Details

Time bar (total: 10.3s)

sample59.0ms

Algorithm
intervals
Results
36.0ms112×body1280valid
8.0ms112×body80valid
5.0ms17×body640valid
1.0ms7×body320valid
1.0ms8×body160valid

simplify5.0ms

Counts
1 → 1
Iterations
IterNodes
312
212
111
06

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.5b

localize22.0ms

Local error

Found 2 expressions with local error:

0.0b
(atan (+ N 1))
1.6b
(- (atan (+ N 1)) (atan N))

rewrite7.0ms

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 insert-posit16 log1p-expm1-u
1×sub-neg flip3-- diff-log diff-atan flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 40
Calls
2 calls:
1.0ms
(atan (+ N 1))
5.0ms
(- (atan (+ N 1)) (atan N))

series13.0ms

Counts
2 → 6
Calls
2 calls:
2.0ms
(atan (+ N 1))
12.0ms
(- (atan (+ N 1)) (atan N))

simplify730.0ms

Counts
46 → 46
Iterations
IterNodes
42149
3771
2288
1140
067

prune329.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ 1 (fma N N N))
0.6b
(atan2 1 (+ 1 (fma N N N)))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
5×*-un-lft-identity
4×add-log-exp
3×add-sqr-sqrt fma-def add-cube-cbrt
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
1×+-commutative associate-+r+ sum-log flip3-+ flip-+ fma-udef distribute-lft-out
Counts
2 → 29
Calls
2 calls:
4.0ms
(+ 1 (fma N N N))
0.0ms
(atan2 1 (+ 1 (fma N N N)))

series29.0ms

Counts
2 → 6
Calls
2 calls:
25.0ms
(+ 1 (fma N N N))
4.0ms
(atan2 1 (+ 1 (fma N N N)))

simplify1.2s

Counts
35 → 35
Iterations
IterNodes
43407
3493
2185
197
047

prune269.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (fma N N 1) N)
0.6b
(atan2 1 (+ (fma N N 1) N))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
5×*-un-lft-identity
4×add-log-exp
3×add-sqr-sqrt fma-def add-cube-cbrt
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
1×+-commutative associate-+l+ sum-log flip3-+ flip-+ fma-udef distribute-lft-out
Counts
2 → 29
Calls
2 calls:
5.0ms
(+ (fma N N 1) N)
0.0ms
(atan2 1 (+ (fma N N 1) N))

series31.0ms

Counts
2 → 6
Calls
2 calls:
28.0ms
(+ (fma N N 1) N)
2.0ms
(atan2 1 (+ (fma N N 1) N))

simplify2.4s

Counts
35 → 35
Iterations
IterNodes
45160
31136
2319
1103
046

prune205.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(atan2 1 (fma (* (cbrt (fma N N 1)) (cbrt (fma N N 1))) (cbrt (fma N N 1)) N))
18.8b
(cbrt (fma N N 1))
18.8b
(cbrt (fma N N 1))
18.8b
(cbrt (fma N N 1))

rewrite3.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×pow1/3
Counts
4 → 52
Calls
4 calls:
0.0ms
(atan2 1 (fma (* (cbrt (fma N N 1)) (cbrt (fma N N 1))) (cbrt (fma N N 1)) N))
1.0ms
(cbrt (fma N N 1))
1.0ms
(cbrt (fma N N 1))
1.0ms
(cbrt (fma N N 1))

series305.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(atan2 1 (fma (* (cbrt (fma N N 1)) (cbrt (fma N N 1))) (cbrt (fma N N 1)) N))
100.0ms
(cbrt (fma N N 1))
96.0ms
(cbrt (fma N N 1))
105.0ms
(cbrt (fma N N 1))

simplify2.5s

Counts
64 → 64
Iterations
IterNodes
56483
41965
3743
2302
1125
063

prune480.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.5b

regimes55.0ms

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
28
18
05

end0.0ms

sample1.5s

Algorithm
intervals
Results
1.0s2910×body1280valid
245.0ms4042×body80valid
106.0ms609×body640valid
40.0ms292×body320valid
14.0ms147×body160valid