgt-in` `sub-neg` `frac-2neg` `distribute-lft-in` `flip3-+` `clear-num` `frac-sub` `flip-+`
1×	`+-commutative` `flip3--` `pow-flip` `pow-prod-down` `prod-exp` `sum-log` `*-commutative` `flip--` `cbrt-unprod` `inv-pow` `unswap-sqr`

Counts

4 → 144

Calls

4 calls:

28.0ms	(* 2.0 (- (/ -1 (pow x 6)) (+ (pow x -2) (/ 1 (pow x 4)))))
12.0ms	(+ (pow x -2) (/ 1 (pow x 4)))
4.0ms	(/ -1 (pow x 6))
5.0ms	(/ 1 (pow x 4))

series20.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(* 2.0 (- (/ -1 (pow x 6)) (+ (pow x -2) (/ 1 (pow x 4)))))
8.0ms	(+ (pow x -2) (/ 1 (pow x 4)))
4.0ms	(/ -1 (pow x 6))
3.0ms	(/ 1 (pow x 4))

simplify83.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (70.0ms)

Iter	Nodes	Cost
0	532	951
1	2566	781
2	5002	754

prune208.0ms

Filtered

156 candidates to 80 candidates (48.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	156	0	156
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	156	4	160

Merged error: 0.0b

Counts

160 → 4

regimes42.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 26.7b

bsearch26.0ms

Steps

Iters	Range		Point
9	0.00021166572504141735	1495.4209016812965	193.10110706229617
10	-249197998.3190651	-3.6532051617239265e-06	-1.018192898139174

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	18
1	37	18

end0.0ms

sample575.0ms

Algorithm

intervals

Results

204.0ms	1929×	body	640	valid
119.0ms	4216×	body	80	valid
93.0ms	1207×	body	320	valid
35.0ms	648×	body	160	valid

Details

sample21.0ms

simplify4.0ms

prune2.0ms

localize6.0ms

rewrite36.0ms

series14.0ms

simplify41.0ms

prune160.0ms

localize8.0ms

rewrite59.0ms

series28.0ms

simplify91.0ms

prune313.0ms

localize13.0ms

rewrite51.0ms

series15.0ms

simplify72.0ms

prune189.0ms

localize12.0ms

rewrite54.0ms

series20.0ms

simplify83.0ms

prune208.0ms

regimes42.0ms

bsearch26.0ms

simplify1.0ms

end0.0ms

sample575.0ms

Profiling