Details

sample44.0ms

Algorithm

intervals

Results

10.0ms	55×	body	1280	valid
9.0ms	64×	body	640	valid
8.0ms	246×	body	80	nan
5.0ms	118×	body	80	valid
2.0ms	15×	body	320	valid
0.0ms	4×	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

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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

rewrite53.0ms

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))
35.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series285.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ x 1.0))
77.0ms	(/ 1.0 (sqrt (+ x 1.0)))
44.0ms	(/ 1.0 (sqrt x))
133.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify51.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	443	1097
1	1434	1038
2	5002	992

prune291.0ms

Filtered

145 candidates to 98 candidates (67.6%)

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: 20.3b

Counts

146 → 12

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ x 1.0))
0.1b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.3b	(* (sqrt x) (sqrt (+ x 1.0)))
2.1b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite41.0ms

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:

5.0ms	(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))

series423.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(sqrt (+ x 1.0))
259.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
61.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
70.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify66.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	511	884
1	2548	762
2	5002	749

prune206.0ms

Filtered

105 candidates to 73 candidates (69.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	104	13	117

Merged error: 20.1b

Counts

117 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b	(/ (* 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)))
1.9b	(+ x (- 1.0 x))

rewrite59.0ms

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:

15.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
25.0ms	(/ (* 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)))
6.0ms	(+ x (- 1.0 x))

series708.0ms

Counts

4 → 12

Calls

4 calls:

146.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
499.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
62.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(+ x (- 1.0 x))

simplify99.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (83.0ms)

Iter	Nodes	Cost
0	710	1587
1	3837	1359
2	5002	1323

prune262.0ms

Filtered

148 candidates to 84 candidates (56.8%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	146	2	148
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	151	10	161

Merged error: 0.2b

Counts

161 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

3.0ms	(sqrt (+ x 1.0))
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)))

series741.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(sqrt (+ x 1.0))
149.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
503.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
60.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

simplify92.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	664	1231
1	3475	1048
2	5002	1018

prune230.0ms

Filtered

130 candidates to 82 candidates (63.1%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	120	10	130
Fresh	5	4	9
Picked	1	0	1
Done	0	0	0
Total	126	14	140

Merged error: 0.0b

Counts

140 → 14

regimes51.0ms

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

sample1.2s

Algorithm

intervals

Results

293.0ms	8240×	body	80	nan
270.0ms	1853×	body	640	valid
221.0ms	1165×	body	1280	valid
158.0ms	4049×	body	80	valid
64.0ms	596×	body	320	valid
24.0ms	337×	body	160	valid

Details

sample44.0ms

simplify5.0ms

prune2.0ms

localize7.0ms

rewrite53.0ms

series285.0ms

simplify51.0ms

prune291.0ms

localize8.0ms

rewrite41.0ms

series423.0ms

simplify66.0ms

prune206.0ms

localize11.0ms

rewrite59.0ms

series708.0ms

simplify99.0ms

prune262.0ms

localize9.0ms

rewrite42.0ms

series741.0ms

simplify92.0ms

prune230.0ms

regimes51.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.2s

Profiling