Details

Time bar (total: 16.9s)

sample64.0ms

Algorithm
intervals
Results
17.0ms43×body1280valid
15.0ms53×body640valid
11.0ms128×body80valid
4.0ms23×body320valid
1.0ms9×body160valid

simplify650.0ms

Counts
1 → 1

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.3b

localize16.0ms

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)))
2.7b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite140.0ms

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:
30.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
14.0ms
(+ 1.0 (exp (* -2.0 x)))
92.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series197.0ms

Counts
3 → 9
Calls
3 calls:
62.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
20.0ms
(+ 1.0 (exp (* -2.0 x)))
115.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify1.1s

Counts
69 → 69

prune241.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

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

rewrite761.0ms

Algorithm
rewrite-expression-head
Rules
36×add-sqr-sqrt
22×*-un-lft-identity
20×sqrt-prod
12×difference-of-squares
11×associate-*r*
10×add-log-exp
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
5×flip3-+ associate-*l* flip-+
4×frac-times flip3-- times-frac flip-- distribute-lft-out distribute-lft-out--
3×sub-neg
2×+-commutative distribute-rgt-in distribute-lft-in associate-*r/ associate-*l/ sum-log
1×diff-log pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 84
Calls
4 calls:
8.0ms
(+ 1.0 (exp (* -2.0 x)))
8.0ms
(+ 1.0 (exp (* -2.0 x)))
627.0ms
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
115.0ms
(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series759.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(+ 1.0 (exp (* -2.0 x)))
21.0ms
(+ 1.0 (exp (* -2.0 x)))
538.0ms
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
183.0ms
(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify885.0ms

Counts
96 → 96

prune320.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)
0.3b
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (cbrt (pow (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)))
0.3b
(cbrt (pow (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3))
3.2b
(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
122×add-sqr-sqrt
65×sqrt-prod
60×cbrt-prod
47×*-un-lft-identity
42×difference-of-squares
34×unpow-prod-down cube-prod
31×associate-*r*
15×add-cube-cbrt
14×times-frac distribute-lft-out--
10×cube-div
8×cbrt-div
7×pow1 add-exp-log
6×flip3-- add-cbrt-cube flip-- add-log-exp
5×associate-*l* unswap-sqr
4×frac-times sqr-pow
3×cube-mult pow-unpow flip3-+ unpow3 flip-+
2×associate-*r/ associate-*l/ distribute-lft-out
1×pow-to-exp sub-neg pow-pow pow1/3 diff-log pow-prod-down pow-exp prod-exp *-commutative rem-cbrt-cube cbrt-unprod rem-cube-cbrt
Counts
4 → 160
Calls
4 calls:
155.0ms
(pow (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)
803.0ms
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (cbrt (pow (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)))
121.0ms
(cbrt (pow (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3))
150.0ms
(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

series1.4s

Counts
4 → 12
Calls
4 calls:
474.0ms
(pow (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)
545.0ms
(* (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) (cbrt (pow (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3)))
165.0ms
(cbrt (pow (- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)) 3))
183.0ms
(- (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0))

simplify1.3s

Counts
172 → 172

prune494.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (exp (* -2.0 x)))
0.3b
(/ (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (+ (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))))
2.7b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite1.2s

Algorithm
rewrite-expression-head
Rules
112×*-un-lft-identity
95×add-sqr-sqrt
73×times-frac
36×associate-*r*
30×add-cube-cbrt
29×distribute-lft-out
28×sqrt-prod
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 → 146
Calls
4 calls:
8.0ms
(+ 1.0 (exp (* -2.0 x)))
315.0ms
(/ (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
718.0ms
(* (+ (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))))
126.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series814.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(+ 1.0 (exp (* -2.0 x)))
488.0ms
(/ (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (+ (sqrt (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (sqrt 1.0)))
151.0ms
(* (+ (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))))
153.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify1.6s

Counts
158 → 158

prune544.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes316.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.0b

bsearch2.0ms

simplify826.0ms

end0.0ms

sample2.0s

Algorithm
intervals
Results
973.0ms1642×body1280valid
355.0ms1285×body640valid
219.0ms4141×body80valid
92.0ms595×body320valid
33.0ms337×body160valid