Details

Time bar (total: 1.1m)

sample401.0ms

Algorithm
intervals
Results
180.0ms104×body1280valid
40.0ms113×body80valid
6.0ms22×body640valid
2.0ms10×body320valid
1.0ms7×body160valid

simplify15.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune1.0s

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 20.6b

localize35.0ms

Local error

Found 2 expressions with local error:

0.0b
(atan (+ N 1.0))
1.8b
(- (atan (+ N 1.0)) (atan N))

rewrite54.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
1×sub-neg flip3-- diff-log diff-atan flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 22
Calls
2 calls:
13.0ms
(atan (+ N 1.0))
30.0ms
(- (atan (+ N 1.0)) (atan N))

series101.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(atan (+ N 1.0))
98.0ms
(- (atan (+ N 1.0)) (atan N))

simplify18.7s

Counts
28 → 28
Iterations
IterNodes
done5005
64894
51470
4574
3274
2150
176
040

prune206.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize32.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1 (* (+ N 1.0) N))
0.0b
(* (+ N 1.0) N)
0.5b
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

rewrite122.0ms

Algorithm
rewrite-expression-head
Rules
7×add-sqr-sqrt *-un-lft-identity
5×pow1 add-exp-log add-cube-cbrt add-cbrt-cube add-log-exp
4×associate-*l*
3×associate-*r*
2×flip3-+ associate-*l/ flip-+
1×+-commutative pow-prod-down prod-exp sum-log *-commutative cbrt-unprod distribute-lft-out unswap-sqr
Counts
3 → 39
Calls
3 calls:
31.0ms
(+ 1 (* (+ N 1.0) N))
66.0ms
(* (+ N 1.0) N)
7.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

series277.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(+ 1 (* (+ N 1.0) N))
222.0ms
(* (+ N 1.0) N)
8.0ms
(atan2 1.0 (+ 1 (* (+ N 1.0) N)))

simplify7.2s

Counts
48 → 48
Iterations
IterNodes
done5001
31524
2523
1187
073

prune580.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.4b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ 1 (+ (* 1.0 N) (* N N)))
0.0b
(+ (* 1.0 N) (* N N))
0.5b
(atan2 1.0 (+ 1 (+ (* 1.0 N) (* N N))))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
10×add-log-exp
5×*-un-lft-identity
4×sum-log
3×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt add-cbrt-cube
2×+-commutative flip3-+ flip-+
1×associate-+r+ distribute-rgt-out distribute-lft-out
Counts
3 → 33
Calls
3 calls:
47.0ms
(+ 1 (+ (* 1.0 N) (* N N)))
13.0ms
(+ (* 1.0 N) (* N N))
1.0ms
(atan2 1.0 (+ 1 (+ (* 1.0 N) (* N N))))

series212.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(+ 1 (+ (* 1.0 N) (* N N)))
146.0ms
(+ (* 1.0 N) (* N N))
12.0ms
(atan2 1.0 (+ 1 (+ (* 1.0 N) (* N N))))

simplify8.8s

Counts
42 → 42
Iterations
IterNodes
done5004
32341
2649
1192
063

prune441.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

localize67.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (cbrt N) (cbrt N))
0.6b
(cbrt N)
0.6b
(cbrt N)
0.6b
(cbrt N)

rewrite195.0ms

Algorithm
rewrite-expression-head
Rules
25×cbrt-prod
23×add-sqr-sqrt
15×add-cube-cbrt *-un-lft-identity
11×pow1
9×pow1/3
6×add-exp-log swap-sqr associate-*r* associate-*l*
4×add-cbrt-cube add-log-exp unswap-sqr
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod
Counts
4 → 73
Calls
4 calls:
26.0ms
(* (cbrt N) (cbrt N))
2.0ms
(cbrt N)
2.0ms
(cbrt N)
7.0ms
(cbrt N)

series3.4s

Counts
4 → 12
Calls
4 calls:
1.1s
(* (cbrt N) (cbrt N))
780.0ms
(cbrt N)
602.0ms
(cbrt N)
866.0ms
(cbrt N)

simplify15.3s

Counts
85 → 85
Iterations
IterNodes
done5002
43625
31001
2372
1137
061

prune1.5s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.4b

regimes267.0ms

Accuracy

0% (0.0b remaining)

Error of 0.4b against oracle of 0.3b and baseline of 0.4b

bsearch0.0ms

simplify6.0ms

Iterations
IterNodes
done13
113
08

end12.0ms

sample5.6s

Algorithm
intervals
Results
3.7s2872×body1280valid
1.1s4010×body80valid
319.0ms631×body640valid
145.0ms332×body320valid
35.0ms155×body160valid