Details

sample35.0ms

Algorithm

intervals

Results

11.0ms	49×	body	1280	valid
6.0ms	40×	body	640	valid
5.0ms	144×	body	80	valid
2.0ms	14×	body	320	valid
1.0ms	9×	body	160	valid

simplify50.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4800	10
1	4800	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: 26.0b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ 1.0 (exp (* -2.0 x)))
1.9b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

7×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-log-exp`
2×	`pow1` `add-exp-log` `add-cube-cbrt` `add-cbrt-cube` `difference-of-squares`
1×	`+-commutative` `sub-neg` `flip3--` `flip3-+` `times-frac` `diff-log` `sum-log` `flip--` `flip-+` `distribute-lft-out` `distribute-lft-out--`

Counts

2 → 27

Calls

2 calls:

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

series11.0ms

Counts

2 → 6

Calls

2 calls:

2.0ms	(+ 1.0 (exp (* -2.0 x)))
9.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify42.0ms

Algorithm

egg-herbie

Counts

33 → 33

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5331	399

prune80.0ms

Filtered

27 candidates to 33 candidates (-22.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	30	3	33
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	31	3	34

Merged error: 0.0b

Counts

34 → 3

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ 1.0 (pow (exp -2.0) x))
1.8b	(log (exp (- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)))
1.9b	(- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt`
11×	`*-un-lft-identity`
7×	`log-pow` `add-log-exp`
6×	`exp-prod`
5×	`add-cube-cbrt` `log-prod`
4×	`pow1` `difference-of-squares`
3×	`add-exp-log` `add-cbrt-cube`
2×	`sub-neg` `times-frac` `exp-sum` `distribute-lft-out--`
1×	`+-commutative` `log-div` `flip3--` `flip3-+` `exp-diff` `diff-log` `rem-log-exp` `sum-log` `flip--` `flip-+` `distribute-lft-out`

Counts

3 → 48

Calls

3 calls:

4.0ms	(+ 1.0 (pow (exp -2.0) x))
11.0ms	(log (exp (- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)))
11.0ms	(- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)

series28.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ 1.0 (pow (exp -2.0) x))
13.0ms	(log (exp (- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)))
12.0ms	(- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)

simplify56.0ms

Algorithm

egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4955	688
1	4955	688

prune106.0ms

Filtered

40 candidates to 57 candidates (-42.5%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	57	0	57
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	57	3	60

Merged error: 0.0b

Counts

60 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0)) (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))
0.0b	(* (+ 1.0 (pow (exp -2.0) x)) (+ 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))))
1.8b	(- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

41×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
19×	`add-cube-cbrt`
15×	`times-frac`
13×	`add-exp-log` `flip3-+` `add-cbrt-cube` `flip-+`
11×	`pow1`
10×	`associate-/r/` `distribute-lft-out`
8×	`frac-times`
6×	`swap-sqr` `associate-/l*` `add-log-exp`
5×	`associate-/r*`
4×	`associate-r/` `associate-r` `associate-l` `associate-l/`
3×	`cbrt-undiv` `div-exp`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `div-inv` `associate-/l/`
1×	`pow2` `distribute-rgt-in` `sub-neg` `distribute-lft-in` `pow-plus` `diff-log` `div-sub` `pow-prod-down` `pow-sqr` `*-commutative` `pow-prod-up` `unswap-sqr`

Counts

4 → 117

Calls

4 calls:

25.0ms	(/ (- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0)) (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))
11.0ms	(* (+ 1.0 (pow (exp -2.0) x)) (+ 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))))
13.0ms	(- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0))

series66.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(/ (- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0)) (+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))))
6.0ms	(* (+ 1.0 (pow (exp -2.0) x)) (+ 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))))
18.0ms	(- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0))

simplify67.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4980	2714
1	4980	2714

prune361.0ms

Filtered

86 candidates to 129 candidates (-50.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	129	3	132

Merged error: 0.0b

Counts

132 → 3

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b	(* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `associate-l`
6×	`add-exp-log`
5×	`add-cube-cbrt` `*-un-lft-identity`
4×	`unpow-prod-down` `cube-prod` `unswap-sqr`
3×	`associate-r` `prod-exp` `add-cbrt-cube`
2×	`associate-*r/` `sqr-pow`
1×	`pow1` `distribute-rgt-in` `cube-mult` `pow-to-exp` `distribute-lft-in` `flip3-+` `unpow3` `pow-exp` `*-commutative` `cbrt-unprod` `flip-+` `add-log-exp`

Counts

1 → 35

Calls

1 calls:

8.0ms

(* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337))

series8.0ms

Counts

1 → 3

Calls

1 calls:

8.0ms

(* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337))

simplify50.0ms

Algorithm

egg-herbie

Counts

38 → 38

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4995	411
1	4995	411

prune42.0ms

Filtered

24 candidates to 38 candidates (-58.3%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	38	0	38
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	38	3	41

Merged error: 0.0b

Counts

41 → 3

regimes128.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.1b

bsearch29.0ms

Steps

Iters	Range		Point
7	0.00032549292108535743	0.009091900342010817	0.0009274277440223232
8	-0.5589967429191678	-0.00011600335009663597	-0.0009662156427104407

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	65
1	40	65

end0.0ms

sample1.1s

Algorithm

intervals

Results

422.0ms	1721×	body	1280	valid
194.0ms	1194×	body	640	valid
127.0ms	4119×	body	80	valid
69.0ms	623×	body	320	valid
25.0ms	343×	body	160	valid

Details

sample35.0ms

simplify50.0ms

prune6.0ms

localize7.0ms

rewrite14.0ms

series11.0ms

simplify42.0ms

prune80.0ms

localize12.0ms

rewrite28.0ms

series28.0ms

simplify56.0ms

prune106.0ms

localize17.0ms

rewrite65.0ms

series66.0ms

simplify67.0ms

prune361.0ms

localize8.0ms

rewrite9.0ms

series8.0ms

simplify50.0ms

prune42.0ms

regimes128.0ms

bsearch29.0ms

simplify1.0ms

end0.0ms

sample1.1s

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