Details

analyze2.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
99.9%	0%	0.1%	1

sample68.0ms

Algorithm

intervals

Results

14.0ms	61×	body	1280	valid
8.0ms	135×	body	80	valid
6.0ms	38×	body	640	valid
2.0ms	16×	body	320	valid
0.0ms	6×	body	160	valid

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	5238	10

prune6.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 28.4b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
28.4b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 59

Calls

3 calls:

3.0ms	(+ 1.0 (exp (* -2.0 x)))
5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
10.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series16.0ms

Counts

3 → 9

Calls

3 calls:

2.0ms	(+ 1.0 (exp (* -2.0 x)))
6.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
8.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify52.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5224	834

prune138.0ms

Filtered

53 candidates to 68 candidates (-28.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	66	2	68
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	2	69

Merged error: 0.0b

Counts

69 → 2

localize60.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (pow (exp -2.0) x)))
0.0b	(+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))
0.0b	(/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))
28.4b	(- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

25×	`*-un-lft-identity`
15×	`add-sqr-sqrt` `add-cube-cbrt` `times-frac`
11×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r/`
8×	`flip3-+` `flip-+` `add-log-exp`
6×	`associate-/l*`
5×	`associate-/r*` `distribute-lft-out`
4×	`pow1` `frac-times`
3×	`cbrt-undiv` `div-exp`
2×	`frac-2neg` `associate-r/` `associate-l/` `clear-num` `div-inv`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `prod-exp` `sum-log` `flip--` `cbrt-unprod`

Counts

4 → 85

Calls

4 calls:

6.0ms	(/ 2.0 (+ 1.0 (pow (exp -2.0) x)))
10.0ms	(+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))
14.0ms	(/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))
14.0ms	(- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0))

series43.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(/ 2.0 (+ 1.0 (pow (exp -2.0) x)))
9.0ms	(+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))
11.0ms	(/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))
15.0ms	(- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0))

simplify44.0ms

Algorithm

egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4984	1372
1	4984	1372

prune279.0ms

Filtered

72 candidates to 97 candidates (-34.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	96	3	99

Merged error: 0.0b

Counts

99 → 3

localize62.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))
0.0b	(/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))
0.8b	(* (sqrt (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))) (sqrt (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))))
28.4b	(- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

30×	`*-un-lft-identity`
26×	`add-sqr-sqrt` `sqrt-prod`
19×	`pow1`
14×	`add-cube-cbrt`
13×	`flip3-+` `flip-+`
12×	`sqrt-div`
11×	`add-exp-log` `swap-sqr` `add-cbrt-cube`
8×	`frac-times` `sqrt-pow1` `pow1/2` `associate-/r/` `add-log-exp`
7×	`associate-r` `associate-l` `distribute-lft-out`
5×	`pow-prod-up`
4×	`associate-r/` `associate-l/` `unswap-sqr`
3×	`times-frac` `pow-prod-down` `pow-sqr` `associate-/l*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `pow2` `sub-neg` `flip3--` `frac-2neg` `pow-plus` `sqrt-unprod` `diff-log` `clear-num` `associate-/r` `sum-log` `rem-square-sqrt` `-commutative` `flip--` `div-inv`

Counts

4 → 114

Calls

4 calls:

10.0ms	(+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))
12.0ms	(/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))
24.0ms	(* (sqrt (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))) (sqrt (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))))
16.0ms	(- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0))

series47.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))
11.0ms	(/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))
13.0ms	(* (sqrt (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))) (sqrt (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))))
14.0ms	(- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0))

simplify45.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5179	1922

prune396.0ms

Filtered

73 candidates to 126 candidates (-72.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	126	3	129

Merged error: 0.0b

Counts

129 → 3

localize69.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (sqrt (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))))
0.0b	(pow (cbrt (sqrt (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))) 4)
0.3b	(* (cbrt (sqrt (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))) (cbrt (sqrt (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))))
28.4b	(- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

62×	`cbrt-prod`
44×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
36×	`sqrt-prod`
22×	`add-cube-cbrt`
14×	`cbrt-div` `sqrt-div` `swap-sqr`
12×	`pow1`
10×	`unpow-prod-down` `associate-r` `associate-l`
9×	`unswap-sqr`
8×	`pow1/3` `distribute-lft-out`
7×	`add-exp-log` `flip3-+` `flip-+`
6×	`add-log-exp`
4×	`frac-times` `add-cbrt-cube`
3×	`pow-unpow`
2×	`pow-pow` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-to-exp` `sub-neg` `flip3--` `pow-plus` `diff-log` `pow-exp` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `sqr-pow`

Counts

4 → 122

Calls

4 calls:

10.0ms	(cbrt (sqrt (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))))
13.0ms	(pow (cbrt (sqrt (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))) 4)
26.0ms	(* (cbrt (sqrt (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))) (cbrt (sqrt (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))))
16.0ms	(- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0))

series110.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(cbrt (sqrt (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))))
35.0ms	(pow (cbrt (sqrt (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))) 4)
28.0ms	(* (cbrt (sqrt (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))) (cbrt (sqrt (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))))
17.0ms	(- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0))

simplify49.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5066	2736

prune638.0ms

Filtered

83 candidates to 134 candidates (-61.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	134	3	137

Merged error: 0.0b

Counts

137 → 3

regimes137.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.6b

bsearch53.0ms

Steps

Iters	Range		Point
11	1.1839468066592235e-18	248211207.36567843	0.0007377208164153443
6	-0.0036147537029945502	-0.00024248563252909715	-0.000745180152594863

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	166	134
1	166	134

end0.0ms

sample1.7s

Algorithm

intervals

Results

409.0ms	1734×	body	1280	valid
205.0ms	1287×	body	640	valid
118.0ms	4058×	body	80	valid
64.0ms	613×	body	320	valid
21.0ms	308×	body	160	valid

Details

analyze2.0ms

sample68.0ms

simplify72.0ms

prune6.0ms

localize11.0ms

rewrite20.0ms

series16.0ms

simplify52.0ms

prune138.0ms

localize60.0ms

rewrite47.0ms

series43.0ms

simplify44.0ms

prune279.0ms

localize62.0ms

rewrite66.0ms

series47.0ms

simplify45.0ms

prune396.0ms

localize69.0ms

rewrite70.0ms

series110.0ms

simplify49.0ms

prune638.0ms

regimes137.0ms

bsearch53.0ms

simplify3.0ms

end0.0ms

sample1.7s

Profiling