Details

analyze316.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

sample30.0ms

Algorithm

intervals

Results

12.0ms	68×	body	1280	valid
6.0ms	56×	body	640	valid
3.0ms	33×	body	320	valid
2.0ms	87×	body	80	valid
1.0ms	12×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	5	7
1	5	7

prune2.0ms

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: 42.2b

Counts

2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

0.3b	(/ (exp x) (- (exp x) 1.0))
3.5b	(- (exp x) 1.0)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

22×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`times-frac`
12×	`add-cube-cbrt`
5×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
4×	`add-cbrt-cube` `add-log-exp`
3×	`add-exp-log` `associate-/l*`
2×	`pow1` `flip3--` `associate-/r/` `flip--`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `clear-num` `div-inv`

Counts

2 → 50

Calls

2 calls:

7.0ms	(/ (exp x) (- (exp x) 1.0))
4.0ms	(- (exp x) 1.0)

series9.0ms

Counts

2 → 6

Calls

2 calls:

6.0ms	(/ (exp x) (- (exp x) 1.0))
2.0ms	(- (exp x) 1.0)

simplify66.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4925	575
1	4925	575

prune77.0ms

Filtered

41 candidates to 56 candidates (-36.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	52	4	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	4	57

Merged error: 0b

Counts

57 → 4

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1/2 (+ (* x 1/12) (/ 1 x)))
0.0b	(+ (* x 1/12) (/ 1 x))
0.4b	(* x 1/12)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
7×	`add-sqr-sqrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`sum-log`
3×	`associate-r` `associate-l`
2×	`+-commutative` `flip3-+` `flip-+`
1×	`associate-+r+` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `distribute-lft-out` `unswap-sqr`

Counts

3 → 43

Calls

3 calls:

7.0ms	(+ 1/2 (+ (* x 1/12) (/ 1 x)))
5.0ms	(+ (* x 1/12) (/ 1 x))
3.0ms	(* x 1/12)

series9.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(+ 1/2 (+ (* x 1/12) (/ 1 x)))
4.0ms	(+ (* x 1/12) (/ 1 x))
2.0ms	(* x 1/12)

simplify76.0ms

Algorithm

egg-herbie

Counts

52 → 52

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4849	420
1	4849	420

prune57.0ms

Filtered

36 candidates to 52 candidates (-44.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	52	4	56

Merged error: 0b

Counts

56 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 1 (- 1 (/ 1.0 (exp x))))
0.0b	(/ 1.0 (exp x))
3.5b	(- 1 (/ 1.0 (exp x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
43×	`times-frac`
24×	`add-cube-cbrt`
20×	`difference-of-squares`
11×	`associate-/r*`
8×	`add-exp-log`
7×	`add-cbrt-cube`
6×	`associate-/l*`
5×	`distribute-lft-out--` `add-log-exp`
4×	`pow1`
3×	`div-exp`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `clear-num` `associate-/r/` `flip--` `div-inv`
1×	`sub-neg` `rec-exp` `pow-flip` `diff-log` `1-exp` `inv-pow`

Counts

3 → 96

Calls

3 calls:

8.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
4.0ms	(/ 1.0 (exp x))
6.0ms	(- 1 (/ 1.0 (exp x)))

series19.0ms

Counts

3 → 9

Calls

3 calls:

9.0ms	(/ 1 (- 1 (/ 1.0 (exp x))))
4.0ms	(/ 1.0 (exp x))
6.0ms	(- 1 (/ 1.0 (exp x)))

simplify46.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5114	1131

prune98.0ms

Filtered

65 candidates to 105 candidates (-61.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	105	0	105
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	105	4	109

Merged error: 0b

Counts

109 → 4

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (sqrt (exp x)) (sqrt 1.0))
0.0b	(* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0)))
0.3b	(/ (exp x) (* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0))))
3.3b	(- (sqrt (exp x)) (sqrt 1.0))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
16×	`sqrt-prod`
11×	`add-cbrt-cube`
9×	`add-exp-log` `associate-r`
8×	`frac-times` `add-cube-cbrt` `associate-/r/` `add-log-exp` `difference-of-squares`
7×	`flip3--` `flip3-+` `flip--` `flip-+`
6×	`pow1`
5×	`associate-l`
4×	`associate-r/` `associate-l/` `distribute-lft-out` `distribute-lft-out--`
3×	`sub-neg` `times-frac` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `distribute-rgt-in` `frac-2neg` `distribute-lft-in` `diff-log` `pow-prod-down` `clear-num` `associate-/r` `sum-log` `-commutative` `div-inv` `unswap-sqr`

Counts

4 → 95

Calls

4 calls:

6.0ms	(+ (sqrt (exp x)) (sqrt 1.0))
15.0ms	(* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0)))
15.0ms	(/ (exp x) (* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0))))
6.0ms	(- (sqrt (exp x)) (sqrt 1.0))

series39.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ (sqrt (exp x)) (sqrt 1.0))
10.0ms	(* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0)))
20.0ms	(/ (exp x) (* (+ (sqrt (exp x)) (sqrt 1.0)) (- (sqrt (exp x)) (sqrt 1.0))))
5.0ms	(- (sqrt (exp x)) (sqrt 1.0))

simplify64.0ms

Algorithm

egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4955	1261
1	4955	1261

prune134.0ms

Filtered

76 candidates to 107 candidates (-40.8%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	107	4	111

Merged error: 0b

Counts

111 → 4

regimes93.0ms

Accuracy

96.3% (0.8b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 21.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	22
1	20	22

end0.0ms

analyze313.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

sample847.0ms

Algorithm

intervals

Results

398.0ms	2295×	body	1280	valid
181.0ms	1619×	body	640	valid
66.0ms	2836×	body	80	valid
65.0ms	886×	body	320	valid
20.0ms	364×	body	160	valid
0.0ms	2×	body	1280	invalid

Details

analyze316.0ms

sample30.0ms

simplify3.0ms

prune2.0ms

localize4.0ms

rewrite14.0ms

series9.0ms

simplify66.0ms

prune77.0ms

localize6.0ms

rewrite16.0ms

series9.0ms

simplify76.0ms

prune57.0ms

localize7.0ms

rewrite22.0ms

series19.0ms

simplify46.0ms

prune98.0ms

localize9.0ms

rewrite47.0ms

series39.0ms

simplify64.0ms

prune134.0ms

regimes93.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze313.0ms

sample847.0ms

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