Details

Time bar (total: 18.6s)

sample44.0ms

Algorithm
intervals
Results
23.0ms102×body1280valid
7.0ms122×body80valid
4.0ms20×body640valid
1.0ms8×body320valid
0.0ms4×body160valid

simplify8.0ms

Counts
1 → 1
Iterations
IterNodes
310
210
19
06

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.4b

localize23.0ms

Local error

Found 2 expressions with local error:

0.0b
(atan (+ N 1))
1.3b
(- (atan (+ N 1)) (atan N))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×prod-diff add-cube-cbrt
4×add-log-exp
3×fma-neg
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u
1×sub-neg flip3-- diff-log diff-atan flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 38
Calls
2 calls:
2.0ms
(atan (+ N 1))
10.0ms
(- (atan (+ N 1)) (atan N))

series45.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(atan (+ N 1))
42.0ms
(- (atan (+ N 1)) (atan N))

simplify1.3s

Counts
44 → 44
Iterations
IterNodes
42128
3760
2283
1136
065

prune379.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.7b

localize12.0ms

Local error

Found 1 expressions with local error:

0.7b
(atan2 1 (+ 1 (fma N N N)))

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
1×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt log1p-expm1-u add-log-exp
Counts
1 → 9
Calls
1 calls:
0.0ms
(atan2 1 (+ 1 (fma N N N)))

series4.0ms

Counts
1 → 3
Calls
1 calls:
4.0ms
(atan2 1 (+ 1 (fma N N N)))

simplify6.9s

Counts
12 → 12
Iterations
IterNodes
107341
91513
8542
7260
6153
595
466
348
231
121
016

prune116.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.7b
(atan2 1 (+ 1 (fma N N N)))
0.7b
(atan2 1 (+ 1 (fma N N N)))
17.0b
(sqrt (atan2 1 (+ 1 (fma N N N))))
17.0b
(sqrt (atan2 1 (+ 1 (fma N N N))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 48
Calls
4 calls:
0.0ms
(atan2 1 (+ 1 (fma N N N)))
0.0ms
(atan2 1 (+ 1 (fma N N N)))
2.0ms
(sqrt (atan2 1 (+ 1 (fma N N N))))
1.0ms
(sqrt (atan2 1 (+ 1 (fma N N N))))

series44.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan2 1 (+ 1 (fma N N N)))
2.0ms
(atan2 1 (+ 1 (fma N N N)))
17.0ms
(sqrt (atan2 1 (+ 1 (fma N N N))))
23.0ms
(sqrt (atan2 1 (+ 1 (fma N N N))))

simplify4.3s

Counts
60 → 60
Iterations
IterNodes
85896
71455
6608
5241
4129
387
259
140
031

prune554.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.6b

localize35.0ms

Local error

Found 4 expressions with local error:

0.7b
(atan2 1 (+ 1 (fma N N N)))
17.0b
(sqrt (atan2 1 (+ 1 (fma N N N))))
17.0b
(sqrt (atan2 1 (+ 1 (fma N N N))))
17.0b
(sqrt (atan2 1 (+ 1 (fma N N N))))

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 54
Calls
4 calls:
0.0ms
(atan2 1 (+ 1 (fma N N N)))
1.0ms
(sqrt (atan2 1 (+ 1 (fma N N N))))
1.0ms
(sqrt (atan2 1 (+ 1 (fma N N N))))
1.0ms
(sqrt (atan2 1 (+ 1 (fma N N N))))

series58.0ms

Counts
4 → 12
Calls
4 calls:
2.0ms
(atan2 1 (+ 1 (fma N N N)))
13.0ms
(sqrt (atan2 1 (+ 1 (fma N N N))))
21.0ms
(sqrt (atan2 1 (+ 1 (fma N N N))))
22.0ms
(sqrt (atan2 1 (+ 1 (fma N N N))))

simplify2.9s

Counts
66 → 66
Iterations
IterNodes
85896
71455
6608
5241
4129
387
259
140
031

prune529.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.6b

regimes38.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Iterations
IterNodes
26
16
05

end0.0ms

sample1.2s

Algorithm
intervals
Results
644.0ms2908×body1280valid
218.0ms633×body640valid
178.0ms3965×body80valid
72.0ms329×body320valid
15.0ms165×body160valid