Details

analyze2.0ms

Algorithm

Search

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

sample40.0ms

Algorithm

intervals

Results

14.0ms	58×	body	1280	valid
11.0ms	40×	body	640	valid
4.0ms	134×	body	80	valid
2.0ms	14×	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: 28.4b

Counts

2 → 1

localize7.0ms

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))))
2.3b	(- (/ 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)))
5.0ms	(/ 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

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp -2.0) x)
0.0b	(pow (exp -2.0) x)
0.0b	(pow (exp -2.0) x)
2.3b	(- (* 2.0 (/ 2.0 (* (+ 1.0 (pow (exp -2.0) x)) (+ 1.0 (pow (exp -2.0) x))))) (* 1.0 1.0))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`pow-pow`
9×	`unpow-prod-down` `pow-unpow` `exp-prod`
7×	`pow1`
6×	`add-log-exp`
4×	`add-exp-log` `add-cbrt-cube`
3×	`pow-to-exp` `pow-exp` `sqr-pow`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 71

Calls

4 calls:

3.0ms	(pow (exp -2.0) x)
3.0ms	(pow (exp -2.0) x)
3.0ms	(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))

series25.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (exp -2.0) x)
3.0ms	(pow (exp -2.0) x)
3.0ms	(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))

simplify27.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5254	662

prune208.0ms

Filtered

60 candidates to 83 candidates (-38.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	82	3	85

Merged error: 0b

Counts

85 → 3

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (* 1.0 x) (* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337)))
0.1b	(* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 48

Calls

2 calls:

4.0ms	(- (* 1.0 x) (* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337)))
8.0ms	(* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337))

series13.0ms

Counts

2 → 6

Calls

2 calls:

5.0ms	(- (* 1.0 x) (* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337)))
8.0ms	(* (pow x 3) (+ (* x 5.551115123125783e-17) 0.33333333333333337))

simplify51.0ms

Algorithm

egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5070	688

prune72.0ms

Filtered

37 candidates to 54 candidates (-45.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	54	0	54
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	54	3	57

Merged error: 0b

Counts

57 → 3

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (exp -2.0) x)
0.3b	(* (sqrt (- (* 2.0 (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2))) (* 1.0 1.0))) (sqrt (- (* 2.0 (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2))) (* 1.0 1.0))))
2.3b	(- (* 2.0 (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2))) (* 1.0 1.0))
2.3b	(- (* 2.0 (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2))) (* 1.0 1.0))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
20×	`pow1`
18×	`sqrt-prod`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`sqrt-div`
8×	`flip3--` `sqrt-pow1` `pow1/2` `swap-sqr` `flip--` `add-log-exp`
6×	`add-exp-log` `associate-r` `associate-l` `add-cbrt-cube`
5×	`pow-prod-up`
4×	`frac-times` `pow-pow` `unswap-sqr`
3×	`unpow-prod-down` `pow-unpow` `exp-prod` `pow-prod-down` `pow-sqr`
2×	`sub-neg` `diff-log` `associate-r/` `associate-l/`
1×	`pow2` `pow-to-exp` `pow-plus` `sqrt-unprod` `pow-exp` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `sqr-pow`

Counts

4 → 99

Calls

4 calls:

3.0ms	(pow (exp -2.0) x)
27.0ms	(* (sqrt (- (* 2.0 (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2))) (* 1.0 1.0))) (sqrt (- (* 2.0 (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2))) (* 1.0 1.0))))
11.0ms	(- (* 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))

series48.0ms

Counts

4 → 12

Calls

4 calls:

3.0ms	(pow (exp -2.0) x)
14.0ms	(* (sqrt (- (* 2.0 (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2))) (* 1.0 1.0))) (sqrt (- (* 2.0 (/ 2.0 (pow (+ 1.0 (pow (exp -2.0) x)) 2))) (* 1.0 1.0))))
17.0ms	(- (* 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))

simplify40.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	4952	1985
1	4952	1985

prune327.0ms

Filtered

68 candidates to 111 candidates (-63.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	111	3	114

Merged error: 0b

Counts

114 → 3

regimes146.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 29.8b

bsearch33.0ms

Steps

Iters	Range		Point
9	2.2684534848708779e-10	0.09933005889074589	0.0007660910756910471
10	-33350045966.624374	-3.6874776486001954e-05	-0.0009253208756512028

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	114	54
1	114	54

end0.0ms

sample979.0ms

Algorithm

intervals

Results

413.0ms	1718×	body	1280	valid
200.0ms	1264×	body	640	valid
128.0ms	4020×	body	80	valid
79.0ms	672×	body	320	valid
25.0ms	326×	body	160	valid

Details

analyze2.0ms

sample40.0ms

simplify73.0ms

prune6.0ms

localize7.0ms

rewrite20.0ms

series16.0ms

simplify52.0ms

prune138.0ms

localize16.0ms

rewrite28.0ms

series25.0ms

simplify27.0ms

prune208.0ms

localize9.0ms

rewrite13.0ms

series13.0ms

simplify51.0ms

prune72.0ms

localize22.0ms

rewrite56.0ms

series48.0ms

simplify40.0ms

prune327.0ms

regimes146.0ms

bsearch33.0ms

simplify2.0ms

end0.0ms

sample979.0ms

Profiling