Details

sample45.0ms

Algorithm

intervals

Results

9.0ms	60×	body	640	valid
9.0ms	243×	body	80	nan
7.0ms	36×	body	1280	valid
5.0ms	119×	body	80	valid
3.0ms	28×	body	320	valid
1.0ms	13×	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: 21.5b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ 1.0 (sqrt (+ x 1.0)))
0.2b	(/ 1.0 (sqrt x))
3.9b	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

rewrite50.0ms

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))
34.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

series250.0ms

Counts

3 → 9

Calls

3 calls:

75.0ms	(/ 1.0 (sqrt (+ x 1.0)))
38.0ms	(/ 1.0 (sqrt x))
137.0ms	(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))

simplify46.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	410	1006
1	1310	954
2	5001	912

prune266.0ms

Filtered

126 candidates to 84 candidates (66.7%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	116	10	126
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	117	10	127

Merged error: 20.9b

Counts

127 → 10

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
3.9b	(- (sqrt (+ x 1.0)) (sqrt x))

rewrite39.0ms

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:

18.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
11.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

series395.0ms

Counts

3 → 9

Calls

3 calls:

267.0ms	(/ (* 1.0 (- (sqrt (+ x 1.0)) (sqrt x))) (* (sqrt x) (sqrt (+ x 1.0))))
55.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
72.0ms	(- (sqrt (+ x 1.0)) (sqrt x))

simplify64.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	492	793
1	2495	678
2	5002	667

prune187.0ms

Filtered

86 candidates to 59 candidates (68.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	83	3	86
Fresh	0	9	9
Picked	1	0	1
Done	0	0	0
Total	84	12	96

Merged error: 20.2b

Counts

96 → 12

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ 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))))
0.2b	(* (sqrt x) (sqrt (+ x 1.0)))
3.1b	(+ x (- 1.0 x))

rewrite57.0ms

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)))
23.0ms	(/ (* 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))

series687.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))
482.0ms	(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
60.0ms	(* (sqrt x) (sqrt (+ x 1.0)))
1.0ms	(+ x (- 1.0 x))

simplify96.0ms

Algorithm

egg-herbie

Counts

148 → 148

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	710	1587
1	3837	1359
2	5001	1323

prune279.0ms

Filtered

148 candidates to 84 candidates (56.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	145	3	148
Fresh	6	5	11
Picked	1	0	1
Done	0	0	0
Total	152	8	160

Merged error: 0.3b

Counts

160 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite52.0ms

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:

8.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
22.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
10.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

series772.0ms

Counts

4 → 12

Calls

4 calls:

69.0ms	(+ (sqrt (+ x 1.0)) (sqrt x))
502.0ms	(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
143.0ms	(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
57.0ms	(* (sqrt x) (sqrt (+ x 1.0)))

simplify85.0ms

Algorithm

egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	671	1264
1	3514	1071
2	5002	1042

prune260.0ms

Filtered

128 candidates to 81 candidates (63.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	114	14	128
Fresh	4	3	7
Picked	1	0	1
Done	0	0	0
Total	119	17	136

Merged error: 0.0b

Counts

136 → 17

regimes68.0ms

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

sample1.3s

Algorithm

intervals

Results

310.0ms	8097×	body	80	nan
290.0ms	1838×	body	640	valid
228.0ms	1134×	body	1280	valid
164.0ms	4099×	body	80	valid
71.0ms	618×	body	320	valid
24.0ms	311×	body	160	valid