Details

Time bar (total: 31.2s)

sample74.0ms

Algorithm
intervals
Results
26.0ms57×body1280valid
13.0ms39×body640valid
8.0ms130×body80valid
3.0ms13×body320valid
2.0ms17×body160valid

simplify9.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0910
12210
25310
318810
done500010

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.3b

localize10.0ms

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)

rewrite160.0ms

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:
33.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
14.0ms
(+ 1.0 (exp (* -2.0 x)))
109.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

series232.0ms

Counts
3 → 9
Calls
3 calls:
73.0ms
(/ 2.0 (+ 1.0 (exp (* -2.0 x))))
32.0ms
(+ 1.0 (exp (* -2.0 x)))
127.0ms
(- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)

simplify4.1s

Counts
69 → 69
Iterations

Useful iterations: done (4.1s)

IterNodesCost
0116947
1550895
done5001847

prune295.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

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)

rewrite573.0ms

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))))
91.0ms
(/ (/ 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)))))
388.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)

series426.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(sqrt (+ 1.0 (exp (* -2.0 x))))
69.0ms
(/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x)))))
128.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
142.0ms
(- (/ (/ 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
117988547
done50008091

prune908.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
0.5b
(cbrt (pow (sqrt (+ (exp (* -2.0 x)) 1.0)) 3))
0.5b
(pow (sqrt (+ (exp (* -2.0 x)) 1.0)) 3)
4.3b
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (pow (sqrt (+ (exp (* -2.0 x)) 1.0)) 3))) 1.0)

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
106×add-sqr-sqrt
56×times-frac
48×*-un-lft-identity
45×sqrt-prod
38×cbrt-prod
30×add-cube-cbrt
22×difference-of-squares
20×unpow-prod-down cube-prod
8×distribute-lft-out
7×add-exp-log associate-/r* add-cbrt-cube
6×pow1 sqrt-div add-log-exp
5×sqr-pow
4×cube-div
3×pow-unpow pow-pow flip3-+ flip-+ associate-/l*
2×cube-mult cbrt-div unpow3 associate-/r/
1×cbrt-undiv pow-to-exp sub-neg flip3-- frac-2neg sqrt-pow1 pow1/2 pow1/3 diff-log div-exp pow-exp clear-num sqrt-pow2 flip-- rem-cbrt-cube div-inv distribute-lft-out-- rem-cube-cbrt
Counts
4 → 147
Calls
4 calls:
32.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
33.0ms
(cbrt (pow (sqrt (+ (exp (* -2.0 x)) 1.0)) 3))
31.0ms
(pow (sqrt (+ (exp (* -2.0 x)) 1.0)) 3)
894.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (pow (sqrt (+ (exp (* -2.0 x)) 1.0)) 3))) 1.0)

series471.0ms

Counts
4 → 12
Calls
4 calls:
132.0ms
(/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x)))))
79.0ms
(cbrt (pow (sqrt (+ (exp (* -2.0 x)) 1.0)) 3))
138.0ms
(pow (sqrt (+ (exp (* -2.0 x)) 1.0)) 3)
121.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (cbrt (pow (sqrt (+ (exp (* -2.0 x)) 1.0)) 3))) 1.0)

simplify4.9s

Counts
159 → 159
Iterations

Useful iterations: done (4.9s)

IterNodesCost
02573655
133582786
done50012546

prune555.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b
(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
0.1b
(* 0.33333333333333337 (pow x 3))
7.2b
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×associate-*r*
10×add-log-exp
8×add-exp-log
7×add-cube-cbrt *-un-lft-identity
5×add-cbrt-cube
4×unpow-prod-down cube-prod unswap-sqr
3×pow1 associate-*l* prod-exp
2×diff-log sum-log sqr-pow
1×+-commutative cube-mult pow-to-exp sub-neg flip3-- flip3-+ unpow3 pow-exp *-commutative flip-- cbrt-unprod flip-+ associate--r+
Counts
3 → 56
Calls
3 calls:
23.0ms
(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
24.0ms
(* 0.33333333333333337 (pow x 3))
11.0ms
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

series755.0ms

Counts
3 → 9
Calls
3 calls:
66.0ms
(- (* 1.0 x) (+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3))))
79.0ms
(* 0.33333333333333337 (pow x 3))
609.0ms
(+ (* 5.551115123125783e-17 (pow x 4)) (* 0.33333333333333337 (pow x 3)))

simplify1.3s

Counts
65 → 65
Iterations

Useful iterations: done (1.3s)

IterNodesCost
0102898
1763813
done5000765

prune194.0ms

Pruning

2 alts after pruning (0 fresh and 2 done)

Merged error: 0.0b

regimes147.0ms

Accuracy

95.9% (1.2b remaining)

Error of 1.3b against oracle of 0.0b and baseline of 30.1b

bsearch3.0ms

simplify6.0ms

Iterations

Useful iterations: 1 (4.0ms)

IterNodesCost
03271
14050
done4050

end0.0ms

sample2.0s

Algorithm
intervals
Results
733.0ms1726×body1280valid
472.0ms1263×body640valid
317.0ms4060×body80valid
163.0ms641×body320valid
36.0ms310×body160valid