Details

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	74.6%	25.4%	0
0%	74.6%	25.4%	1
37.3%	37.3%	25.4%	2
37.3%	18.7%	44%	3
46.7%	9.3%	44%	4
46.7%	4.7%	48.7%	5
49%	2.3%	48.7%	6
49%	1.2%	49.8%	7
49.6%	0.6%	49.8%	8
49.9%	0.3%	49.8%	9
49.9%	0.1%	50%	10
49.9%	0.1%	50.1%	11
49.9%	0%	50.1%	12
49.9%	0%	50.1%	13
49.9%	0%	50.1%	14

sample36.0ms

Algorithm

intervals

Results

16.0ms	106×	body	1280	valid
7.0ms	73×	body	640	valid
3.0ms	45×	body	320	valid
3.0ms	256×	pre	80	true
1.0ms	25×	body	160	valid
0.0ms	7×	body	80	valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	68	4
1	68	4

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: 58.7b

Counts

2 → 1

localize3.0ms

Local error

Found 1 expressions with local error:

7.1b	(- (exp x) 1.0)

rewrite4.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `*-un-lft-identity` `add-log-exp`
1×	`pow1` `add-exp-log` `add-cube-cbrt` `sub-neg` `flip3--` `diff-log` `add-cbrt-cube` `flip--` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 13

Calls

1 calls:

4.0ms

(- (exp x) 1.0)

series3.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(- (exp x) 1.0)

simplify64.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4883	115
1	4883	115

prune38.0ms

Filtered

12 candidates to 16 candidates (-33.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	13	3	16
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	14	3	17

Merged error: 0.1b

Counts

17 → 3

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* x (* x (+ 1/2 (* x 1/6)))))
0.0b	(* x (* x (+ 1/2 (* x 1/6))))
0.0b	(* x (+ 1/2 (* x 1/6)))
0.3b	(* x 1/6)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 79

Calls

4 calls:

4.0ms	(+ x (* x (* x (+ 1/2 (* x 1/6)))))
6.0ms	(* x (* x (+ 1/2 (* x 1/6))))
5.0ms	(* x (+ 1/2 (* x 1/6)))
3.0ms	(* x 1/6)

series18.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ x (* x (* x (+ 1/2 (* x 1/6)))))
6.0ms	(* x (* x (+ 1/2 (* x 1/6))))
6.0ms	(* x (+ 1/2 (* x 1/6)))
2.0ms	(* x 1/6)

simplify47.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5003	799

prune96.0ms

Filtered

62 candidates to 91 candidates (-46.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	90	4	94

Merged error: 0.1b

Counts

94 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* x (log (pow (exp x) (+ (* x 1/6) 1/2))))
0.0b	(pow (exp x) (+ (* x 1/6) 1/2))
0.3b	(* x 1/6)
7.1b	(log (pow (exp x) (+ (* x 1/6) 1/2)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

24×	`log-prod`
21×	`add-sqr-sqrt`
17×	`add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
9×	`pow1` `add-exp-log`
8×	`distribute-rgt-in` `distribute-lft-in` `add-cbrt-cube`
7×	`associate-r`
6×	`associate-l`
4×	`unpow-prod-up` `pow-pow` `add-log-exp` `sqr-pow`
3×	`pow-unpow` `exp-prod` `rem-log-exp`
2×	`pow-to-exp` `pow-prod-down` `pow-exp` `prod-exp` `log-pow` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 93

Calls

4 calls:

6.0ms	(* x (log (pow (exp x) (+ (* x 1/6) 1/2))))
5.0ms	(pow (exp x) (+ (* x 1/6) 1/2))
3.0ms	(* x 1/6)
3.0ms	(log (pow (exp x) (+ (* x 1/6) 1/2)))

series47.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(* x (log (pow (exp x) (+ (* x 1/6) 1/2))))
5.0ms	(pow (exp x) (+ (* x 1/6) 1/2))
2.0ms	(* x 1/6)
19.0ms	(log (pow (exp x) (+ (* x 1/6) 1/2)))

simplify68.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4973	1060
1	4973	1060

prune114.0ms

Filtered

63 candidates to 105 candidates (-66.7%)

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: 0.1b

Counts

109 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (pow (exp x) 2) (* 1.0 (+ (exp x) 1.0))))
0.0b	(pow (exp x) 2)
0.0b	(pow (exp x) 3)
7.0b	(- (pow (exp x) 3) (pow 1.0 3))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

161×	`add-sqr-sqrt`
91×	`*-un-lft-identity`
80×	`difference-of-squares`
75×	`times-frac`
66×	`unpow-prod-down`
63×	`cube-prod`
42×	`sqr-pow`
41×	`add-cube-cbrt`
25×	`associate-/l*` `distribute-lft-out--`
8×	`pow-pow`
7×	`add-cbrt-cube`
6×	`pow1` `add-exp-log` `pow-unpow` `exp-prod` `add-log-exp`
5×	`difference-cubes`
3×	`associate-/r*`
2×	`pow-to-exp` `flip3--` `pow-exp` `associate-/r/` `flip--` `associate-/l/`
1×	`cbrt-undiv` `cube-mult` `sub-neg` `frac-2neg` `flip3-+` `diff-log` `unpow3` `div-sub` `div-exp` `clear-num` `flip-+` `div-inv` `unpow2` `rem-cube-cbrt`

Counts

4 → 200

Calls

4 calls:

21.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (pow (exp x) 2) (* 1.0 (+ (exp x) 1.0))))
3.0ms	(pow (exp x) 2)
3.0ms	(pow (exp x) 3)
11.0ms	(- (pow (exp x) 3) (pow 1.0 3))

series35.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(/ (- (pow (exp x) 3) (pow 1.0 3)) (+ (pow (exp x) 2) (* 1.0 (+ (exp x) 1.0))))
3.0ms	(pow (exp x) 2)
4.0ms	(pow (exp x) 3)
6.0ms	(- (pow (exp x) 3) (pow 1.0 3))

simplify64.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5165	4891

prune313.0ms

Filtered

111 candidates to 212 candidates (-91.0%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	210	2	212
Fresh	1	0	1
Picked	1	0	1
Done	0	2	2
Total	212	4	216

Merged error: 0.0b

Counts

216 → 4

regimes65.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	11
1	13	11

end0.0ms

sample1.1s

Algorithm

intervals

Results

533.0ms	3397×	body	1280	valid
234.0ms	2432×	body	640	valid
87.0ms	8000×	pre	80	true
87.0ms	1345×	body	320	valid
26.0ms	643×	body	160	valid
4.0ms	183×	body	80	valid

Details

analyze3.0ms

sample36.0ms

simplify4.0ms

prune2.0ms

localize3.0ms

rewrite4.0ms

series3.0ms

simplify64.0ms

prune38.0ms

localize6.0ms

rewrite20.0ms

series18.0ms

simplify47.0ms

prune96.0ms

localize11.0ms

rewrite20.0ms

series47.0ms

simplify68.0ms

prune114.0ms

localize12.0ms

rewrite48.0ms

series35.0ms

simplify64.0ms

prune313.0ms

regimes65.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample1.1s

Profiling