Details

sample81.0ms

Algorithm

intervals

Results

56.0ms	185×	body	1280	valid
6.0ms	41×	body	640	valid
6.0ms	251×	body	80	valid
1.0ms	16×	body	320	valid
0.0ms	8×	body	160	valid

simplify225.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	14	5
1	26	5
2	41	5
3	55	5
4	67	5
5	104	5
6	161	5
7	344	5
8	1452	5
9	5002	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: 29.5b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp x) 2.0)
4.0b	(+ (- (exp x) 2.0) (exp (- x)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

4×	`frac-add`
3×	`flip3--` `flip--`
2×	`neg-sub0` `exp-neg` `sub-neg` `associate-+l+` `exp-diff`
1×	`+-commutative` `associate-+l-` `flip3-+` `flip-+`

Counts

2 → 14

Calls

2 calls:

2.0ms	(- (exp x) 2.0)
4.0ms	(+ (- (exp x) 2.0) (exp (- x)))

series72.0ms

Counts

2 → 6

Calls

2 calls:

16.0ms	(- (exp x) 2.0)
56.0ms	(+ (- (exp x) 2.0) (exp (- x)))

simplify65.0ms

Algorithm

egg-herbie

Counts

20 → 20

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	175	161
1	551	149
2	2525	142
3	5002	137

prune46.0ms

Filtered

20 candidates to 13 candidates (65.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	18	2	20
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	19	2	21

Merged error: 0.0b

Counts

21 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
0.0b	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
0.1b	(* 1/12 (pow x 4))

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 4

Calls

3 calls:

1.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
1.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
3.0ms	(* 1/12 (pow x 4))

series222.0ms

Counts

3 → 9

Calls

3 calls:

56.0ms	(fma x x (fma 1/360 (pow x 6) (* 1/12 (pow x 4))))
128.0ms	(fma 1/360 (pow x 6) (* 1/12 (pow x 4)))
37.0ms	(* 1/12 (pow x 4))

simplify68.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	35	41
1	110	38
2	313	38
3	1249	38
4	5002	38

prune15.0ms

Filtered

13 candidates to 4 candidates (30.8%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	13	0	13
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	13	2	15

Merged error: 0.0b

Counts

15 → 2

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (fma (- 2.0) 2.0 (exp (+ x x))) 1)
0.0b	(/ (fma (+ (fma (- 2.0) 2.0 (exp (+ x x))) 1) (exp x) 2.0) (* (+ (exp x) 2.0) (exp x)))
0.0b	(* (+ (exp x) 2.0) (exp x))
3.1b	(fma (+ (fma (- 2.0) 2.0 (exp (+ x x))) 1) (exp x) 2.0)

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 15

Calls

4 calls:

2.0ms	(+ (fma (- 2.0) 2.0 (exp (+ x x))) 1)
4.0ms	(/ (fma (+ (fma (- 2.0) 2.0 (exp (+ x x))) 1) (exp x) 2.0) (* (+ (exp x) 2.0) (exp x)))
4.0ms	(* (+ (exp x) 2.0) (exp x))
1.0ms	(fma (+ (fma (- 2.0) 2.0 (exp (+ x x))) 1) (exp x) 2.0)

series347.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(+ (fma (- 2.0) 2.0 (exp (+ x x))) 1)
197.0ms	(/ (fma (+ (fma (- 2.0) 2.0 (exp (+ x x))) 1) (exp x) 2.0) (* (+ (exp x) 2.0) (exp x)))
23.0ms	(* (+ (exp x) 2.0) (exp x))
84.0ms	(fma (+ (fma (- 2.0) 2.0 (exp (+ x x))) 1) (exp x) 2.0)

simplify87.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 3 (83.0ms)

Iter	Nodes	Cost
0	211	209
1	720	203
2	2893	195
3	5003	190

prune82.0ms

Filtered

27 candidates to 22 candidates (81.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	26	1	27
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	27	2	29

Merged error: 0.0b

Counts

29 → 2

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (exp x) (- 1 (* 2.0 2.0)) (pow (exp x) 3))
0.0b	(* (+ (exp x) 2.0) (exp x))
0.0b	(pow (exp x) 3)
2.7b	(+ (fma (exp x) (- 1 (* 2.0 2.0)) (pow (exp x) 3)) 2.0)

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

2×	`flip3-+` `associate-*l/` `flip-+` `fma-udef`
1×	`+-commutative` `pow-to-exp` `associate-+l+` `unpow3` `pow-exp` `*-commutative` `sqr-pow`

Counts

4 → 12

Calls

4 calls:

1.0ms	(fma (exp x) (- 1 (* 2.0 2.0)) (pow (exp x) 3))
4.0ms	(* (+ (exp x) 2.0) (exp x))
2.0ms	(pow (exp x) 3)
2.0ms	(+ (fma (exp x) (- 1 (* 2.0 2.0)) (pow (exp x) 3)) 2.0)

series216.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(fma (exp x) (- 1 (* 2.0 2.0)) (pow (exp x) 3))
23.0ms	(* (+ (exp x) 2.0) (exp x))
24.0ms	(pow (exp x) 3)
93.0ms	(+ (fma (exp x) (- 1 (* 2.0 2.0)) (pow (exp x) 3)) 2.0)

simplify46.0ms

Algorithm

egg-herbie

Counts

24 → 24

Iterations

Useful iterations: 3 (43.0ms)

Iter	Nodes	Cost
0	152	133
1	429	131
2	1495	125
3	5001	119

prune57.0ms

Filtered

24 candidates to 17 candidates (70.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	23	1	24
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	23	3	26

Merged error: 0.0b

Counts

26 → 3

regimes20.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	5
1	11	5

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.7s	5678×	body	1280	valid
196.0ms	1238×	body	640	valid
189.0ms	8156×	body	80	valid
60.0ms	602×	body	320	valid
23.0ms	336×	body	160	valid