Details

Time bar (total: 11.4s)

sample34.0ms

Algorithm
intervals
Results
12.0ms57×body1280valid
5.0ms35×body640valid
4.0ms131×body80valid
2.0ms20×body320valid
1.0ms13×body160valid

simplify2.1s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0910
11510
22210
33110
45510
512010
627810
781910
8301910
done500110

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.1b

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))))
3.6b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
99×*-un-lft-identity
68×add-sqr-sqrt
63×add-cube-cbrt
61×times-frac
54×prod-diff
18×fma-neg
17×distribute-lft-out
10×associate-/r/
7×add-log-exp
6×flip3-+ flip-+
5×add-exp-log add-cbrt-cube div-inv
4×associate-/r*
3×pow1 expm1-log1p-u fma-def log1p-expm1-u associate-/l*
2×difference-of-squares
1×cbrt-undiv +-commutative sub-neg flip3-- frac-2neg diff-log div-exp clear-num sum-log flip-- distribute-lft-out--
Counts
3 → 141
Calls
3 calls:
9.0ms
(+ 1.0 (exp (* -2.0 x)))
13.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
82.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series135.0ms

Counts
3 → 9
Calls
3 calls:
17.0ms
(+ 1.0 (exp (* -2.0 x)))
37.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
82.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify1.6s

Counts
150 → 150
Iterations

Useful iterations: done (1.6s)

IterNodesCost
01803092
14002501
28562219
324011982
done50011796

prune249.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(expm1 (log1p (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.3b
(log1p (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
3.6b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite104.0ms

Algorithm
rewrite-expression-head
Rules
97×*-un-lft-identity
68×add-sqr-sqrt
63×add-cube-cbrt
61×times-frac
54×prod-diff
18×fma-neg
16×distribute-lft-out
10×associate-/r/
6×add-exp-log add-cbrt-cube add-log-exp
5×expm1-log1p-u flip3-+ flip-+ div-inv
4×pow1 associate-/r* log1p-expm1-u
3×associate-/l*
2×difference-of-squares
1×cbrt-undiv sub-neg log1p-udef expm1-log1p flip3-- frac-2neg diff-log log1p-expm1 div-exp clear-num flip-- distribute-lft-out-- expm1-udef
Counts
4 → 146
Calls
4 calls:
0.0ms
(expm1 (log1p (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
14.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
1.0ms
(log1p (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
81.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series539.0ms

Counts
4 → 12
Calls
4 calls:
244.0ms
(expm1 (log1p (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
43.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
178.0ms
(log1p (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0))
74.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify1.7s

Counts
158 → 158
Iterations

Useful iterations: done (1.7s)

IterNodesCost
02023318
14372706
29292394
326052157
done50011971

prune297.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
0.0b
(pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)
0.1b
(cbrt (pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
3.6b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite238.0ms

Algorithm
rewrite-expression-head
Rules
111×*-un-lft-identity
94×add-sqr-sqrt
69×add-cube-cbrt
65×times-frac
54×prod-diff
18×cbrt-prod fma-neg
16×distribute-lft-out
12×unpow-prod-down cube-prod
10×associate-/r/ difference-of-squares
7×add-exp-log add-cbrt-cube
6×add-log-exp
5×pow1 flip3-+ flip-+ div-inv distribute-lft-out--
4×cube-div expm1-log1p-u associate-/r* log1p-expm1-u
3×pow-unpow flip3-- flip-- associate-/l*
2×cube-mult cbrt-div unpow3 sqr-pow
1×cbrt-undiv pow-to-exp sub-neg pow-pow frac-2neg pow1/3 diff-log div-exp pow-exp clear-num rem-cbrt-cube rem-cube-cbrt
Counts
4 → 188
Calls
4 calls:
15.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
72.0ms
(pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)
61.0ms
(cbrt (pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
82.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series318.0ms

Counts
4 → 12
Calls
4 calls:
36.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
126.0ms
(pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3)
74.0ms
(cbrt (pow (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) 3))
82.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify726.0ms

Counts
200 → 200
Iterations

Useful iterations: done (719.0ms)

IterNodesCost
02384457
15463634
213443259
done50003087

prune414.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize11.0ms

Local error

Found 2 expressions with local error:

0.1b
(* 0.33333333333333337 (pow x 3))
7.5b
(fma 6.938893903907228e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*r*
7×add-exp-log
6×add-cube-cbrt *-un-lft-identity
4×unpow-prod-down cube-prod add-cbrt-cube unswap-sqr
3×associate-*l* prod-exp
2×pow1 expm1-log1p-u log1p-expm1-u add-log-exp sqr-pow
1×cube-mult pow-to-exp unpow3 pow-exp *-commutative cbrt-unprod fma-udef
Counts
2 → 43
Calls
2 calls:
12.0ms
(* 0.33333333333333337 (pow x 3))
0.0ms
(fma 6.938893903907228e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

series144.0ms

Counts
2 → 6
Calls
2 calls:
43.0ms
(* 0.33333333333333337 (pow x 3))
100.0ms
(fma 6.938893903907228e-17 (pow x 4) (* 0.33333333333333337 (pow x 3)))

simplify1.2s

Counts
49 → 49
Iterations

Useful iterations: 2 (63.0ms)

IterNodesCost
070445
1141409
2388369
31882369
done5000369

prune117.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes295.0ms

Accuracy

99.6% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.6b

bsearch2.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
02951
13351
done3351

end0.0ms

sample926.0ms

Algorithm
intervals
Results
362.0ms1725×body1280valid
173.0ms1265×body640valid
111.0ms4067×body80valid
55.0ms621×body320valid
19.0ms322×body160valid