Details

Time bar (total: 3.7s)

sample36.0ms

Algorithm
intervals
Results
15.0ms62×body1280valid
6.0ms35×body640valid
4.0ms131×body80valid
2.0ms18×body320valid
1.0ms10×body160valid

simplify61.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0155
1225
2315
3545
41195
53335
616465
750015

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.2b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
2.8b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
95×*-un-lft-identity
66×add-sqr-sqrt
61×add-cube-cbrt times-frac
54×prod-diff
18×fma-neg
16×distribute-lft-out
10×associate-/r/
5×flip3-+ flip-+ div-inv
4×add-exp-log associate-/r* add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u difference-of-squares
1×cbrt-undiv sub-neg flip3-- frac-2neg diff-log div-exp clear-num flip-- distribute-lft-out--
Counts
2 → 124
Calls
2 calls:
5.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
13.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series116.0ms

Counts
2 → 6
Calls
2 calls:
38.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
79.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify48.0ms

Algorithm
egg-herbie
Counts
130 → 130
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
03761556
111701155
250011121

prune176.0ms

Filtered
130 candidates to 69 candidates (53.1%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1273130
Fresh000
Picked101
Done000
Total1283131

Merged error: 0.0b

Counts
131 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b
(pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)
0.0b
(cbrt (pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
2.8b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
111×*-un-lft-identity
94×add-sqr-sqrt
69×add-cube-cbrt
65×times-frac
54×prod-diff
18×cbrt-prod fma-neg
16×distribute-lft-out
12×unpow-prod-down cube-prod
10×associate-/r/ difference-of-squares
7×add-exp-log add-cbrt-cube
6×add-log-exp
5×pow1 flip3-+ flip-+ div-inv distribute-lft-out--
4×cube-div expm1-log1p-u associate-/r* log1p-expm1-u
3×pow-unpow flip3-- flip-- associate-/l*
2×cube-mult cbrt-div unpow3 sqr-pow
1×cbrt-undiv pow-to-exp sub-neg pow-pow frac-2neg pow1/3 diff-log div-exp pow-exp clear-num rem-cbrt-cube rem-cube-cbrt
Counts
4 → 188
Calls
4 calls:
5.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
15.0ms
(pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)
11.0ms
(cbrt (pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
13.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series325.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
124.0ms
(pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)
79.0ms
(cbrt (pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
80.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify77.0ms

Algorithm
egg-herbie
Counts
200 → 200
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
05442246
120411819
250011794

prune310.0ms

Filtered
200 candidates to 109 candidates (54.5%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New2000200
Fresh022
Picked011
Done000
Total2003203

Merged error: 0.0b

Counts
203 → 3

localize10.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.33333333333333337 (pow x 3))
9.6b
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*r*
7×add-exp-log
6×add-cube-cbrt *-un-lft-identity
4×unpow-prod-down cube-prod add-cbrt-cube unswap-sqr
3×associate-*l* prod-exp
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
1×cube-mult pow-to-exp unpow3 pow-exp *-commutative cbrt-unprod fma-udef
Counts
2 → 43
Calls
2 calls:
6.0ms
(* 0.33333333333333337 (pow x 3))
1.0ms
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series135.0ms

Counts
2 → 6
Calls
2 calls:
39.0ms
(* 0.33333333333333337 (pow x 3))
95.0ms
(fma 5.551115123125783e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify211.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0142198
1582175
23723174
35001174

prune99.0ms

Filtered
49 candidates to 33 candidates (67.3%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New49049
Fresh011
Picked011
Done011
Total49352

Merged error: 0.0b

Counts
52 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (exp (* -2.0 x)) (exp (* -2.0 x)))
0.0b
(pow (exp (* -2.0 x)) 3)
3.0b
(fma (/ 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))
3.2b
(- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
19×add-log-exp
13×add-sqr-sqrt exp-prod exp-to-pow
12×pow1
11×add-cube-cbrt *-un-lft-identity
7×add-cbrt-cube
5×pow-prod-down pow-sqr pow-prod-up
4×add-exp-log expm1-log1p-u log1p-expm1-u
3×unpow-prod-down pow-unpow pow-pow cube-prod swap-sqr associate-*r* associate-*l*
1×pow2 cube-mult pow-to-exp sub-neg flip3-- distribute-rgt-out-- pow-plus fma-neg diff-log unpow3 prod-diff pow-exp prod-exp *-commutative flip-- cbrt-unprod fma-udef rem-cube-cbrt unswap-sqr sqr-pow
Counts
4 → 93
Calls
4 calls:
7.0ms
(* (exp (* -2.0 x)) (exp (* -2.0 x)))
3.0ms
(pow (exp (* -2.0 x)) 3)
1.0ms
(fma (/ 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))
9.0ms
(- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))

series383.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(* (exp (* -2.0 x)) (exp (* -2.0 x)))
36.0ms
(pow (exp (* -2.0 x)) 3)
245.0ms
(fma (/ 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))
76.0ms
(- (* (exp (* -2.0 x)) (exp (* -2.0 x))) (* 1.0 (exp (* -2.0 x))))

simplify80.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
0370778
11892666
25001648

prune241.0ms

Filtered
105 candidates to 63 candidates (60.0%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1041105
Fresh000
Picked101
Done022
Total1053108

Merged error: 0.0b

Counts
108 → 3

regimes239.0ms

Accuracy

99.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 29.4b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04636
14636

end0.0ms

sample987.0ms

Algorithm
intervals
Results
402.0ms1676×body1280valid
219.0ms1313×body640valid
129.0ms4085×body80valid
64.0ms597×body320valid
26.0ms329×body160valid

Profiling

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