Details

Time bar (total: 4.5s)

sample40.0ms

Algorithm
intervals
Results
14.0ms56×body1280valid
8.0ms45×body640valid
6.0ms124×body80valid
2.0ms20×body320valid
1.0ms11×body160valid

simplify62.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0155
1225
2305
3525
41145
53225
616275
750025

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.8b

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

rewrite46.0ms

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:
9.0ms
(/ 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)

series132.0ms

Counts
3 → 9
Calls
3 calls:
36.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
19.0ms
(+ 1.0 (exp (* -2.0 x)))
77.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify91.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0251494
1731465
22785460
35002460

prune151.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
0.1b
(* 0.33333333333333337 (pow x 3))
0.2b
(* 5.551115123125783e-17 (pow x 4))
7.6b
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
19×associate-*r*
14×add-exp-log
11×add-cube-cbrt *-un-lft-identity add-log-exp
8×unpow-prod-down add-cbrt-cube
7×unswap-sqr
6×associate-*l* prod-exp
4×pow1 cube-prod sqr-pow
2×pow-to-exp diff-log pow-exp sum-log *-commutative cbrt-unprod
1×+-commutative cube-mult sub-neg flip3-- flip3-+ unpow3 flip-- flip-+ associate--r+
Counts
4 → 81
Calls
4 calls:
9.0ms
(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
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)))

series229.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
38.0ms
(* 0.33333333333333337 (pow x 3))
36.0ms
(* 5.551115123125783e-17 (pow x 4))
106.0ms
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

simplify52.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 1 (10.0ms)

IterNodesCost
0344493
11475459
25001459

prune195.0ms

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

rewrite123.0ms

Algorithm
rewrite-expression-head
Rules
29×*-un-lft-identity
25×add-sqr-sqrt
15×add-cube-cbrt
14×times-frac
8×add-log-exp
7×log-pow
6×add-exp-log exp-prod add-cbrt-cube
5×pow1 log-prod distribute-lft-out
4×associate-/r* difference-of-squares
3×associate-/l*
2×sub-neg flip3-+ exp-sum associate-/r/ flip-+ distribute-lft-out--
1×cbrt-undiv +-commutative log-div flip3-- frac-2neg exp-diff diff-log div-exp rem-log-exp clear-num sum-log flip-- div-inv
Counts
4 → 81
Calls
4 calls:
6.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
3.0ms
(+ 1.0 (exp (* -2.0 x)))
77.0ms
(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
35.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series214.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
16.0ms
(+ 1.0 (exp (* -2.0 x)))
80.0ms
(log (exp (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
80.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify100.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (21.0ms)

IterNodesCost
0291672
1849622
23009617
35002617

prune204.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1.0 (exp (* -2.0 x))))
0.0b
(+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
0.3b
(* (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
3.3b
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite441.0ms

Algorithm
rewrite-expression-head
Rules
66×add-sqr-sqrt
30×sqrt-prod
20×difference-of-squares
17×*-un-lft-identity
16×times-frac
14×associate-*l*
8×add-log-exp
7×pow1 add-cube-cbrt
6×add-exp-log add-cbrt-cube
5×flip3-+ flip-+
4×frac-times flip3-- associate-*r* flip--
3×distribute-lft-out
2×sqrt-div associate-*r/ associate-*l/ distribute-lft-out--
1×+-commutative distribute-rgt-in sub-neg rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 diff-log pow-prod-down prod-exp sum-log *-commutative cbrt-unprod unswap-sqr
Counts
4 → 91
Calls
4 calls:
4.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
48.0ms
(+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
325.0ms
(* (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
60.0ms
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series653.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
112.0ms
(+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
378.0ms
(* (- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (+ (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
123.0ms
(- (/ (sqrt 2.0) (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify57.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
04521804
119801641
250031628

prune255.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes313.0ms

Accuracy

98.8% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 32.1b

bsearch2.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03716
13716

end0.0ms

sample1.1s

Algorithm
intervals
Results
422.0ms1693×body1280valid
215.0ms1244×body640valid
191.0ms4112×body80valid
80.0ms649×body320valid
26.0ms302×body160valid