Details

Time bar (total: 3.4s)

sample38.0ms

Algorithm
intervals
Results
11.0ms49×body1280valid
8.0ms46×body640valid
4.0ms131×body80valid
2.0ms22×body320valid
1.0ms8×body160valid

simplify42.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
0480010
1480010

prune6.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 29.4b

Counts
2 → 1

localize11.0ms

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)))
3.1b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite23.0ms

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:
6.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms
(+ 1.0 (exp (* -2.0 x)))
12.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series18.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
2.0ms
(+ 1.0 (exp (* -2.0 x)))
9.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify43.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
04913836
14913836

prune159.0ms

Filtered
53 candidates to 69 candidates (-30.2%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New66369
Fresh000
Picked101
Done000
Total67370

Merged error: 0.0b

Counts
70 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (pow (exp -2.0) x))
0.0b
(+ (sqrt (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))) (sqrt 1.0))
0.3b
(* (+ (sqrt (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))) (sqrt 1.0)))
3.6b
(- (sqrt (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))) (sqrt 1.0))

rewrite81.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
24×*-un-lft-identity
22×sqrt-prod
12×difference-of-squares
11×associate-*r*
10×add-log-exp
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
5×flip3-+ associate-*l* flip-+ distribute-lft-out
4×frac-times flip3-- times-frac flip-- distribute-lft-out--
3×sub-neg
2×+-commutative distribute-rgt-in distribute-lft-in associate-*r/ associate-*l/ sum-log
1×diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 85
Calls
4 calls:
5.0ms
(+ 1.0 (pow (exp -2.0) x))
19.0ms
(+ (sqrt (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))) (sqrt 1.0))
36.0ms
(* (+ (sqrt (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))) (sqrt 1.0)))
17.0ms
(- (sqrt (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))) (sqrt 1.0))

series75.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(+ 1.0 (pow (exp -2.0) x))
15.0ms
(+ (sqrt (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))) (sqrt 1.0))
39.0ms
(* (+ (sqrt (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))) (sqrt 1.0)))
17.0ms
(- (sqrt (/ 2.0 (+ 1.0 (pow (exp -2.0) x)))) (sqrt 1.0))

simplify48.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
060731923

prune322.0ms

Filtered
68 candidates to 97 candidates (-42.6%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New96197
Fresh022
Picked101
Done000
Total973100

Merged error: 0.0b

Counts
100 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (/ 2.0 (sqrt (+ 1.0 (pow (exp -2.0) x)))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.0b
(+ 1.0 (exp (* -2.0 x)))
0.5b
(/ 2.0 (sqrt (+ 1.0 (pow (exp -2.0) x))))
3.1b
(- (/ (/ 2.0 (sqrt (+ 1.0 (pow (exp -2.0) x)))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
388×times-frac
304×*-un-lft-identity
229×sqrt-prod
212×add-sqr-sqrt
188×add-cube-cbrt
57×distribute-lft-out
30×associate-/l*
20×sqrt-div associate-/r/
14×associate-/r*
11×add-exp-log flip3-+ add-cbrt-cube flip-+
10×div-inv
8×add-log-exp
7×difference-of-squares
4×pow1 cbrt-undiv div-exp
2×frac-2neg clear-num
1×+-commutative sub-neg flip3-- diff-log sum-log flip-- associate-/l/ distribute-lft-out--
Counts
4 → 317
Calls
4 calls:
23.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (pow (exp -2.0) x)))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
4.0ms
(+ 1.0 (exp (* -2.0 x)))
8.0ms
(/ 2.0 (sqrt (+ 1.0 (pow (exp -2.0) x))))
74.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (pow (exp -2.0) x)))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series56.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (pow (exp -2.0) x)))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
2.0ms
(+ 1.0 (exp (* -2.0 x)))
12.0ms
(/ 2.0 (sqrt (+ 1.0 (pow (exp -2.0) x))))
19.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (pow (exp -2.0) x)))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify102.0ms

Algorithm
egg-herbie
Counts
329 → 329
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
049837424
149837424

prune654.0ms

Filtered
144 candidates to 329 candidates (-128.5%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New3281329
Fresh112
Picked101
Done000
Total3302332

Merged error: 0.0b

Counts
332 → 2

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))
0.5b
(pow (sqrt (+ 1.0 (pow (exp -2.0) x))) 4)
30.0b
(- (/ 2.0 (/ (pow (sqrt (+ 1.0 (pow (exp -2.0) x))) 4) 2.0)) (* 1.0 1.0))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
21×add-sqr-sqrt
13×*-un-lft-identity
10×add-log-exp
9×unpow-prod-down times-frac
7×add-cube-cbrt
6×pow1 difference-of-squares
5×add-exp-log sqrt-prod
4×add-cbrt-cube
3×pow-unpow pow-pow distribute-lft-out
2×+-commutative flip3-+ sum-log flip-+ sqr-pow
1×pow-to-exp sub-neg flip3-- sqrt-pow1 pow1/2 diff-log pow-exp sqrt-pow2 flip--
Counts
4 → 66
Calls
4 calls:
6.0ms
(+ 1.0 (pow (exp -2.0) x))
5.0ms
(+ 1.0 (pow (exp -2.0) x))
8.0ms
(pow (sqrt (+ 1.0 (pow (exp -2.0) x))) 4)
41.0ms
(- (/ 2.0 (/ (pow (sqrt (+ 1.0 (pow (exp -2.0) x))) 4) 2.0)) (* 1.0 1.0))

series37.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(+ 1.0 (pow (exp -2.0) x))
4.0ms
(+ 1.0 (pow (exp -2.0) x))
12.0ms
(pow (sqrt (+ 1.0 (pow (exp -2.0) x))) 4)
16.0ms
(- (/ 2.0 (/ (pow (sqrt (+ 1.0 (pow (exp -2.0) x))) 4) 2.0)) (* 1.0 1.0))

simplify29.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
05664932

prune203.0ms

Filtered
53 candidates to 78 candidates (-47.2%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New78078
Fresh011
Picked011
Done000
Total78280

Merged error: 0.0b

Counts
80 → 2

regimes117.0ms

Accuracy

100% (0.0b remaining)

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

bsearch40.0ms

Steps
ItersRangePoint
8
1.1764544588561992e-06
0.009971872296741319
0.0009469128784776477
11
-878796860755045.6
-2.2616434563553712e-05
-0.0008657354540751481

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04150
14150

end0.0ms

sample1.1s

Algorithm
intervals
Results
404.0ms1750×body1280valid
194.0ms1182×body640valid
142.0ms4127×body80valid
70.0ms629×body320valid
23.0ms312×body160valid

Profiling

Loading profile data...