Details

sample32.0ms

Algorithm

intervals

Results

13.0ms	64×	body	1280	valid
5.0ms	40×	body	640	valid
3.0ms	130×	body	80	valid
1.0ms	15×	body	320	valid
0.0ms	7×	body	160	valid

simplify59.0ms

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: 29.7b

Counts

2 → 1

localize6.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

3×	`fma-neg`
2×	`associate-/r/`
1×	`sub-neg` `flip3--` `flip3-+` `flip--` `flip-+` `div-inv`

Counts

1 → 7

Calls

1 calls:

5.0ms

(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series78.0ms

Counts

1 → 3

Calls

1 calls:

78.0ms

(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify102.0ms

Algorithm

egg-herbie

Counts

10 → 10

Iterations

Useful iterations: 3 (23.0ms)

Iter	Nodes	Cost
0	92	61
1	211	59
2	672	56
3	2849	55
4	5002	55

prune30.0ms

Filtered

10 candidates to 7 candidates (70.0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	7	3	10
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	8	3	11

Merged error: 0.0b

Counts

11 → 3

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))

0.0b

(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))

2.0b

(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

34×	`associate-/r/`
23×	`*-commutative`
22×	`prod-diff`
17×	`flip3-+` `flip-+` `div-inv`
12×	`swap-sqr` `associate-r` `associate-l`
11×	`fma-neg`
10×	`clear-num`
9×	`frac-times` `frac-2neg`
8×	`difference-of-squares`
4×	`associate-/l*`
3×	`associate-r/` `associate-l/`
2×	`flip3--` `flip--` `associate-/l/`
1×	`pow2` `sub-neg` `div-sub` `un-div-inv`

Counts

3 → 80

Calls

3 calls:

20.0ms

(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))

8.0ms

(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))

14.0ms

(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

series326.0ms

Counts

3 → 9

Calls

3 calls:

197.0ms

(/ (- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))

46.0ms

(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))

83.0ms

(- (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* 1.0 1.0))

simplify57.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	371	1093
1	1598	978
2	5001	938

prune190.0ms

Filtered

89 candidates to 52 candidates (58.4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	85	4	89
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	88	4	92

Merged error: 0.0b

Counts

92 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) (* (* 1.0 1.0) (* 1.0 1.0))) (* (fma (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
0.0b	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
0.0b	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
1.9b	(- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) (* (* 1.0 1.0) (* 1.0 1.0)))

rewrite404.0ms

Algorithm

rewrite-expression-head

Rules

1439×	`*-commutative`
865×	`swap-sqr`
574×	`prod-diff`
544×	`unswap-sqr`
498×	`associate-/r/`
433×	`associate-r` `associate-l`
400×	`difference-of-squares`
249×	`flip3-+` `flip-+` `div-inv`
200×	`times-frac`
100×	`associate-/l*`
41×	`fma-neg`
19×	`clear-num`
18×	`frac-times`
17×	`frac-2neg`
8×	`associate-*r/`
6×	`associate-*l/`
2×	`pow2` `flip3--` `associate-/r*` `un-div-inv` `flip--` `associate-/l/`
1×	`sub-neg` `div-sub`

Counts

4 → 1083

Calls

4 calls:

171.0ms	(/ (- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) (* (* 1.0 1.0) (* 1.0 1.0))) (* (fma (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
15.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
15.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
96.0ms	(- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) (* (* 1.0 1.0) (* 1.0 1.0)))

series547.0ms

Counts

4 → 12

Calls

4 calls:

344.0ms	(/ (- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) (* (* 1.0 1.0) (* 1.0 1.0))) (* (fma (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (* 1.0 1.0)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
42.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
48.0ms	(* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))
113.0ms	(- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x)))))) (* (* 1.0 1.0) (* 1.0 1.0)))

simplify366.0ms

Algorithm

egg-herbie

Counts

1095 → 1095

Iterations

Useful iterations: 2 (118.0ms)

Iter	Nodes	Cost
0	807	36117
1	3953	23407
2	5001	22471

prune446.0ms

Filtered

1095 candidates to 98 candidates (8.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	1092	3	1095
Fresh	3	0	3
Picked	0	1	1
Done	0	0	0
Total	1095	4	1099

Merged error: 0.0b

Counts

1099 → 4

localize8.0ms

Local error

Found 1 expressions with local error:

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

3×	`fma-neg`
2×	`associate-/r/`
1×	`sub-neg` `flip3--` `flip3-+` `flip--` `flip-+` `div-inv`

Counts

1 → 7

Calls

1 calls:

5.0ms

(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series80.0ms

Counts

1 → 3

Calls

1 calls:

79.0ms

(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify99.0ms

Algorithm

egg-herbie

Counts

10 → 10

Iterations

Useful iterations: 3 (23.0ms)

Iter	Nodes	Cost
0	92	61
1	211	59
2	672	56
3	2849	55
4	5002	55

prune25.0ms

Filtered

10 candidates to 7 candidates (70.0%)

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

regimes292.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.0b

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	54
1	46	54
2	46	54

end0.0ms

sample852.0ms

Algorithm

intervals

Results

367.0ms	1761×	body	1280	valid
160.0ms	1171×	body	640	valid
107.0ms	4134×	body	80	valid
56.0ms	603×	body	320	valid
19.0ms	331×	body	160	valid