Details

Time bar (total: 7.1s)

sample33.0ms

Algorithm
intervals
Results
9.0ms45×body1280valid
9.0ms41×body640valid
4.0ms144×body80valid
2.0ms19×body320valid
0.0ms7×body160valid

simplify63.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0155
1225
2305
3525
41145
53225
616275
750025

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 26.4b

localize7.0ms

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)))
3.2b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite40.0ms

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)))
30.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series131.0ms

Counts
3 → 9
Calls
3 calls:
37.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
15.0ms
(+ 1.0 (exp (* -2.0 x)))
78.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify90.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0251494
1731465
22785460
35002460

prune156.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (exp (* -2.0 x)))
0.0b
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.4b
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
3.2b
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite204.0ms

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:
3.0ms
(+ 1.0 (exp (* -2.0 x)))
21.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
6.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
156.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series198.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(+ 1.0 (exp (* -2.0 x)))
38.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
66.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
78.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify90.0ms

Algorithm
egg-herbie
Counts
329 → 329
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
07875699
127915067
250024914

prune482.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ (/ 2.0 (sqrt (cbrt (+ 1.0 (exp (* -2.0 x)))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
0.4b
(cbrt (+ 1.0 (exp (* -2.0 x))))
0.4b
(cbrt (+ 1.0 (exp (* -2.0 x))))
27.0b
(- (* (/ 1 (* (fabs (cbrt (+ 1.0 (exp (* -2.0 x))))) (* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x)))))))) (/ (/ 2.0 (sqrt (cbrt (+ 1.0 (exp (* -2.0 x)))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))) 1.0)

rewrite260.0ms

Algorithm
rewrite-expression-head
Rules
690×times-frac
481×*-un-lft-identity
399×cbrt-prod
379×sqrt-prod
337×add-sqr-sqrt add-cube-cbrt
72×distribute-lft-out
36×associate-/l*
28×cbrt-div
24×sqrt-div associate-/r/
14×flip3-+ flip-+
12×div-inv
10×associate-/r*
9×add-exp-log
7×add-cbrt-cube
6×add-log-exp
4×pow1
3×cbrt-undiv div-exp
2×pow1/3
1×sub-neg flip3-- frac-2neg diff-log clear-num flip-- associate-/l/
Counts
4 → 463
Calls
4 calls:
29.0ms
(/ (/ 2.0 (sqrt (cbrt (+ 1.0 (exp (* -2.0 x)))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
2.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
2.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
191.0ms
(- (* (/ 1 (* (fabs (cbrt (+ 1.0 (exp (* -2.0 x))))) (* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x)))))))) (/ (/ 2.0 (sqrt (cbrt (+ 1.0 (exp (* -2.0 x)))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))) 1.0)

series638.0ms

Counts
4 → 12
Calls
4 calls:
148.0ms
(/ (/ 2.0 (sqrt (cbrt (+ 1.0 (exp (* -2.0 x)))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
131.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
134.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
224.0ms
(- (* (/ 1 (* (fabs (cbrt (+ 1.0 (exp (* -2.0 x))))) (* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x)))))))) (/ (/ 2.0 (sqrt (cbrt (+ 1.0 (exp (* -2.0 x)))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))) 1.0)

simplify118.0ms

Algorithm
egg-herbie
Counts
475 → 475
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
0131711967
1500111440

prune1.5s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (+ 1.0 (exp (* -2.0 x))))
0.4b
(cbrt (+ 1.0 (exp (* -2.0 x))))
26.9b
(log (exp (- (* (/ 1 (* (fabs (cbrt (+ 1.0 (exp (* -2.0 x))))) (* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x)))))))) (/ (/ 2.0 (sqrt (cbrt (+ 1.0 (exp (* -2.0 x)))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))) 1.0)))
27.0b
(- (* (/ 1 (* (fabs (cbrt (+ 1.0 (exp (* -2.0 x))))) (* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x)))))))) (/ (/ 2.0 (sqrt (cbrt (+ 1.0 (exp (* -2.0 x)))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))) 1.0)

rewrite949.0ms

Algorithm
rewrite-expression-head
Rules
12×*-un-lft-identity
8×cbrt-prod add-sqr-sqrt add-cube-cbrt
6×add-log-exp
5×pow1 log-prod
4×add-exp-log cbrt-div log-pow add-cbrt-cube
3×exp-prod
2×sub-neg flip3-+ pow1/3 exp-sum flip-+ distribute-lft-out
1×log-div flip3-- exp-diff diff-log rem-log-exp flip--
Counts
4 → 58
Calls
4 calls:
2.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
2.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
751.0ms
(log (exp (- (* (/ 1 (* (fabs (cbrt (+ 1.0 (exp (* -2.0 x))))) (* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x)))))))) (/ (/ 2.0 (sqrt (cbrt (+ 1.0 (exp (* -2.0 x)))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))) 1.0)))
192.0ms
(- (* (/ 1 (* (fabs (cbrt (+ 1.0 (exp (* -2.0 x))))) (* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x)))))))) (/ (/ 2.0 (sqrt (cbrt (+ 1.0 (exp (* -2.0 x)))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))) 1.0)

series705.0ms

Counts
4 → 12
Calls
4 calls:
129.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
136.0ms
(cbrt (+ 1.0 (exp (* -2.0 x))))
217.0ms
(log (exp (- (* (/ 1 (* (fabs (cbrt (+ 1.0 (exp (* -2.0 x))))) (* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x)))))))) (/ (/ 2.0 (sqrt (cbrt (+ 1.0 (exp (* -2.0 x)))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))) 1.0)))
223.0ms
(- (* (/ 1 (* (fabs (cbrt (+ 1.0 (exp (* -2.0 x))))) (* (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x)))))))) (/ (/ 2.0 (sqrt (cbrt (+ 1.0 (exp (* -2.0 x)))))) (cbrt (sqrt (+ 1.0 (exp (* -2.0 x))))))) 1.0)

simplify43.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
03121786
110651588
250021535

prune331.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes141.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 28.9b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05243
15243

end0.0ms

sample818.0ms

Algorithm
intervals
Results
331.0ms1600×body1280valid
166.0ms1259×body640valid
108.0ms4210×body80valid
54.0ms620×body320valid
17.0ms311×body160valid