Details

sample62.0ms

Algorithm

intervals

Results

28.0ms	128×	body	5120	exit
11.0ms	205×	body	80	valid
4.0ms	124×	body	80	overflowed
3.0ms	24×	body	320	valid
3.0ms	16×	body	640	valid
1.0ms	14×	body	160	valid

simplify47.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 3 (7.0ms)

Iter	Nodes	Cost
0	20	9
1	48	9
2	107	9
3	224	8
4	1514	8
5	5001	8

prune6.0ms

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: 12.4b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ wj (+ wj 1))
0.0b	(/ x (+ wj 1))
0.0b	(/ (/ x (+ wj 1)) (exp wj))
4.1b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

127×	`times-frac`
118×	`*-un-lft-identity`
78×	`add-sqr-sqrt`
73×	`add-cube-cbrt`
24×	`associate-/l*`
21×	`distribute-lft-out`
13×	`add-cbrt-cube`
12×	`associate-/r/`
11×	`add-exp-log` `associate-/r*`
9×	`add-log-exp`
7×	`flip3-+` `flip-+` `div-inv`
5×	`cbrt-undiv` `div-exp`
4×	`pow1`
3×	`frac-2neg` `clear-num`
2×	`diff-log` `frac-sub` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--` `associate-/l/`

Counts

4 → 176

Calls

4 calls:

5.0ms	(/ wj (+ wj 1))
8.0ms	(/ x (+ wj 1))
9.0ms	(/ (/ x (+ wj 1)) (exp wj))
29.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series136.0ms

Counts

4 → 12

Calls

4 calls:

20.0ms	(/ wj (+ wj 1))
22.0ms	(/ x (+ wj 1))
41.0ms	(/ (/ x (+ wj 1)) (exp wj))
53.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify84.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	718	1538
1	3300	1483
2	5002	1481

prune377.0ms

Filtered

188 candidates to 138 candidates (73.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	182	6	188
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	184	6	190

Merged error: 0.4b

Counts

190 → 6

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (pow wj 2))
0.0b	(- (+ x (pow wj 2)) (* 2 (* wj x)))
0.0b	(* 2 (* wj x))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`*-un-lft-identity`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`diff-log` `sum-log`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `associate-r` `associate--l+` `*-commutative` `flip--` `flip-+` `distribute-lft-out`

Counts

3 → 44

Calls

3 calls:

4.0ms	(+ x (pow wj 2))
7.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
5.0ms	(* 2 (* wj x))

series79.0ms

Counts

3 → 9

Calls

3 calls:

29.0ms	(+ x (pow wj 2))
31.0ms	(- (+ x (pow wj 2)) (* 2 (* wj x)))
19.0ms	(* 2 (* wj x))

simplify130.0ms

Algorithm

egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	202	247
1	793	231
2	4232	228
3	5001	228

prune83.0ms

Filtered

53 candidates to 32 candidates (60.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	52	1	53
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	52	7	59

Merged error: 0.4b

Counts

59 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (/ x (sqrt (exp wj))) (/ (/ 1 (+ wj 1)) (sqrt (exp wj))))
0.0b	(/ 1 (+ wj 1))
0.0b	(/ (/ 1 (+ wj 1)) (sqrt (exp wj)))
4.1b	(- (+ (* (/ x (sqrt (exp wj))) (/ (/ 1 (+ wj 1)) (sqrt (exp wj)))) wj) (/ wj (+ wj 1)))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

447×	`times-frac`
299×	`*-un-lft-identity`
290×	`add-sqr-sqrt`
205×	`add-cube-cbrt`
136×	`sqrt-prod`
112×	`associate-r`
52×	`add-exp-log`
43×	`distribute-lft-out`
32×	`add-cbrt-cube`
28×	`associate-/r/`
25×	`div-exp`
22×	`associate-l`
21×	`associate-/l*` `unswap-sqr`
17×	`div-inv`
15×	`flip3-+` `flip-+`
13×	`cbrt-undiv`
10×	`prod-exp` `associate-/r*`
9×	`add-log-exp`
7×	`pow1`
6×	`cbrt-unprod`
4×	`rec-exp` `1-exp`
2×	`frac-2neg` `diff-log` `clear-num` `frac-sub` `difference-of-squares`
1×	`frac-times` `sub-neg` `flip3--` `pow-flip` `associate-r/` `pow-prod-down` `associate-l/` `associate--l+` `sum-log` `*-commutative` `flip--` `associate-/l/` `distribute-lft-out--` `inv-pow`

Counts

4 → 388

Calls

4 calls:

63.0ms	(* (/ x (sqrt (exp wj))) (/ (/ 1 (+ wj 1)) (sqrt (exp wj))))
5.0ms	(/ 1 (+ wj 1))
12.0ms	(/ (/ 1 (+ wj 1)) (sqrt (exp wj)))
28.0ms	(- (+ (* (/ x (sqrt (exp wj))) (/ (/ 1 (+ wj 1)) (sqrt (exp wj)))) wj) (/ wj (+ wj 1)))

series135.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (/ x (sqrt (exp wj))) (/ (/ 1 (+ wj 1)) (sqrt (exp wj))))
13.0ms	(/ 1 (+ wj 1))
30.0ms	(/ (/ 1 (+ wj 1)) (sqrt (exp wj)))
54.0ms	(- (+ (* (/ x (sqrt (exp wj))) (/ (/ 1 (+ wj 1)) (sqrt (exp wj)))) wj) (/ wj (+ wj 1)))

simplify81.0ms

Algorithm

egg-herbie

Counts

400 → 400

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1403	4781
1	5002	4155

prune548.0ms

Filtered

400 candidates to 182 candidates (45.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	400	0	400
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	400	7	407

Merged error: 0.4b

Counts

407 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt (- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1))))
4.1b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))
4.1b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))
4.1b	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-log-exp`
8×	`frac-sub` `distribute-lft-out--` `difference-of-squares`
7×	`cbrt-prod`
6×	`diff-log`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `cbrt-div` `flip3--` `flip3-+` `times-frac` `add-cbrt-cube` `flip--` `flip-+` `distribute-lft-out`
3×	`sub-neg` `associate--l+` `sum-log`
1×	`pow1/3`

Counts

4 → 79

Calls

4 calls:

30.0ms	(cbrt (- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1))))
33.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))
30.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))
31.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

series280.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(cbrt (- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1))))
52.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))
54.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))
57.0ms	(- (+ (/ (/ x (+ wj 1)) (exp wj)) wj) (/ wj (+ wj 1)))

simplify46.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	368	1425
1	1204	1352
2	5002	1319

prune247.0ms

Filtered

91 candidates to 70 candidates (76.9%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	88	3	91
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	89	9	98

Merged error: 0.3b

Counts

98 → 9

regimes95.0ms

Accuracy

64.3% (0.7b remaining)

Error of 1.0b against oracle of 0.3b and baseline of 2.2b

bsearch23.0ms

Steps

Iters	Range		Point
5	3.7253391743722696e-11	1.3393947446404039e-10	1.305370283524307e-10

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	18
1	30	18

end0.0ms

sample1.7s

Algorithm

intervals

Results

844.0ms	3695×	body	5120	exit
237.0ms	6335×	body	80	valid
131.0ms	3782×	body	80	overflowed
89.0ms	747×	body	320	valid
85.0ms	465×	body	640	valid
40.0ms	525×	body	160	valid