Details

Time bar (total: 18.4s)

sample67.0ms

Algorithm
intervals
Results
21.0ms45×body1280valid
12.0ms46×body640valid
8.0ms134×body80valid
5.0ms21×body320valid
1.0ms10×body160valid

simplify3.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0910
11510
22210
33110
45510
512210
645410
7350310
done500110

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.0b

localize21.0ms

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)

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
99×*-un-lft-identity
68×add-sqr-sqrt
63×add-cube-cbrt
61×times-frac
54×prod-diff
18×fma-neg
17×distribute-lft-out
10×associate-/r/
7×add-log-exp
6×flip3-+ flip-+
5×add-cbrt-cube add-exp-log div-inv
4×associate-/r*
3×expm1-log1p-u pow1 fma-def log1p-expm1-u associate-/l*
2×difference-of-squares
1×cbrt-undiv +-commutative clear-num sum-log sub-neg frac-2neg flip3-- diff-log div-exp flip-- distribute-lft-out--
Counts
3 → 141
Calls
3 calls:
23.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
8.0ms
(+ 1.0 (exp (* -2.0 x)))
79.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series202.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
29.0ms
(+ 1.0 (exp (* -2.0 x)))
127.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify815.0ms

Counts
150 → 150
Iterations

Useful iterations: done (806.0ms)

IterNodesCost
01803092
14202518
212942225
done50012060

prune533.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b
(+ 1.0 (exp (* -2.0 x)))
3.0b
(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
3.1b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite319.0ms

Algorithm
rewrite-expression-head
Rules
164×*-un-lft-identity
118×add-sqr-sqrt
108×prod-diff add-cube-cbrt
98×times-frac
59×log-prod
56×exp-sum
26×distribute-lft-out
18×fma-neg
16×associate-/r/
9×flip3-+ flip-+
8×div-inv add-log-exp
7×log-pow
6×exp-prod add-cbrt-cube add-exp-log
5×pow1
4×expm1-log1p-u associate-/r* log1p-expm1-u difference-of-squares
3×fma-def associate-/l*
2×sub-neg distribute-lft-out--
1×cbrt-undiv +-commutative log-div clear-num sum-log frac-2neg flip3-- exp-diff diff-log div-exp rem-log-exp flip--
Counts
4 → 218
Calls
4 calls:
17.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
5.0ms
(+ 1.0 (exp (* -2.0 x)))
175.0ms
(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
106.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series284.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
24.0ms
(+ 1.0 (exp (* -2.0 x)))
116.0ms
(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
101.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify1.1s

Counts
230 → 230
Iterations

Useful iterations: done (1.0s)

IterNodesCost
03075763
15694394
215953829
done50013517

prune788.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 2 expressions with local error:

0.4b
(* 5.551115123125783e-17 (pow x 4))
8.0b
(fma 0.33333333333333337 (pow x 3) (* 5.551115123125783e-17 (pow x 4)))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
7×associate-*r* add-exp-log
5×*-un-lft-identity add-cube-cbrt
4×unpow-prod-down add-cbrt-cube
3×associate-*l* prod-exp unswap-sqr
2×expm1-log1p-u pow1 log1p-expm1-u add-log-exp sqr-pow
1×pow-to-exp pow-exp *-commutative cbrt-unprod fma-udef
Counts
2 → 37
Calls
2 calls:
17.0ms
(* 5.551115123125783e-17 (pow x 4))
1.0ms
(fma 0.33333333333333337 (pow x 3) (* 5.551115123125783e-17 (pow x 4)))

series242.0ms

Counts
2 → 6
Calls
2 calls:
73.0ms
(* 5.551115123125783e-17 (pow x 4))
168.0ms
(fma 0.33333333333333337 (pow x 3) (* 5.551115123125783e-17 (pow x 4)))

simplify2.5s

Counts
43 → 43
Iterations

Useful iterations: 3 (730.0ms)

IterNodesCost
067403
1135377
2432347
32510342
done5001342

prune239.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (exp (* -2.0 x)) 3)
3.0b
(log (exp (- (* (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (+ (* 1.0 1.0) (- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x)))))) 1.0)))
3.1b
(- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))
3.1b
(- (* (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (+ (* 1.0 1.0) (- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x)))))) 1.0)

rewrite357.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
10×log-prod
9×add-log-exp
7×exp-sum prod-diff
6×pow1
5×add-cbrt-cube
4×expm1-log1p-u exp-prod associate--l+ add-exp-log log-pow log1p-expm1-u
3×pow-unpow sub-neg unpow-prod-down pow-pow cube-prod
2×distribute-rgt-in distribute-lft-in flip3-- fma-neg diff-log flip--
1×cube-mult pow-to-exp log-div exp-to-pow distribute-rgt-out-- exp-diff unpow3 rem-log-exp pow-exp rem-cube-cbrt sqr-pow
Counts
4 → 89
Calls
4 calls:
5.0ms
(pow (exp (* -2.0 x)) 3)
235.0ms
(log (exp (- (* (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (+ (* 1.0 1.0) (- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x)))))) 1.0)))
13.0ms
(- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))
102.0ms
(- (* (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (+ (* 1.0 1.0) (- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x)))))) 1.0)

series1.5s

Counts
4 → 12
Calls
4 calls:
69.0ms
(pow (exp (* -2.0 x)) 3)
645.0ms
(log (exp (- (* (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (+ (* 1.0 1.0) (- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x)))))) 1.0)))
88.0ms
(- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))
724.0ms
(- (* (/ 2.0 (+ (pow 1.0 3) (pow (exp (* -2.0 x)) 3))) (+ (* 1.0 1.0) (- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x)))))) 1.0)

simplify2.6s

Counts
101 → 101
Iterations

Useful iterations: done (2.6s)

IterNodesCost
02043094
15622475
228412241
done50002239

prune708.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0.0b

regimes601.0ms

Accuracy

100% (0.0b remaining)

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

bsearch2.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02750
13439
done3439

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.0s1768×body1280valid
352.0ms1235×body640valid
286.0ms4058×body80valid
98.0ms626×body320valid
30.0ms313×body160valid