Details

analyze1.0ms

Algorithm

Search

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

sample32.0ms

Algorithm

intervals

Results

9.0ms	30×	body	1280	valid
9.0ms	65×	body	640	valid
5.0ms	133×	body	80	valid
2.0ms	19×	body	320	valid
1.0ms	9×	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

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 3 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
2.7b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite46.0ms

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))
29.0ms	(- (/ 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))))

simplify31.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (19.0ms)

Iter	Nodes	Cost
0	5082	1654

prune217.0ms

Filtered

87 candidates to 125 candidates (-43.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	114	11	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	115	11	126

Merged error: 19.9b

Counts

126 → 11

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
0.2b	(* (sqrt x) (sqrt (+ 1.0 x)))
2.7b	(- (sqrt (+ 1.0 x)) (sqrt x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

23×	`add-sqr-sqrt`
19×	`sqrt-prod`
17×	`add-exp-log` `add-cbrt-cube`
16×	`*-un-lft-identity`
7×	`pow1` `add-cube-cbrt` `associate-r`
6×	`associate-r/` `associate-l*`
5×	`prod-exp` `cbrt-unprod` `add-log-exp`
4×	`cbrt-undiv` `sqrt-div` `div-exp` `difference-of-squares` `unswap-sqr`
3×	`pow-prod-down` `distribute-lft-out--`
2×	`flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `associate-/r/` `flip--` `flip-+` `associate-/l/` `distribute-lft-out`
1×	`sub-neg` `frac-2neg` `times-frac` `sqrt-unprod` `diff-log` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*`

Counts

3 → 76

Calls

3 calls:

17.0ms	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
10.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))
8.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

series45.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
6.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))
10.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

simplify37.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	4987	1388
1	4987	1388

prune155.0ms

Filtered

61 candidates to 85 candidates (-39.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	89	7	96

Merged error: 0.2b

Counts

96 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ 1.0 x)) (sqrt x))
0.1b	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.2b	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
0.2b	(* (sqrt x) (sqrt (+ 1.0 x)))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

78×	`*-un-lft-identity`
35×	`sqrt-prod`
32×	`distribute-lft-out`
29×	`add-exp-log` `add-cbrt-cube`
28×	`add-sqr-sqrt`
25×	`times-frac`
20×	`add-cube-cbrt`
9×	`cbrt-undiv` `div-exp`
8×	`pow1` `prod-exp` `cbrt-unprod`
7×	`associate-r` `associate-/r*`
6×	`associate-l` `add-log-exp`
5×	`flip3-+` `associate-r/` `flip-+` `associate-/l`
4×	`sqrt-div` `associate-/r/` `unswap-sqr`
3×	`pow-prod-down` `associate-/l/`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `div-inv`
1×	`+-commutative` `sqrt-unprod` `sum-log` `*-commutative`

Counts

4 → 125

Calls

4 calls:

7.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
12.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
20.0ms	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
8.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))

series57.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(+ (sqrt (+ 1.0 x)) (sqrt x))
9.0ms	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
36.0ms	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))
6.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))

simplify60.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5523	2087

prune251.0ms

Filtered

91 candidates to 137 candidates (-50.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	127	10	137
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	133	11	144

Merged error: 0b

Counts

144 → 11

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* (sqrt x) (sqrt (+ x 1.0))))
0.1b	(/ (/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ 1.0 x)))
0.1b	(/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0)))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

106×	`times-frac`
72×	`*-un-lft-identity`
67×	`add-sqr-sqrt`
55×	`sqrt-prod`
48×	`add-cube-cbrt`
23×	`distribute-lft-out`
20×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
12×	`flip3-+` `flip-+`
11×	`associate-/r` `associate-/l`
10×	`div-inv`
8×	`pow1`
7×	`cbrt-undiv` `div-exp` `associate-r`
6×	`associate-l` `add-log-exp`
4×	`sqrt-div` `unswap-sqr`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `associate-*r/` `clear-num`
1×	`+-commutative` `sqrt-unprod` `sum-log` `*-commutative` `associate-/l/`

Counts

4 → 176

Calls

4 calls:

3.0ms	(+ x (* (sqrt x) (sqrt (+ x 1.0))))
15.0ms	(/ (/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ 1.0 x)))
6.0ms	(/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0)))))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

series46.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ x (* (sqrt x) (sqrt (+ x 1.0))))
25.0ms	(/ (/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0))))) (sqrt (+ 1.0 x)))
9.0ms	(/ (* 1.0 1.0) (+ x (* (sqrt x) (sqrt (+ x 1.0)))))
6.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

simplify88.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4975	4295
1	4975	4295

prune330.0ms

Filtered

126 candidates to 188 candidates (-49.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	189	10	199

Merged error: 0b

Counts

199 → 10

regimes56.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	18
1	14	18

end0.0ms

sample785.0ms

Algorithm

intervals

Results

255.0ms	1801×	body	640	valid
203.0ms	1144×	body	1280	valid
151.0ms	4093×	body	80	valid
66.0ms	655×	body	320	valid
21.0ms	307×	body	160	valid

Details

analyze1.0ms

sample32.0ms

simplify12.0ms

prune5.0ms

localize7.0ms

rewrite46.0ms

series26.0ms

simplify31.0ms

prune217.0ms

localize8.0ms

rewrite38.0ms

series45.0ms

simplify37.0ms

prune155.0ms

localize13.0ms

rewrite53.0ms

series57.0ms

simplify60.0ms

prune251.0ms

localize12.0ms

rewrite39.0ms

series46.0ms

simplify88.0ms

prune330.0ms

regimes56.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample785.0ms

Profiling