Details

analyze1.0s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
25%	74.9%	0.1%	3
25%	74.9%	0.1%	4
25%	74.9%	0.1%	5
31.2%	68.6%	0.1%	6
32.8%	67.1%	0.1%	7
34.3%	65.5%	0.1%	8
38.2%	61.2%	0.5%	9
39.6%	53%	7.4%	10
40.3%	52.4%	7.4%	11
41.6%	49.6%	8.8%	12
42%	39.9%	18.1%	13
42.3%	39.6%	18.2%	14

sample40.0ms

Algorithm

intervals

Results

16.0ms	256×	body	80	valid
8.0ms	98×	body	80	invalid
2.0ms	53×	body	80	nan

simplify83.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4961	13
1	4961	13

prune14.0ms

Filtered

1 candidates to 1 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: 1.4b

Counts

2 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (* 10.0 k))
1.4b	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-exp-log`
7×	`add-cbrt-cube`
4×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `div-exp` `add-log-exp`
3×	`times-frac` `prod-exp` `associate-/r*`
2×	`pow1` `cbrt-undiv` `flip3-+` `associate-/r/` `flip-+`
1×	`+-commutative` `pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

2 → 36

Calls

2 calls:

3.0ms	(+ 1.0 (* 10.0 k))
9.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

series35.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(+ 1.0 (* 10.0 k))
32.0ms	(/ (* a (pow k m)) (+ (+ 1.0 (* 10.0 k)) (* k k)))

simplify50.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4942	567
1	4942	567

prune60.0ms

Filtered

31 candidates to 42 candidates (-35.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	39	3	42
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	40	4	44

Merged error: 0.0b

Counts

44 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (pow k m) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
0.0b	(* (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (/ (pow k m) (sqrt (+ 1.0 (* k (+ 10.0 k))))))
17.5b	(sqrt (+ 1.0 (* k (+ 10.0 k))))
17.5b	(sqrt (+ 1.0 (* k (+ 10.0 k))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

146×	`add-sqr-sqrt`
134×	`times-frac`
76×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
48×	`associate-r`
45×	`unpow-prod-down`
33×	`add-exp-log`
24×	`associate-l`
21×	`unswap-sqr`
19×	`sqr-pow`
18×	`add-cbrt-cube`
13×	`div-exp`
10×	`sqrt-div`
8×	`pow1` `prod-exp`
7×	`associate-/l*`
6×	`associate-/r*` `associate-/r/`
5×	`cbrt-undiv` `flip3-+` `flip-+`
4×	`cbrt-unprod` `add-log-exp`
3×	`pow-to-exp` `pow-exp` `div-inv`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 218

Calls

4 calls:

7.0ms	(/ (pow k m) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
30.0ms	(* (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (/ (pow k m) (sqrt (+ 1.0 (* k (+ 10.0 k))))))
3.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))
3.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))

series62.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(/ (pow k m) (sqrt (+ 1.0 (* k (+ 10.0 k)))))
32.0ms	(* (/ a (sqrt (+ 1.0 (* k (+ 10.0 k))))) (/ (pow k m) (sqrt (+ 1.0 (* k (+ 10.0 k))))))
3.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))
8.0ms	(sqrt (+ 1.0 (* k (+ 10.0 k))))

simplify87.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4967	5224
1	4967	5224

prune381.0ms

Filtered

151 candidates to 230 candidates (-52.3%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	230	0	230
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	230	4	234

Merged error: 0.0b

Counts

234 → 4

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (* k (+ 10.0 k)))
0.0b	(* k (+ 10.0 k))
0.1b	(/ 1 (/ (+ 1.0 (* k (+ 10.0 k))) (* a (pow k m))))
1.5b	(/ (+ 1.0 (* k (+ 10.0 k))) (* a (pow k m)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

54×	`add-exp-log`
36×	`times-frac`
26×	`add-sqr-sqrt` `*-un-lft-identity` `div-exp`
24×	`add-cube-cbrt`
20×	`add-cbrt-cube`
13×	`prod-exp`
8×	`associate-/r*`
7×	`pow1` `cbrt-undiv`
6×	`div-inv` `associate-/l*` `add-log-exp`
5×	`rec-exp` `1-exp`
4×	`pow-to-exp` `associate-r` `pow-exp`
3×	`flip3-+` `associate-l` `cbrt-unprod` `flip-+`
2×	`distribute-rgt-in` `associate-+r+` `frac-2neg` `distribute-lft-in` `associate-*r/` `clear-num` `associate-/l/`
1×	`+-commutative` `pow-flip` `pow-prod-down` `sum-log` `associate-/r/` `*-commutative` `distribute-lft-out` `inv-pow` `unswap-sqr`

Counts

4 → 123

Calls

4 calls:

3.0ms	(+ 1.0 (* k (+ 10.0 k)))
6.0ms	(* k (+ 10.0 k))
8.0ms	(/ 1 (/ (+ 1.0 (* k (+ 10.0 k))) (* a (pow k m))))
7.0ms	(/ (+ 1.0 (* k (+ 10.0 k))) (* a (pow k m)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(+ 1.0 (* k (+ 10.0 k)))
5.0ms	(* k (+ 10.0 k))
29.0ms	(/ 1 (/ (+ 1.0 (* k (+ 10.0 k))) (* a (pow k m))))
30.0ms	(/ (+ 1.0 (* k (+ 10.0 k))) (* a (pow k m)))

simplify64.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4951	1975
1	4951	1975

prune128.0ms

Filtered

83 candidates to 135 candidates (-62.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	135	4	139

Merged error: 0.0b

Counts

139 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* (/ (pow k m) (pow k 3)) a) (- (/ 99.0 k) 10.0))
2.9b	(* (/ (pow k m) (pow k 3)) a)
3.8b	(* (/ a k) (/ (pow k m) k))
10.2b	(/ (pow k m) (pow k 3))

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

221×	`times-frac`
183×	`add-sqr-sqrt`
138×	`unpow-prod-down`
125×	`*-un-lft-identity`
123×	`add-cube-cbrt`
102×	`associate-l`
98×	`add-exp-log`
52×	`sqr-pow`
48×	`cube-prod`
39×	`prod-exp`
37×	`div-exp`
34×	`associate-r`
32×	`add-cbrt-cube`
21×	`unswap-sqr`
20×	`pow-to-exp` `pow-exp`
15×	`cube-mult` `unpow3`
13×	`pow1`
12×	`associate-/r*`
11×	`cbrt-unprod`
7×	`cbrt-undiv` `associate-/l*`
6×	`associate-*l/`
5×	`pow-prod-down`
4×	`div-inv` `add-log-exp`
3×	`frac-times` `associate-r/` `-commutative`
2×	`sub-neg` `flip3--` `flip--` `difference-of-squares`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num` `distribute-lft-out--` `pow-div`

Counts

4 → 358

Calls

4 calls:

19.0ms	(* (* (/ (pow k m) (pow k 3)) a) (- (/ 99.0 k) 10.0))
20.0ms	(* (/ (pow k m) (pow k 3)) a)
14.0ms	(* (/ a k) (/ (pow k m) k))
7.0ms	(/ (pow k m) (pow k 3))

series96.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* (* (/ (pow k m) (pow k 3)) a) (- (/ 99.0 k) 10.0))
24.0ms	(* (/ (pow k m) (pow k 3)) a)
24.0ms	(* (/ a k) (/ (pow k m) k))
13.0ms	(/ (pow k m) (pow k 3))

simplify57.0ms

Algorithm

egg-herbie

Counts

370 → 370

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5256	4786

prune424.0ms

Filtered

230 candidates to 370 candidates (-60.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	369	1	370
Fresh	0	0	0
Picked	1	0	1
Done	0	3	3
Total	370	4	374

Merged error: 0b

Counts

374 → 4

regimes198.0ms

Accuracy

96.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 2.2b

bsearch21.0ms

Steps

Iters	Range		Point
8	1.1622163863564346e+145	1.9930530255535673e+148	7.924264108290504e+146

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	45	44
1	45	44

end0.0ms

sample1.2s

Algorithm

intervals

Results

524.0ms	8000×	body	80	valid
257.0ms	3258×	body	80	invalid
91.0ms	2047×	body	80	nan

Details

analyze1.0s

sample40.0ms

simplify83.0ms

prune14.0ms

localize10.0ms

rewrite12.0ms

series35.0ms

simplify50.0ms

prune60.0ms

localize13.0ms

rewrite52.0ms

series62.0ms

simplify87.0ms

prune381.0ms

localize10.0ms

rewrite30.0ms

series66.0ms

simplify64.0ms

prune128.0ms

localize15.0ms

rewrite78.0ms

series96.0ms

simplify57.0ms

prune424.0ms

regimes198.0ms

bsearch21.0ms

simplify2.0ms

end0.0ms

sample1.2s

Profiling