Details

sample19.0ms

Algorithm

intervals

Results

9.0ms

441×

body

valid

simplify297.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	13	7
1	23	6
2	35	4
3	45	4
4	54	4
5	87	4
6	156	4
7	206	4
8	219	4
9	312	4
10	640	4
11	3180	4
12	5001	4

prune5.0ms

Filtered

1 candidates to 1 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: 0.1b

Counts

2 → 2

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(+ (+ (* x x) (* y y)) (* y y))
0.1b	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

rewrite93.0ms

Algorithm

rewrite-expression-head

Rules

137×	`*-un-lft-identity`
86×	`distribute-lft-out`
54×	`associate-l`
19×	`add-log-exp`
10×	`sum-log`
9×	`swap-sqr`
8×	`associate-+l+`
6×	`+-commutative`
3×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `add-cbrt-cube` `flip-+`

Counts

3 → 81

Calls

3 calls:

16.0ms	(+ (* x x) (* y y))
26.0ms	(+ (+ (* x x) (* y y)) (* y y))
44.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

series110.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(+ (* x x) (* y y))
37.0ms	(+ (+ (* x x) (* y y)) (* y y))
39.0ms	(+ (+ (+ (* x x) (* y y)) (* y y)) (* y y))

simplify133.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 3 (125.0ms)

Iter	Nodes	Cost
0	214	564
1	1024	474
2	3935	448
3	5002	441

prune104.0ms

Filtered

90 candidates to 44 candidates (48.9%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	83	7	90
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	85	7	92

Merged error: 0.0b

Counts

92 → 7

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (pow x 2) (* y (+ y y)))
0.1b	(+ (* y y) (+ (pow x 2) (* y (+ y y))))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
14×	`associate-+r+`
12×	`distribute-lft-out`
9×	`add-log-exp`
7×	`+-commutative`
6×	`associate-l`
4×	`distribute-rgt-in` `distribute-lft-in` `sum-log`
2×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `flip3-+` `add-cbrt-cube` `flip-+`

Counts

2 → 41

Calls

2 calls:

17.0ms	(+ (pow x 2) (* y (+ y y)))
29.0ms	(+ (* y y) (+ (pow x 2) (* y (+ y y))))

series78.0ms

Counts

2 → 6

Calls

2 calls:

43.0ms	(+ (pow x 2) (* y (+ y y)))
36.0ms	(+ (* y y) (+ (pow x 2) (* y (+ y y))))

simplify122.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	178	305
1	816	273
2	3555	268
3	5002	268

prune68.0ms

Filtered

47 candidates to 25 candidates (53.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	43	4	47
Fresh	5	1	6
Picked	0	1	1
Done	0	0	0
Total	48	6	54

Merged error: 0.0b

Counts

54 → 6

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* (* 3 y) y) (pow x 2))
0.2b	(* (* 3 y) y)

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

18×	`associate-l`
13×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-cube-cbrt` `associate-r`
4×	`add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod` `distribute-lft-out`
2×	`*-commutative`
1×	`+-commutative` `flip3-+` `sum-log` `flip-+`

Counts

2 → 45

Calls

2 calls:

18.0ms	(+ (* (* 3 y) y) (pow x 2))
8.0ms	(* (* 3 y) y)

series65.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(+ (* (* 3 y) y) (pow x 2))
29.0ms	(* (* 3 y) y)

simplify128.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 3 (123.0ms)

Iter	Nodes	Cost
0	192	215
1	798	193
2	4100	187
3	5001	186

prune87.0ms

Filtered

51 candidates to 33 candidates (64.7%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	50	7	57

Merged error: 0b

Counts

57 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (* y y) (* (sqrt (+ (pow x 2) (* y (+ y y)))) (sqrt (+ (pow x 2) (* y (+ y y))))))
0.2b	(* (sqrt (+ (pow x 2) (* y (+ y y)))) (sqrt (+ (pow x 2) (* y (+ y y)))))
5.8b	(sqrt (+ (pow x 2) (* y (+ y y))))
5.8b	(sqrt (+ (pow x 2) (* y (+ y y))))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

70×	`*-un-lft-identity`
48×	`sqrt-prod`
28×	`add-sqr-sqrt`
25×	`distribute-lft-out`
22×	`associate-l`
21×	`pow1`
18×	`swap-sqr`
16×	`sqrt-div`
14×	`add-cube-cbrt`
10×	`sqrt-pow1` `pow1/2`
9×	`flip3-+` `flip-+`
8×	`associate-r`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `pow-sqr`
2×	`rem-sqrt-square` `associate-r/` `associate-l/`
1×	`+-commutative` `pow2` `pow-plus` `sqrt-unprod` `prod-exp` `sum-log` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

4 → 119

Calls

4 calls:

64.0ms	(+ (* y y) (* (sqrt (+ (pow x 2) (* y (+ y y)))) (sqrt (+ (pow x 2) (* y (+ y y))))))
37.0ms	(* (sqrt (+ (pow x 2) (* y (+ y y)))) (sqrt (+ (pow x 2) (* y (+ y y)))))
19.0ms	(sqrt (+ (pow x 2) (* y (+ y y))))
16.0ms	(sqrt (+ (pow x 2) (* y (+ y y))))

series197.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (* y y) (* (sqrt (+ (pow x 2) (* y (+ y y)))) (sqrt (+ (pow x 2) (* y (+ y y))))))
45.0ms	(* (sqrt (+ (pow x 2) (* y (+ y y)))) (sqrt (+ (pow x 2) (* y (+ y y)))))
54.0ms	(sqrt (+ (pow x 2) (* y (+ y y))))
61.0ms	(sqrt (+ (pow x 2) (* y (+ y y))))

simplify64.0ms

Algorithm

egg-herbie

Counts

131 → 131

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	248	1124
1	1153	994
2	5001	963

prune179.0ms

Filtered

131 candidates to 68 candidates (51.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	131	0	131
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	131	7	138

Merged error: 0b

Counts

138 → 7

regimes105.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	6
1	12	6

end0.0ms

sample535.0ms

Algorithm

intervals

Results

321.0ms

14005×

body

valid