Details

sample44.0ms

Algorithm

intervals

Results

10.0ms	65×	body	640	valid
8.0ms	255×	body	80	nan
8.0ms	42×	body	1280	valid
5.0ms	120×	body	80	valid
3.0ms	24×	body	320	valid
0.0ms	5×	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: 21.7b

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))
1.6b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite52.0ms

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))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
4.0ms	(/ 1.0 (sqrt x))
34.0ms	(- (/ 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)))
8.0ms	(/ 1.0 (sqrt x))
13.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify36.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	5072	1846

prune254.0ms

Filtered

103 candidates to 145 candidates (-40.8%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	133	12	145
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	12	146

Merged error: 21.1b

Counts

146 → 12

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ 1.0 x))
0.2b	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
0.3b	(* (sqrt x) (sqrt (+ 1.0 x)))
1.6b	(- (sqrt (+ 1.0 x)) (sqrt x))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 93

Calls

4 calls:

3.0ms	(sqrt (+ 1.0 x))
16.0ms	(/ (* 1.0 (- (sqrt (+ 1.0 x)) (sqrt x))) (* (sqrt x) (sqrt (+ 1.0 x))))
8.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))
10.0ms	(- (sqrt (+ 1.0 x)) (sqrt x))

series53.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(sqrt (+ 1.0 x))
33.0ms	(/ (* 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

105 → 105

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5280	1580

prune188.0ms

Filtered

76 candidates to 105 candidates (-38.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	103	2	105
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	110	7	117

Merged error: 0.3b

Counts

117 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ 1.0 x)) (sqrt x))
0.2b	(/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.3b	(* (sqrt x) (sqrt (+ 1.0 x)))
0.3b	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))

rewrite54.0ms

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)))
8.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))
22.0ms	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))

series59.0ms

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)))
6.0ms	(* (sqrt x) (sqrt (+ 1.0 x)))
37.0ms	(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ 1.0 x)) (sqrt x)))) (* (sqrt x) (sqrt (+ 1.0 x))))

simplify72.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4885	2087
1	4885	2087

prune253.0ms

Filtered

90 candidates to 137 candidates (-52.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	128	9	137
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	133	11	144

Merged error: 0.0b

Counts

144 → 11

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ 1.0 (sqrt x)) (/ 1.0 (+ (+ 1.0 x) (* (sqrt (+ 1.0 x)) (sqrt x)))))
0.2b	(/ 1.0 (+ (+ 1.0 x) (* (sqrt (+ 1.0 x)) (sqrt x))))
0.3b	(* (sqrt (+ 1.0 x)) (sqrt x))
0.3b	(/ 1.0 (sqrt x))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

87×	`add-sqr-sqrt`
67×	`times-frac`
55×	`*-un-lft-identity`
53×	`add-cube-cbrt`
34×	`sqrt-prod`
29×	`associate-l`
28×	`associate-r`
22×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r/`
11×	`flip3-+` `associate-*l/` `flip-+`
10×	`pow1` `sqrt-div` `associate-/r*` `unswap-sqr`
8×	`frac-add` `distribute-lft-out`
6×	`cbrt-undiv` `div-exp` `associate-/l*`
5×	`prod-exp` `cbrt-unprod`
4×	`pow-prod-down` `div-inv` `add-log-exp`
2×	`frac-2neg` `sqrt-pow1` `pow1/2` `clear-num` `*-commutative`
1×	`frac-times` `sqrt-unprod` `associate-*r/`

Counts

4 → 179

Calls

4 calls:

23.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (+ (+ 1.0 x) (* (sqrt (+ 1.0 x)) (sqrt x)))))
7.0ms	(/ 1.0 (+ (+ 1.0 x) (* (sqrt (+ 1.0 x)) (sqrt x))))
8.0ms	(* (sqrt (+ 1.0 x)) (sqrt x))
4.0ms	(/ 1.0 (sqrt x))

series39.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(* (/ 1.0 (sqrt x)) (/ 1.0 (+ (+ 1.0 x) (* (sqrt (+ 1.0 x)) (sqrt x)))))
7.0ms	(/ 1.0 (+ (+ 1.0 x) (* (sqrt (+ 1.0 x)) (sqrt x))))
6.0ms	(* (sqrt (+ 1.0 x)) (sqrt x))
8.0ms	(/ 1.0 (sqrt x))

simplify51.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5073	3163

prune333.0ms

Filtered

149 candidates to 191 candidates (-28.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	187	4	191
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	189	13	202

Merged error: 0.0b

Counts

202 → 13

regimes68.0ms

Accuracy

0% (0.3b 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	14	18
1	14	18

end0.0ms

sample1.3s

Algorithm

intervals

Results

278.0ms	1830×	body	640	valid
261.0ms	8049×	body	80	nan
224.0ms	1131×	body	1280	valid
170.0ms	4073×	body	80	valid
75.0ms	652×	body	320	valid
24.0ms	314×	body	160	valid

Details

sample44.0ms

simplify3.0ms

prune5.0ms

localize7.0ms

rewrite52.0ms

series31.0ms

simplify36.0ms

prune254.0ms

localize8.0ms

rewrite40.0ms

series53.0ms

simplify37.0ms

prune188.0ms

localize11.0ms

rewrite54.0ms

series59.0ms

simplify72.0ms

prune253.0ms

localize9.0ms

rewrite49.0ms

series39.0ms

simplify51.0ms

prune333.0ms

regimes68.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.3s

Profiling