Details

Time bar (total: 10.8s)

sample37.0ms

Algorithm
intervals
Results
12.0ms52×body1280valid
7.0ms42×body640valid
5.0ms139×body80valid
2.0ms16×body320valid
1.0ms7×body160valid

simplify55.0ms

Counts
1 → 1

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.3b

localize8.0ms

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))))
1.4b
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

rewrite111.0ms

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:
10.0ms
(+ 1.0 (exp (* -2.0 x)))
15.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
83.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series138.0ms

Counts
3 → 9
Calls
3 calls:
17.0ms
(+ 1.0 (exp (* -2.0 x)))
38.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
83.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify86.0ms

Counts
69 → 69

prune157.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize12.0ms

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)))))
0.4b
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
1.4b
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

rewrite346.0ms

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:
11.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
46.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
17.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
250.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series238.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
37.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
70.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
85.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

simplify82.0ms

Counts
333 → 333

prune535.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
0.4b
(/ 1 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
0.4b
(/ (sqrt (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))))
27.8b
(- (/ (/ 1 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (/ (sqrt (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))))) 1.0)

rewrite5.2s

Algorithm
rewrite-expression-head
Rules
767×times-frac
624×sqrt-prod
600×add-sqr-sqrt
451×*-un-lft-identity
284×add-cube-cbrt
69×distribute-lft-out
64×difference-of-squares
56×associate-/r*
42×sqrt-div
21×associate-/r/
15×add-exp-log
13×add-cbrt-cube associate-/l*
11×flip3-+ flip-+ div-inv
7×pow1
6×div-exp add-log-exp
5×cbrt-undiv pow-flip
4×sqrt-pow1
3×frac-2neg clear-num
2×pow1/2 associate-/l/
1×sub-neg rec-exp flip3-- diff-log 1-exp flip-- distribute-lft-out-- inv-pow
Counts
4 → 511
Calls
4 calls:
18.0ms
(/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
20.0ms
(/ 1 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
46.0ms
(/ (sqrt (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))))
5.0s
(- (/ (/ 1 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (/ (sqrt (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))))) 1.0)

series557.0ms

Counts
4 → 12
Calls
4 calls:
145.0ms
(/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
134.0ms
(/ 1 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x))))))
195.0ms
(/ (sqrt (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))))
84.0ms
(- (/ (/ 1 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))) (/ (sqrt (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (sqrt (sqrt (+ 1.0 (exp (* -2.0 x)))))))) 1.0)

simplify109.0ms

Counts
523 → 523

prune930.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 0.33333333333333337 (pow x 3))
0.4b
(* 5.551115123125783e-17 (pow x 4))
8.0b
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
22×add-sqr-sqrt
19×associate-*r*
13×add-exp-log
10×add-cube-cbrt *-un-lft-identity
8×unpow-prod-down
7×add-cbrt-cube unswap-sqr
6×associate-*l* prod-exp
5×add-log-exp
4×cube-prod sqr-pow
3×pow1
2×pow-to-exp pow-exp *-commutative cbrt-unprod
1×+-commutative cube-mult flip3-+ unpow3 sum-log flip-+
Counts
3 → 67
Calls
3 calls:
13.0ms
(* 0.33333333333333337 (pow x 3))
12.0ms
(* 5.551115123125783e-17 (pow x 4))
10.0ms
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

series200.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(* 0.33333333333333337 (pow x 3))
39.0ms
(* 5.551115123125783e-17 (pow x 4))
117.0ms
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

simplify40.0ms

Counts
76 → 76

prune174.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0b

regimes140.0ms

Accuracy

99.7% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.1b

bsearch1.0ms

simplify1.0ms

end0.0ms

sample1.6s

Algorithm
intervals
Results
821.0ms1669×body1280valid
276.0ms4197×body80valid
204.0ms1245×body640valid
70.0ms605×body320valid
21.0ms284×body160valid