Details

Time bar (total: 12.4s)

sample31.0ms

Algorithm
intervals
Results
11.0ms54×body1280valid
5.0ms33×body640valid
3.0ms135×body80valid
2.0ms24×body320valid
1.0ms10×body160valid

simplify61.0ms

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: 28.4b

localize7.0ms

Local error

Found 3 expressions with local error:

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

rewrite20.0ms

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:
3.0ms
(+ 1.0 (exp (* -2.0 x)))
5.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
10.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series137.0ms

Counts
3 → 9
Calls
3 calls:
16.0ms
(+ 1.0 (exp (* -2.0 x)))
40.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
80.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify93.0ms

Algorithm
egg-herbie
Counts
69 → 69
Iterations

Useful iterations: 2 (19.0ms)

IterNodesCost
0251494
1731465
22785460
35001460

prune146.0ms

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
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b
(+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
0.3b
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
3.4b
(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
45×add-sqr-sqrt
39×*-un-lft-identity
22×sqrt-prod
16×times-frac
15×add-cube-cbrt
12×difference-of-squares
11×associate-*r*
8×add-exp-log add-cbrt-cube distribute-lft-out add-log-exp
6×pow1
5×flip3-+ associate-*l* flip-+
4×frac-times flip3-- associate-/r* flip-- distribute-lft-out--
3×sub-neg associate-/l*
2×distribute-rgt-in distribute-lft-in associate-*r/ associate-*l/ associate-/r/
1×cbrt-undiv +-commutative frac-2neg diff-log div-exp pow-prod-down prod-exp clear-num sum-log *-commutative cbrt-unprod div-inv unswap-sqr
Counts
4 → 106
Calls
4 calls:
5.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
13.0ms
(+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
34.0ms
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
14.0ms
(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series768.0ms

Counts
4 → 12
Calls
4 calls:
38.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
108.0ms
(+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
503.0ms
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
118.0ms
(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify56.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
04551568
119661403
250021374

prune285.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
0.3b
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (/ (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))))
0.3b
(/ (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
3.0b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite105.0ms

Algorithm
rewrite-expression-head
Rules
114×*-un-lft-identity
95×add-sqr-sqrt
73×times-frac
36×associate-*r*
30×add-cube-cbrt sqrt-prod distribute-lft-out
24×difference-of-squares
12×distribute-lft-out--
11×add-exp-log add-cbrt-cube
8×add-log-exp
6×pow1 associate-/l*
5×flip3-+ associate-*l* associate-/r* flip-+
4×associate-/r/
2×cbrt-undiv frac-times flip3-- div-exp associate-*l/ prod-exp flip-- cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative sub-neg frac-2neg diff-log div-sub associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
4 → 147
Calls
4 calls:
16.0ms
(+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
45.0ms
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (/ (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))))
27.0ms
(/ (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
10.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series603.0ms

Counts
4 → 12
Calls
4 calls:
111.0ms
(+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))
82.0ms
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (/ (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))))
330.0ms
(/ (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
79.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify105.0ms

Algorithm
egg-herbie
Counts
159 → 159
Iterations

Useful iterations: 2 (82.0ms)

IterNodesCost
06173117
134942859
250022832

prune376.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (/ (/ (- (/ (pow (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 4) 1) (/ (* 1.0 1.0) 1)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))))
0.3b
(/ (/ (- (/ (pow (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 4) 1) (/ (* 1.0 1.0) 1)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
0.3b
(pow (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 4)
3.0b
(- (/ (pow (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 4) 1) (/ (* 1.0 1.0) 1))

rewrite727.0ms

Algorithm
rewrite-expression-head
Rules
5877×times-frac
4180×*-un-lft-identity
3965×add-sqr-sqrt
1485×difference-of-squares
1194×sqrt-prod
1057×distribute-lft-out
831×unpow-prod-down
806×add-cube-cbrt
796×associate-*r*
271×sqr-pow
158×associate-/l*
104×div-inv
45×distribute-rgt-out-- distribute-lft-out--
28×associate-/r/
19×add-exp-log
18×add-cbrt-cube
16×flip3-+ flip-+
8×pow1
6×cbrt-undiv div-exp add-log-exp
5×associate-*l* associate-/r*
3×pow-unpow pow-pow prod-exp cbrt-unprod unswap-sqr
2×frac-times div-sub associate-*l/
1×pow-to-exp sub-neg flip3-- frac-2neg sqrt-pow1 pow1/2 diff-log associate-*r/ pow-prod-down pow-exp clear-num *-commutative frac-sub sqrt-pow2 flip-- associate-/l/ sub-div
Counts
4 → 1882
Calls
4 calls:
269.0ms
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (/ (/ (- (/ (pow (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 4) 1) (/ (* 1.0 1.0) 1)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))))
101.0ms
(/ (/ (- (/ (pow (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 4) 1) (/ (* 1.0 1.0) 1)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
8.0ms
(pow (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 4)
45.0ms
(- (/ (pow (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 4) 1) (/ (* 1.0 1.0) 1))

series1.7s

Counts
4 → 12
Calls
4 calls:
236.0ms
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (/ (/ (- (/ (pow (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 4) 1) (/ (* 1.0 1.0) 1)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))))
1.2s
(/ (/ (- (/ (pow (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 4) 1) (/ (* 1.0 1.0) 1)) (+ (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
180.0ms
(pow (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 4)
138.0ms
(- (/ (pow (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) 4) 1) (/ (* 1.0 1.0) 1))

simplify620.0ms

Algorithm
egg-herbie
Counts
1894 → 1894
Iterations

Useful iterations: 1 (72.0ms)

IterNodesCost
0485969760
1500169717

prune5.1s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes431.0ms

Accuracy

99.5% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 29.4b

bsearch2.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05362
15362

end0.0ms

sample847.0ms

Algorithm
intervals
Results
361.0ms1762×body1280valid
166.0ms1230×body640valid
108.0ms4099×body80valid
57.0ms625×body320valid
16.0ms284×body160valid