Details

analyze1.0ms

Algorithm: search

sample33.0ms

Algorithm

intervals

Results

9.0ms	136×	body	80	valid
8.0ms	56×	body	640	valid
7.0ms	38×	body	1280	valid
2.0ms	20×	body	320	valid
0.0ms	6×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	11	6
1	14	6
2	14	6

prune3.0ms

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: 19.3b

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))
2.0b	(- (/ 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 → 133

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
5.0ms	(/ 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:

4.0ms	(sqrt (+ x 1.0))
6.0ms	(/ 1.0 (sqrt (+ x 1.0)))
7.0ms	(/ 1.0 (sqrt x))
15.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify62.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	610	1151
1	2301	1116
2	5001	1086

prune265.0ms

Filtered

100 candidates to 145 candidates (-45.0%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	132	13	145
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	133	13	146

Merged error: 18.8b

Counts

146 → 13

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.2b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
2.0b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite39.0ms

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

series48.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
29.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
6.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
9.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify99.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	835	1032
1	4250	935
2	5001	927

prune214.0ms

Filtered

76 candidates to 105 candidates (-38.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	107	11	118

Merged error: 18.1b

Counts

118 → 11

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
1.2b	(+ x (- 1.0 x))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 136

Calls

4 calls:

14.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
22.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
7.0ms	(+ x (- 1.0 x))

series52.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify40.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	938	1674
1	5002	1471

prune256.0ms

Filtered

91 candidates to 148 candidates (-62.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	144	4	148
Fresh	5	5	10
Picked	1	0	1
Done	0	0	0
Total	150	9	159

Merged error: 0.3b

Counts

159 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 116

Calls

4 calls:

7.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
18.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

series56.0ms

Counts

4 → 12

Calls

4 calls:

5.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
33.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

simplify37.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	935	1360
1	5002	1197

prune232.0ms

Filtered

89 candidates to 128 candidates (-43.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	118	10	128
Fresh	5	3	8
Picked	1	0	1
Done	0	0	0
Total	124	13	137

Merged error: 0.0b

Counts

137 → 13

regimes72.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	10
1	14	10

end0.0ms

analyze1.0ms

Algorithm: search

sample820.0ms

Algorithm

intervals

Results

272.0ms	1866×	body	640	valid
210.0ms	1106×	body	1280	valid
156.0ms	4098×	body	80	valid
65.0ms	610×	body	320	valid
23.0ms	320×	body	160	valid

Details

analyze1.0ms

sample33.0ms

simplify5.0ms

prune3.0ms

localize7.0ms

rewrite46.0ms

series31.0ms

simplify62.0ms

prune265.0ms

localize8.0ms

rewrite39.0ms

series48.0ms

simplify99.0ms

prune214.0ms

localize11.0ms

rewrite56.0ms

series52.0ms

simplify40.0ms

prune256.0ms

localize9.0ms

rewrite46.0ms

series56.0ms

simplify37.0ms

prune232.0ms

regimes72.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.0ms

sample820.0ms

Profiling