Details

Time bar (total: 4.5s)

sample35.0ms

Algorithm
intervals
Results
15.0ms58×body1280valid
6.0ms45×body640valid
3.0ms123×body80valid
2.0ms23×body320valid
0.0ms7×body160valid

simplify62.0ms

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: 31.4b

localize6.0ms

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)))
2.2b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite43.0ms

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)))
32.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series135.0ms

Counts
3 → 9
Calls
3 calls:
39.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
16.0ms
(+ 1.0 (exp (* -2.0 x)))
80.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify90.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (20.0ms)

IterNodesCost
0251494
1731465
22785460
35002460

prune143.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 0.33333333333333337 (pow x 3))
0.2b
(* 5.551115123125783e-17 (pow x 4))
9.0b
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×associate-*r*
13×add-exp-log
10×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down
7×add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
5×add-log-exp
4×cube-prod sqr-pow
3×pow1
2×pow-to-exp pow-exp *-commutative cbrt-unprod
1×+-commutative cube-mult flip3-+ unpow3 sum-log flip-+
Counts
3 → 67
Calls
3 calls:
7.0ms
(* 0.33333333333333337 (pow x 3))
5.0ms
(* 5.551115123125783e-17 (pow x 4))
3.0ms
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

series183.0ms

Counts
3 → 9
Calls
3 calls:
41.0ms
(* 0.33333333333333337 (pow x 3))
36.0ms
(* 5.551115123125783e-17 (pow x 4))
107.0ms
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

simplify45.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0268323
11157293
25001293

prune161.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
2.2b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
2.2b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
2.2b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
55×add-sqr-sqrt
32×cbrt-prod *-un-lft-identity
14×difference-of-squares
12×add-cube-cbrt cbrt-div
11×pow1 swap-sqr
10×add-log-exp
9×flip3-- associate-*r* associate-*l* flip-- distribute-lft-out--
7×times-frac
6×add-exp-log pow1/3
4×frac-times add-cbrt-cube unswap-sqr
3×sub-neg diff-log
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 104
Calls
4 calls:
136.0ms
(* (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
33.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
35.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
33.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series455.0ms

Counts
4 → 12
Calls
4 calls:
224.0ms
(* (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (cbrt (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
77.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
77.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
77.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify127.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 3 (112.0ms)

IterNodesCost
02621573
18151472
239831340
350021315

prune288.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.7b
(cbrt (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
2.2b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
2.2b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
2.5b
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
43×add-sqr-sqrt
14×difference-of-squares
13×*-un-lft-identity sqrt-prod
10×times-frac add-log-exp
5×add-cube-cbrt
4×pow1 add-exp-log cbrt-prod add-cbrt-cube
3×sub-neg flip3-- diff-log flip-- distribute-lft-out--
2×cbrt-div
1×flip3-+ pow1/3 flip-+ distribute-lft-out
Counts
4 → 67
Calls
4 calls:
34.0ms
(cbrt (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
34.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
33.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
62.0ms
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series731.0ms

Counts
4 → 12
Calls
4 calls:
449.0ms
(cbrt (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
79.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
81.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)
122.0ms
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify128.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 3 (118.0ms)

IterNodesCost
03421053
11069991
24720939
35003937

prune297.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes222.0ms

Accuracy

98.1% (0.6b remaining)

Error of 0.6b against oracle of 0.0b and baseline of 32.4b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05843
15843

end0.0ms

sample854.0ms

Algorithm
intervals
Results
345.0ms1676×body1280valid
177.0ms1255×body640valid
105.0ms4143×body80valid
60.0ms630×body320valid
17.0ms296×body160valid