Details

Time bar (total: 7.5s)

sample404.0ms

Algorithm
intervals
Results
54.0ms175×body10240exit
12.0ms388×body80nan
10.0ms244×body80valid
1.0ms16×body160valid

simplify70.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0197
1287
2407
3737
41767
55597
626267
750017
done50017

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 3.4b

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
0.5b
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
3.0b
(- (exp (* 2.0 x)) 1.0)
3.1b
(- (exp x) 1.0)

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
78×add-sqr-sqrt
75×*-un-lft-identity
51×times-frac
31×sqrt-prod
27×add-cube-cbrt
24×distribute-lft-out-- difference-of-squares
8×add-log-exp
6×add-exp-log add-cbrt-cube
5×pow1 flip3-- associate-/r* flip-- associate-/l*
4×associate-/r/
2×sub-neg rem-sqrt-square diff-log div-inv associate-/l/
1×cbrt-undiv frac-2neg sqrt-pow1 pow1/2 sqrt-div div-sub div-exp clear-num
Counts
4 → 123
Calls
4 calls:
26.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
41.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
12.0ms
(- (exp (* 2.0 x)) 1.0)
13.0ms
(- (exp x) 1.0)

series204.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(sqrt (/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0)))
62.0ms
(/ (- (exp (* 2.0 x)) 1.0) (- (exp x) 1.0))
26.0ms
(- (exp (* 2.0 x)) 1.0)
24.0ms
(- (exp x) 1.0)

simplify119.0ms

Counts
135 → 135
Iterations

Useful iterations: 3 (107.0ms)

IterNodesCost
03871380
110541314
242871301
350031293
done50031293

prune329.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))
0.2b
(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))))
3.1b
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
3.1b
(- (exp x) 1.0)

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
98×add-sqr-sqrt
70×*-un-lft-identity
45×times-frac
43×sqrt-prod
39×difference-of-squares
25×distribute-lft-out--
20×add-cube-cbrt
9×associate-/l*
8×add-log-exp
7×pow1
6×add-exp-log add-cbrt-cube
5×sqrt-div associate-/r*
4×flip3-- flip--
2×frac-times sub-neg sqrt-pow1 flip3-+ diff-log associate-*l/ associate-/r/ flip-+ associate-/l/
1×cbrt-undiv frac-2neg pow1/2 div-sub associate-*r/ div-exp pow-prod-down clear-num div-inv
Counts
4 → 124
Calls
4 calls:
50.0ms
(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))
34.0ms
(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))))
17.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
10.0ms
(- (exp x) 1.0)

series482.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))
324.0ms
(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (/ (- (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (- (exp x) 1.0))))
48.0ms
(- (sqrt (exp (* 2.0 x))) (sqrt 1.0))
15.0ms
(- (exp x) 1.0)

simplify58.0ms

Counts
136 → 136
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05741847
120281761
250011753
done50011753

prune341.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b
(sqrt (sqrt (exp (* 2.0 x))))
0.2b
(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (* (/ (+ (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))) (+ (sqrt (exp x)) (sqrt 1.0))) (/ (- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))) (- (sqrt (exp x)) (sqrt 1.0))))))
3.2b
(- (sqrt (exp x)) (sqrt 1.0))
3.2b
(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

rewrite238.0ms

Algorithm
rewrite-expression-head
Rules
41×sqrt-prod
34×add-sqr-sqrt
16×*-un-lft-identity
13×difference-of-squares
12×pow1
11×sqrt-pow1 sqrt-div
9×frac-times add-log-exp
6×add-cube-cbrt associate-*r/
5×associate-*l/ distribute-lft-out--
4×add-exp-log flip3-+ add-cbrt-cube flip-+
3×pow1/2 pow-prod-down
2×sub-neg rem-sqrt-square flip3-- diff-log flip--
1×exp-prod exp-to-pow
Counts
4 → 86
Calls
4 calls:
4.0ms
(sqrt (sqrt (exp (* 2.0 x))))
193.0ms
(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (* (/ (+ (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))) (+ (sqrt (exp x)) (sqrt 1.0))) (/ (- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))) (- (sqrt (exp x)) (sqrt 1.0))))))
15.0ms
(- (sqrt (exp x)) (sqrt 1.0))
24.0ms
(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

series1.6s

Counts
4 → 12
Calls
4 calls:
106.0ms
(sqrt (sqrt (exp (* 2.0 x))))
1.3s
(sqrt (* (+ (sqrt (exp (* 2.0 x))) (sqrt 1.0)) (* (/ (+ (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))) (+ (sqrt (exp x)) (sqrt 1.0))) (/ (- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0))) (- (sqrt (exp x)) (sqrt 1.0))))))
37.0ms
(- (sqrt (exp x)) (sqrt 1.0))
155.0ms
(- (sqrt (sqrt (exp (* 2.0 x)))) (sqrt (sqrt 1.0)))

simplify79.0ms

Counts
98 → 98
Iterations

Useful iterations: 2 (65.0ms)

IterNodesCost
06861837
131161778
250011775
done50011775

prune392.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(* x (+ 1.0 (* 0.5 x)))
29.3b
(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
5×pow1 add-cube-cbrt *-un-lft-identity
4×add-exp-log add-cbrt-cube
3×associate-*r* associate-*l* sqrt-prod
2×flip3-+ sqrt-div associate-*r/ flip-+ add-log-exp
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
2 → 37
Calls
2 calls:
18.0ms
(* x (+ 1.0 (* 0.5 x)))
13.0ms
(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

series145.0ms

Counts
2 → 6
Calls
2 calls:
69.0ms
(* x (+ 1.0 (* 0.5 x)))
75.0ms
(sqrt (+ (* x (+ 1.0 (* 0.5 x))) 2.0))

simplify37.0ms

Counts
43 → 43
Iterations

Useful iterations: 2 (33.0ms)

IterNodesCost
0279281
11132268
25002256
done5002256

prune77.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.5b

regimes27.0ms

Accuracy

79.5% (0.6b remaining)

Error of 0.8b against oracle of 0.1b and baseline of 3.2b

bsearch36.0ms

Steps
ItersRangePoint
6
-1.6640733670284383e-05
-3.4900073017642136e-06
-1.2041893277070125e-05

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
04037
14037
done4037

end0.0ms

sample2.5s

Algorithm
intervals
Results
1.3s6666×body10240exit
414.0ms12737×body80nan
249.0ms7414×body80valid
63.0ms728×body160valid