Details

analyze4.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

sample76.0ms

Algorithm

intervals

Results

60.0ms	190×	body	1280	valid
7.0ms	41×	body	640	valid
1.0ms	13×	body	320	valid
1.0ms	10×	body	160	valid
0.0ms	2×	body	80	valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	5718	8

prune8.0ms

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: 28.3b

Counts

2 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (exp (neg x)) 2.0)
3.5b	(+ (exp x) (- (exp (neg x)) 2.0))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+r-` `associate-+r+` `flip3--` `flip3-+` `flip--` `flip-+` `difference-of-squares`

Counts

2 → 29

Calls

2 calls:

5.0ms	(- (exp (neg x)) 2.0)
8.0ms	(+ (exp x) (- (exp (neg x)) 2.0))

series9.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(- (exp (neg x)) 2.0)
7.0ms	(+ (exp x) (- (exp (neg x)) 2.0))

simplify33.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5187	335

prune57.0ms

Filtered

25 candidates to 35 candidates (-40.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	34	1	35
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	35	2	37

Merged error: 0.0b

Counts

37 → 2

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
14×	`add-exp-log` `associate-r`
11×	`add-log-exp`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-cbrt-cube`
6×	`associate-l` `prod-exp` `unswap-sqr`
4×	`pow1` `sum-log` `sqr-pow`
2×	`+-commutative` `pow-to-exp` `flip3-+` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+`
1×	`associate-+r+`

Counts

4 → 74

Calls

4 calls:

5.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
7.0ms	(+ (* x x) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
5.0ms	(* 1/360 (pow x 6))
5.0ms	(* 1/12 (pow x 4))

series24.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4)))
6.0ms	(+ (* x x) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))
4.0ms	(* 1/360 (pow x 6))
4.0ms	(* 1/12 (pow x 4))

simplify54.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5022	849

prune123.0ms

Filtered

56 candidates to 86 candidates (-53.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	85	3	88

Merged error: 0.0b

Counts

88 → 3

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

9×	`*-un-lft-identity` `add-log-exp`
4×	`add-sqr-sqrt` `frac-add`
3×	`flip3--` `flip--`
2×	`pow1` `add-exp-log` `neg-sub0` `exp-neg` `add-cube-cbrt` `sub-neg` `exp-diff` `diff-log` `sum-log` `add-cbrt-cube` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `associate-+l-` `associate-+l+` `flip3-+` `flip-+` `difference-of-squares`

Counts

2 → 33

Calls

2 calls:

4.0ms	(- (exp x) 2.0)
7.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

series9.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(- (exp x) 2.0)
7.0ms	(+ (- (exp x) 2.0) (exp (neg x)))

simplify53.0ms

Algorithm

egg-herbie

Counts

39 → 39

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5310	423

prune40.0ms

Filtered

27 candidates to 39 candidates (-44.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Merged error: 0.0b

Counts

42 → 3

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 1/12 (pow x 4))
0.1b	(* (* x x) 1/360)
1.0b	(pow (+ 1/12 (* (* x x) 1/360)) 3)
54.8b	(/ (+ (pow x 6) (* (pow x 12) (pow (+ 1/12 (* (* x x) 1/360)) 3))) (+ (pow x 4) (* (+ (* 1/12 (pow x 4)) (* 1/360 (pow x 6))) (+ (* 1/12 (pow x 4)) (- (* 1/360 (pow x 6)) (* x x))))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity`
17×	`add-exp-log`
14×	`add-cbrt-cube`
10×	`pow1` `associate-r`
9×	`times-frac`
7×	`unpow-prod-down`
6×	`prod-exp`
4×	`associate-l` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-unpow` `flip3-+` `cube-prod` `pow-prod-down` `associate-/r` `flip-+` `associate-/l` `sqr-pow`
2×	`cube-div` `pow-to-exp` `pow-exp` `associate-/r/` `*-commutative` `associate-/l/`
1×	`cbrt-undiv` `cube-mult` `pow-pow` `frac-2neg` `unpow3` `div-exp` `clear-num` `div-inv` `rem-cube-cbrt`

Counts

4 → 100

Calls

4 calls:

5.0ms	(* 1/12 (pow x 4))
5.0ms	(* (* x x) 1/360)
4.0ms	(pow (+ 1/12 (* (* x x) 1/360)) 3)
10.0ms	(/ (+ (pow x 6) (* (pow x 12) (pow (+ 1/12 (* (* x x) 1/360)) 3))) (+ (pow x 4) (* (+ (* 1/12 (pow x 4)) (* 1/360 (pow x 6))) (+ (* 1/12 (pow x 4)) (- (* 1/360 (pow x 6)) (* x x))))))

series30.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(* 1/12 (pow x 4))
3.0ms	(* (* x x) 1/360)
6.0ms	(pow (+ 1/12 (* (* x x) 1/360)) 3)
18.0ms	(/ (+ (pow x 6) (* (pow x 12) (pow (+ 1/12 (* (* x x) 1/360)) 3))) (+ (pow x 4) (* (+ (* 1/12 (pow x 4)) (* 1/360 (pow x 6))) (+ (* 1/12 (pow x 4)) (- (* 1/360 (pow x 6)) (* x x))))))

simplify38.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5375	2773

prune411.0ms

Filtered

76 candidates to 112 candidates (-47.4%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	110	2	112
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	110	5	115

Merged error: 0b

Counts

115 → 5

regimes107.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	15
1	16	15

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.8s	5659×	body	1280	valid
224.0ms	1269×	body	640	valid
70.0ms	614×	body	320	valid
21.0ms	297×	body	160	valid
6.0ms	161×	body	80	valid
0.0ms	1×	body	80	invalid

Details

analyze4.0ms

sample76.0ms

simplify41.0ms

prune8.0ms

localize6.0ms

rewrite13.0ms

series9.0ms

simplify33.0ms

prune57.0ms

localize9.0ms

rewrite24.0ms

series24.0ms

simplify54.0ms

prune123.0ms

localize6.0ms

rewrite12.0ms

series9.0ms

simplify53.0ms

prune40.0ms

localize21.0ms

rewrite27.0ms

series30.0ms

simplify38.0ms

prune411.0ms

regimes107.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.2s

Profiling