Details

sample47.0ms

Algorithm

intervals

Results

12.0ms	255×	body	80	nan
7.0ms	39×	body	1280	valid
6.0ms	47×	body	640	valid
5.0ms	133×	body	80	valid
2.0ms	21×	body	320	valid
1.0ms	16×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

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: 20.7b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ 1.0 (sqrt (+ x 1.0)))
0.3b	(/ 1.0 (sqrt x))
3.0b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite47.0ms

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 → 117

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))))

series711.0ms

Counts

3 → 9

Calls

3 calls:

147.0ms	(/ 1.0 (sqrt (+ x 1.0)))
231.0ms	(/ 1.0 (sqrt x))
332.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify57.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	541	1048
1	2015	1014
2	5002	983

prune608.0ms

Filtered

126 candidates to 85 candidates (32.5%)

Pruning

18 alts after pruning (18 fresh and 0 done)

	Pruned	Kept	Total
New	108	18	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	109	18	127

Merged error: 20.1b

Counts

127 → 18

localize8.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
3.1b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite33.0ms

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 → 77

Calls

3 calls:

16.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
7.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
8.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series1.2s

Counts

3 → 9

Calls

3 calls:

828.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
146.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
224.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify93.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	785	930
1	4068	833
2	5002	827

prune533.0ms

Filtered

86 candidates to 61 candidates (29.1%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	3	14	17
Picked	1	0	1
Done	0	0	0
Total	87	17	104

Merged error: 18.9b

Counts

104 → 17

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 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)))
1.7b	(+ x (- 1.0 x))

rewrite52.0ms

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:

13.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
21.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
7.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
5.0ms	(+ x (- 1.0 x))

series1.5s

Counts

4 → 12

Calls

4 calls:

423.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
962.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
143.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(+ x (- 1.0 x))

simplify38.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	938	1674
1	5002	1471

prune955.0ms

Filtered

148 candidates to 91 candidates (38.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	144	4	148
Fresh	8	8	16
Picked	1	0	1
Done	0	0	0
Total	153	12	165

Merged error: 0.2b

Counts

165 → 12

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

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)))
16.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
7.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

series1.5s

Counts

4 → 12

Calls

4 calls:

116.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
252.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
951.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
138.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

simplify36.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	935	1360
1	5002	1197

prune889.0ms

Filtered

128 candidates to 89 candidates (30.5%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	114	14	128
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	121	19	140

Merged error: 0.0b

Counts

140 → 19

regimes95.0ms

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

sample1.1s

Algorithm

intervals

Results

252.0ms	8028×	body	80	nan
231.0ms	1771×	body	640	valid
190.0ms	1158×	body	1280	valid
139.0ms	4124×	body	80	valid
59.0ms	620×	body	320	valid
22.0ms	327×	body	160	valid

Details

sample47.0ms

simplify5.0ms

prune3.0ms

localize7.0ms

rewrite47.0ms

series711.0ms

simplify57.0ms

prune608.0ms

localize8.0ms

rewrite33.0ms

series1.2s

simplify93.0ms

prune533.0ms

localize15.0ms

rewrite52.0ms

series1.5s

simplify38.0ms

prune955.0ms

localize9.0ms

rewrite44.0ms

series1.5s

simplify36.0ms

prune889.0ms

regimes95.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling