Details

Time bar (total: 19.2s)

sample62.0ms

Algorithm
intervals
Results
22.0ms57×body1280valid
11.0ms39×body640valid
7.0ms130×body80valid
2.0ms13×body320valid
2.0ms17×body160valid

simplify3.3s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0910
11510
22210
33010
45310
511510
627010
777610
8294810
done500110

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize8.0ms

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)))
4.3b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite115.0ms

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:
26.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
7.0ms
(+ 1.0 (exp (* -2.0 x)))
77.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series234.0ms

Counts
3 → 9
Calls
3 calls:
72.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
30.0ms
(+ 1.0 (exp (* -2.0 x)))
132.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify3.8s

Counts
69 → 69
Iterations

Useful iterations: 4 (1.4s)

IterNodesCost
0116947
1252903
2555847
31212838
43536836
done5000836

prune291.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1.0 (exp (* -2.0 x))))
0.0b
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.5b
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
4.3b
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite445.0ms

Algorithm
rewrite-expression-head
Rules
388×times-frac
305×*-un-lft-identity
233×sqrt-prod
214×add-sqr-sqrt
189×add-cube-cbrt
57×distribute-lft-out
30×associate-/l*
22×sqrt-div
20×associate-/r/
14×associate-/r*
11×add-exp-log flip3-+ add-cbrt-cube flip-+
10×div-inv
7×difference-of-squares
6×add-log-exp
5×pow1
4×cbrt-undiv div-exp
2×frac-2neg clear-num
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 pow1/2 diff-log flip-- associate-/l/ distribute-lft-out--
Counts
4 → 321
Calls
4 calls:
21.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
92.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
23.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
284.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series306.0ms

Counts
4 → 12
Calls
4 calls:
54.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
57.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
98.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
97.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify2.9s

Counts
333 → 333
Iterations

Useful iterations: done (2.9s)

IterNodesCost
035410184
17858589
215587997
342017643
done50007472

prune731.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (exp (* -2.0 x)) 1.0)
0.0b
(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
4.3b
(- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0)

rewrite159.0ms

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:
21.0ms
(+ (exp (* -2.0 x)) 1.0)
27.0ms
(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
107.0ms
(- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0)

series194.0ms

Counts
3 → 9
Calls
3 calls:
19.0ms
(+ (exp (* -2.0 x)) 1.0)
49.0ms
(/ 2.0 (+ (exp (* -2.0 x)) 1.0))
125.0ms
(- (/ 2.0 (+ (exp (* -2.0 x)) 1.0)) 1.0)

simplify2.6s

Counts
69 → 69
Iterations

Useful iterations: 4 (1.1s)

IterNodesCost
0113947
1249905
2545847
31200838
43504836
done5001836

prune178.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 2 expressions with local error:

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

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*l*
7×add-exp-log
6×add-cube-cbrt *-un-lft-identity
4×unpow-prod-down cube-prod add-cbrt-cube add-log-exp unswap-sqr
3×associate-*r* prod-exp
2×pow1 distribute-rgt-in distribute-lft-in associate-*r/ associate--r+ sqr-pow
1×cube-mult pow-to-exp sub-neg flip3-- flip3-+ diff-log unpow3 pow-exp *-commutative flip-- cbrt-unprod flip-+
Counts
2 → 49
Calls
2 calls:
13.0ms
(- (* 1.0 x) (* (pow x 3) (+ 0.33333333333333337 (* 5.551115123125783e-17 x))))
39.0ms
(* (pow x 3) (+ 0.33333333333333337 (* 5.551115123125783e-17 x)))

series191.0ms

Counts
2 → 6
Calls
2 calls:
62.0ms
(- (* 1.0 x) (* (pow x 3) (+ 0.33333333333333337 (* 5.551115123125783e-17 x))))
129.0ms
(* (pow x 3) (+ 0.33333333333333337 (* 5.551115123125783e-17 x)))

simplify1.2s

Counts
55 → 55
Iterations

Useful iterations: 2 (232.0ms)

IterNodesCost
096819
1289762
21227704
done5000704

prune124.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes122.0ms

Accuracy

95.9% (1.2b remaining)

Error of 1.3b against oracle of 0.0b and baseline of 29.6b

bsearch2.0ms

simplify4.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02751
14036
done4036

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.0s1726×body1280valid
313.0ms1263×body640valid
250.0ms4060×body80valid
132.0ms641×body320valid
29.0ms310×body160valid