Details

sample32.0ms

Algorithm

intervals

Results

11.0ms	50×	body	1280	valid
7.0ms	49×	body	640	valid
4.0ms	128×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	11×	body	160	valid

simplify60.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	5
1	22	5
2	31	5
3	54	5
4	119	5
5	333	5
6	1637	5
7	5001	5

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: 29.9b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(+ 1.0 (exp (* -2.0 x)))
3.4b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

4×	`associate-/r/`
3×	`flip3-+` `fma-neg` `flip-+`
2×	`div-inv`
1×	`+-commutative` `sub-neg` `flip3--` `frac-2neg` `clear-num` `flip--`

Counts

3 → 15

Calls

3 calls:

3.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
6.0ms	(+ 1.0 (exp (* -2.0 x)))
5.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series132.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
19.0ms	(+ 1.0 (exp (* -2.0 x)))
77.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify47.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 3 (44.0ms)

Iter	Nodes	Cost
0	153	135
1	409	131
2	1378	126
3	5001	125

prune56.0ms

Filtered

24 candidates to 17 candidates (70.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	21	3	24
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	22	3	25

Merged error: 0.0b

Counts

25 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(+ 1.0 (exp (* -2.0 x)))
3.4b	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

24×	`associate-/r/`
22×	`prod-diff`
18×	`*-commutative`
15×	`flip3-+` `flip-+`
12×	`div-inv`
11×	`fma-neg`
9×	`swap-sqr` `associate-r` `associate-l`
4×	`difference-of-squares`
3×	`+-commutative`
1×	`sub-neg` `flip3--` `flip--`

Counts

4 → 50

Calls

4 calls:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
18.0ms	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

series137.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(+ 1.0 (exp (* -2.0 x)))
17.0ms	(+ 1.0 (exp (* -2.0 x)))
17.0ms	(+ 1.0 (exp (* -2.0 x)))
86.0ms	(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

simplify119.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (111.0ms)

Iter	Nodes	Cost
0	240	759
1	765	682
2	4189	650
3	5001	620

prune132.0ms

Filtered

62 candidates to 33 candidates (53.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	60	2	62
Fresh	1	1	2
Picked	0	1	1
Done	0	0	0
Total	61	4	65

Merged error: 0.0b

Counts

65 → 4

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b	(* 0.33333333333333337 (pow x 3))
9.5b	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

2×	`associate-r`
1×	`unpow3` `*-commutative` `fma-udef` `sqr-pow`

Counts

2 → 4

Calls

2 calls:

3.0ms	(* 0.33333333333333337 (pow x 3))
1.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series133.0ms

Counts

2 → 6

Calls

2 calls:

35.0ms	(* 0.33333333333333337 (pow x 3))
98.0ms	(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify207.0ms

Algorithm

egg-herbie

Counts

10 → 10

Iterations

Useful iterations: 4 (47.0ms)

Iter	Nodes	Cost
0	32	24
1	86	24
2	269	24
3	911	24
4	4146	21
5	5002	21

prune26.0ms

Filtered

10 candidates to 5 candidates (50.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	10	0	10
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	10	4	14

Merged error: 0.0b

Counts

14 → 4

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.7b	(* (+ (* 1.0 1.0) (- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
3.8b	(- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))
3.9b	(fma (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (* (+ (* 1.0 1.0) (- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- (* 1.0 1.0)))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-commutative`
6×	`frac-times` `flip3-+` `flip-+`
4×	`prod-diff` `clear-num`
3×	`frac-2neg` `associate-r/` `associate-r*`
2×	`distribute-rgt-out--` `fma-neg` `associate-*l/` `associate-/r/` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `flip3--` `un-div-inv` `flip--` `fma-udef` `div-inv`

Counts

4 → 34

Calls

4 calls:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
14.0ms	(* (+ (* 1.0 1.0) (- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
9.0ms	(- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))
1.0ms	(fma (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (* (+ (* 1.0 1.0) (- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- (* 1.0 1.0)))

series470.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(+ 1.0 (exp (* -2.0 x)))
119.0ms	(* (+ (* 1.0 1.0) (- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
76.0ms	(- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))
258.0ms	(fma (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (* (+ (* 1.0 1.0) (- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- (* 1.0 1.0)))

simplify45.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	354	656
1	1429	586
2	5001	573

prune173.0ms

Filtered

46 candidates to 32 candidates (69.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	46	0	46
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	46	4	50

Merged error: 0.0b

Counts

50 → 4

regimes245.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 30.0b

bsearch2.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	36	25
1	36	25

end0.0ms

sample897.0ms

Algorithm

intervals

Results

356.0ms	1681×	body	1280	valid
186.0ms	1322×	body	640	valid
113.0ms	4007×	body	80	valid
66.0ms	673×	body	320	valid
19.0ms	317×	body	160	valid