Details

Time bar (total: 20.4s)

sample39.0ms

Algorithm
intervals
Results
13.0ms57×body1280valid
7.0ms39×body640valid
5.0ms130×body80valid
1.0ms13×body320valid
1.0ms17×body160valid

simplify3.6s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

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)

rewrite162.0ms

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:
15.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
7.0ms
(+ 1.0 (exp (* -2.0 x)))
138.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series184.0ms

Counts
3 → 9
Calls
3 calls:
52.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
24.0ms
(+ 1.0 (exp (* -2.0 x)))
108.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify3.1s

Counts
69 → 69
Iterations

Useful iterations: 4 (1.4s)

IterNodesCost
0116947
1252903
2555847
31212838
43536836
done5000836

prune188.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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)

rewrite598.0ms

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:
24.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
86.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
34.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
433.0ms
(- (/ (/ 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:
59.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
50.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
111.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
86.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify3.1s

Counts
333 → 333
Iterations

Useful iterations: done (3.0s)

IterNodesCost
035410184
17858589
215587997
342017643
done50007472

prune849.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ 1 (/ (+ 1.0 (exp (* -2.0 x))) 2.0))
0.0b
(+ 1.0 (exp (* -2.0 x)))
4.3b
(- (/ 1 (/ (+ 1.0 (exp (* -2.0 x))) 2.0)) 1.0)

rewrite182.0ms

Algorithm
rewrite-expression-head
Rules
102×times-frac
83×*-un-lft-identity
66×add-sqr-sqrt
52×add-cube-cbrt
16×associate-/r*
14×add-exp-log
13×distribute-lft-out
8×add-cbrt-cube
7×div-exp add-log-exp
6×div-inv
5×difference-of-squares
4×pow1
3×cbrt-undiv associate-/l*
2×rec-exp 1-exp distribute-lft-out--
1×+-commutative sub-neg flip3-- pow-flip frac-2neg flip3-+ diff-log clear-num sum-log associate-/r/ flip-- flip-+ inv-pow
Counts
3 → 119
Calls
3 calls:
22.0ms
(/ 1 (/ (+ 1.0 (exp (* -2.0 x))) 2.0))
9.0ms
(+ 1.0 (exp (* -2.0 x)))
145.0ms
(- (/ 1 (/ (+ 1.0 (exp (* -2.0 x))) 2.0)) 1.0)

series185.0ms

Counts
3 → 9
Calls
3 calls:
72.0ms
(/ 1 (/ (+ 1.0 (exp (* -2.0 x))) 2.0))
26.0ms
(+ 1.0 (exp (* -2.0 x)))
88.0ms
(- (/ 1 (/ (+ 1.0 (exp (* -2.0 x))) 2.0)) 1.0)

simplify3.5s

Counts
128 → 128
Iterations

Useful iterations: 4 (2.1s)

IterNodesCost
02092306
14631998
29501763
320531730
446691728
done50001728

prune246.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 2 expressions with local error:

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

rewrite74.0ms

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:
14.0ms
(- (* 1.0 x) (* (pow x 3) (+ (* 5.551115123125783e-17 x) 0.33333333333333337)))
57.0ms
(* (pow x 3) (+ (* 5.551115123125783e-17 x) 0.33333333333333337))

series209.0ms

Counts
2 → 6
Calls
2 calls:
69.0ms
(- (* 1.0 x) (* (pow x 3) (+ (* 5.551115123125783e-17 x) 0.33333333333333337)))
140.0ms
(* (pow x 3) (+ (* 5.551115123125783e-17 x) 0.33333333333333337))

simplify1.2s

Counts
55 → 55
Iterations

Useful iterations: 2 (261.0ms)

IterNodesCost
096823
1290766
21223704
done5001704

prune181.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes171.0ms

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
02649
13738
done3738

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.1s1726×body1280valid
384.0ms1263×body640valid
201.0ms4060×body80valid
149.0ms641×body320valid
35.0ms310×body160valid