Details

sample37.0ms

Algorithm

intervals

Results

13.0ms	54×	body	1280	valid
5.0ms	33×	body	640	valid
5.0ms	141×	body	80	valid
2.0ms	18×	body	320	valid
1.0ms	10×	body	160	valid

simplify73.0ms

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: 27.3b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b	(+ 1.0 (exp (* -2.0 x)))
3.5b	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite21.0ms

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 → 60

Calls

3 calls:

5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms	(+ 1.0 (exp (* -2.0 x)))
11.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series16.0ms

Counts

3 → 9

Calls

3 calls:

5.0ms	(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
2.0ms	(+ 1.0 (exp (* -2.0 x)))
8.0ms	(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify53.0ms

Algorithm

egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5224	836

prune152.0ms

Filtered

53 candidates to 69 candidates (-30.2%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	65	4	69
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	4	70

Merged error: 0.0b

Counts

70 → 4

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (pow (exp -2.0) x))
0.0b	(+ 1.0 (pow (exp -2.0) x))
0.0b	(+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))
3.5b	(- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-log-exp`
10×	`*-un-lft-identity`
4×	`pow1` `add-exp-log` `add-sqr-sqrt` `add-cube-cbrt` `add-cbrt-cube`
3×	`+-commutative` `flip3-+` `sum-log` `flip-+` `distribute-lft-out`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 48

Calls

4 calls:

5.0ms	(+ 1.0 (pow (exp -2.0) x))
5.0ms	(+ 1.0 (pow (exp -2.0) x))
12.0ms	(+ 1.0 (/ 2.0 (+ 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))

series32.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ 1.0 (pow (exp -2.0) x))
4.0ms	(+ 1.0 (pow (exp -2.0) x))
9.0ms	(+ 1.0 (/ 2.0 (+ 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))

simplify29.0ms

Algorithm

egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (23.0ms)

Iter	Nodes	Cost
0	5067	746

prune173.0ms

Filtered

45 candidates to 60 candidates (-33.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	59	1	60
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	60	4	64

Merged error: 0.0b

Counts

64 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ 1.0 (pow (exp -2.0) x))
0.0b	(+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))
3.5b	(log (exp (- (* 2.0 (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2))) (* 1.0 1.0))))
3.5b	(- (* 2.0 (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2))) (* 1.0 1.0))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
6×	`add-sqr-sqrt` `add-cube-cbrt`
5×	`pow1` `log-prod`
4×	`add-exp-log` `log-pow` `add-cbrt-cube`
3×	`exp-prod`
2×	`+-commutative` `sub-neg` `flip3-+` `exp-sum` `sum-log` `flip-+` `distribute-lft-out`
1×	`log-div` `flip3--` `exp-diff` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 54

Calls

4 calls:

5.0ms	(+ 1.0 (pow (exp -2.0) x))
10.0ms	(+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))
14.0ms	(log (exp (- (* 2.0 (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2))) (* 1.0 1.0))))
12.0ms	(- (* 2.0 (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2))) (* 1.0 1.0))

series41.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ 1.0 (pow (exp -2.0) x))
9.0ms	(+ 1.0 (/ 2.0 (+ 1.0 (pow (exp -2.0) x))))
14.0ms	(log (exp (- (* 2.0 (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2))) (* 1.0 1.0))))
14.0ms	(- (* 2.0 (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2))) (* 1.0 1.0))

simplify32.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5293	1000

prune193.0ms

Filtered

50 candidates to 66 candidates (-32.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	66	4	70

Merged error: 0.0b

Counts

70 → 4

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0))
3.5b	(- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)
3.5b	(- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)
3.5b	(- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
13×	`*-un-lft-identity`
10×	`add-log-exp`
8×	`difference-of-squares`
6×	`cbrt-prod`
5×	`add-cube-cbrt`
4×	`pow1` `add-exp-log` `flip3--` `times-frac` `add-cbrt-cube` `flip--` `distribute-lft-out--`
3×	`sub-neg` `diff-log`
2×	`cbrt-div`
1×	`pow1/3`

Counts

4 → 61

Calls

4 calls:

11.0ms	(cbrt (- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0))
12.0ms	(- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)
12.0ms	(- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)
12.0ms	(- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)

series65.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(cbrt (- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0))
11.0ms	(- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)
13.0ms	(- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)
11.0ms	(- (/ 2.0 (+ 1.0 (pow (exp -2.0) x))) 1.0)

simplify35.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4992	1101
1	4992	1101

prune252.0ms

Filtered

54 candidates to 73 candidates (-35.2%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	73	4	77

Merged error: 0.0b

Counts

77 → 4

regimes141.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.3b

bsearch32.0ms

Steps

Iters	Range		Point
8	1.2889027181245805e-06	0.005898508865977251	0.0007063694993854554
8	-0.005708457349238343	-9.709340229875236e-07	-0.001125542754715476

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	121	64
1	121	64

end0.0ms

sample1.1s

Algorithm

intervals

Results

429.0ms	1777×	body	1280	valid
202.0ms	1222×	body	640	valid
131.0ms	4098×	body	80	valid
64.0ms	586×	body	320	valid
23.0ms	317×	body	160	valid

Details

sample37.0ms

simplify73.0ms

prune6.0ms

localize6.0ms

rewrite21.0ms

series16.0ms

simplify53.0ms

prune152.0ms

localize16.0ms

rewrite38.0ms

series32.0ms

simplify29.0ms

prune173.0ms

localize19.0ms

rewrite42.0ms

series41.0ms

simplify32.0ms

prune193.0ms

localize15.0ms

rewrite48.0ms

series65.0ms

simplify35.0ms

prune252.0ms

regimes141.0ms

bsearch32.0ms

simplify2.0ms

end0.0ms

sample1.1s

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