Details

Time bar (total: 26.0s)

sample320.0ms

Algorithm
intervals
Results
87.0ms71×body10240exit
83.0ms61×body1280valid
80.0ms312×body80valid
30.0ms45×body640valid
10.0ms19×body320valid
4.0ms14×body160valid

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
done2021
52021
41521
3381
2122
148
019

prune15.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize73.0ms

Local error

Found 4 expressions with local error:

0.0b
(exp (* x (- -1 eps)))
0.0b
(/ (exp (* x (- -1 eps))) eps)
0.0b
(/ (exp (* x (+ -1 eps))) eps)
2.6b
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))

rewrite173.0ms

Algorithm
rewrite-expression-head
Rules
38×*-un-lft-identity
36×times-frac
28×add-sqr-sqrt exp-sum
26×add-cube-cbrt
18×add-log-exp
14×distribute-rgt-in distribute-lft-in
12×sub-neg associate-/l*
8×add-cbrt-cube
6×associate-/r* diff-log add-exp-log distribute-lft-out--
4×pow1 frac-sub insert-posit16
3×flip3-- flip--
2×cbrt-undiv clear-num sum-log frac-2neg flip3-+ div-exp flip-+ div-inv distribute-lft-out associate--r+
1×exp-prod exp-to-pow associate--l+ associate--r- difference-of-squares rem-exp-log
Counts
4 → 124
Calls
4 calls:
6.0ms
(exp (* x (- -1 eps)))
12.0ms
(/ (exp (* x (- -1 eps))) eps)
9.0ms
(/ (exp (* x (+ -1 eps))) eps)
143.0ms
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))

series242.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(exp (* x (- -1 eps)))
39.0ms
(/ (exp (* x (- -1 eps))) eps)
40.0ms
(/ (exp (* x (+ -1 eps))) eps)
148.0ms
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))

simplify1.7s

Counts
136 → 136
Iterations
IterNodes
done2018
32018
21820
1544
0235

prune760.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (* 2/3 (* x x)) x)
0.2b
(* 2/3 (* x x))
6.2b
(- (+ 2 (* (* 2/3 (* x x)) x)) (* x x))

rewrite117.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1 add-cbrt-cube add-exp-log
9×pow-prod-down prod-exp cbrt-unprod
8×add-log-exp
7×add-sqr-sqrt
5×*-un-lft-identity add-cube-cbrt
4×associate-*r* associate-*l*
3×insert-posit16
2×diff-log *-commutative
1×sum-log sub-neg flip3-- associate--l+ flip-- difference-of-squares unswap-sqr
Counts
3 → 58
Calls
3 calls:
61.0ms
(* (* 2/3 (* x x)) x)
16.0ms
(* 2/3 (* x x))
39.0ms
(- (+ 2 (* (* 2/3 (* x x)) x)) (* x x))

series130.0ms

Counts
3 → 9
Calls
3 calls:
64.0ms
(* (* 2/3 (* x x)) x)
29.0ms
(* 2/3 (* x x))
37.0ms
(- (+ 2 (* (* 2/3 (* x x)) x)) (* x x))

simplify1.1s

Counts
67 → 67
Iterations
IterNodes
done2009
32009
2875
1268
092

prune263.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

localize82.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))
2.6b
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
2.6b
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
2.6b
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))

rewrite679.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
40×add-log-exp
24×distribute-lft-out--
18×diff-log
16×frac-sub
13×add-sqr-sqrt
12×flip3-- flip--
8×cbrt-prod flip3-+ flip-+ distribute-lft-out
6×cbrt-div sum-log sub-neg associate--r+
5×add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log insert-posit16 difference-of-squares
3×associate--l+ associate--r-
1×pow1/3
Counts
4 → 110
Calls
4 calls:
123.0ms
(cbrt (- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))
201.0ms
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
200.0ms
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
153.0ms
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))

series699.0ms

Counts
4 → 12
Calls
4 calls:
261.0ms
(cbrt (- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))
147.0ms
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
134.0ms
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
157.0ms
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))

simplify1.6s

Counts
122 → 122
Iterations
IterNodes
done2000
22000
1611
0209

prune923.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize93.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))
2.6b
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
2.6b
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
2.6b
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))

rewrite741.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
40×add-log-exp
24×distribute-lft-out--
18×diff-log
16×frac-sub
13×add-sqr-sqrt
12×flip3-- flip--
8×cbrt-prod flip3-+ flip-+ distribute-lft-out
6×cbrt-div sum-log sub-neg associate--r+
5×add-cube-cbrt
4×pow1 add-cbrt-cube add-exp-log insert-posit16 difference-of-squares
3×associate--l+ associate--r-
1×pow1/3
Counts
4 → 110
Calls
4 calls:
144.0ms
(cbrt (- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))
194.0ms
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
193.0ms
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
206.0ms
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))

series743.0ms

Counts
4 → 12
Calls
4 calls:
269.0ms
(cbrt (- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps))))))
162.0ms
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
149.0ms
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))
161.0ms
(- (+ (exp (* x (+ -1 eps))) (/ (exp (* x (+ -1 eps))) eps)) (- (/ (exp (* x (- -1 eps))) eps) (exp (* x (- -1 eps)))))

simplify1.8s

Counts
122 → 122
Iterations
IterNodes
done2000
22000
1611
0209

prune977.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes103.0ms

Accuracy

96.9% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.6b

bsearch313.0ms

Steps
ItersRangePoint
11
2.3022379716023992e-17
6648347011126.543
54.31805746173307

simplify14.0ms

Iterations
IterNodes
done37
137
029

end0.0ms

sample10.9s

Algorithm
intervals
Results
3.9s1912×body10240exit
2.5s1725×body1280valid
2.1s9846×body80valid
1.1s1296×body640valid
822.0ms590×body320valid
120.0ms338×body160valid