Details

Time bar (total: 8.6s)

sample54.0ms

Algorithm
intervals
Results
31.0ms103×body1280valid
7.0ms114×body80valid
5.0ms25×body640valid
2.0ms10×body320valid
1.0ms4×body160valid

simplify35.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
34.0ms
(- (atan (+ N 1)) (atan N))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.3b

localize13.0ms

Local error

Found 2 expressions with local error:

1.2b
(- (atan (+ N 1)) (atan N))
0.0b
(atan (+ N 1))

rewrite6.0ms

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:
Slowest
5.0ms
(- (atan (+ N 1)) (atan N))
1.0ms
(atan (+ N 1))

series14.0ms

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

simplify1.8s

Counts
32 → 46
Calls
32 calls:
Slowest
216.0ms
(fma (* (cbrt (atan (+ N 1))) (cbrt (atan (+ N 1)))) (cbrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
187.0ms
(fma (sqrt (atan (+ N 1))) (sqrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
165.0ms
(fma 1 (atan (+ N 1)) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
146.0ms
(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))
130.0ms
(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))

prune440.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 1 expressions with local error:

0.1b
(atan2 1 (fma N (+ N 1) 1))

rewrite1.0ms

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 insert-posit16 log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
Slowest
1.0ms
(atan2 1 (fma N (+ N 1) 1))

series3.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
3.0ms
(atan2 1 (fma N (+ N 1) 1))

simplify76.0ms

Counts
3 → 13
Calls
3 calls:
Slowest
32.0ms
(atan2 1 (fma N (+ N 1) 1))
26.0ms
(atan2 1 (fma N (+ N 1) 1))
17.0ms
(atan2 1 (fma N (+ N 1) 1))

prune136.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 3 expressions with local error:

0.4b
(expm1 (log1p (atan2 1 (fma N (+ N 1) 1))))
0.4b
(log1p (atan2 1 (fma N (+ N 1) 1)))
0.1b
(atan2 1 (fma N (+ N 1) 1))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
4×expm1-log1p-u
3×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 log1p-expm1-u add-log-exp
1×log1p-udef expm1-log1p log1p-expm1 expm1-udef
Counts
3 → 34
Calls
3 calls:
Slowest
0.0ms
(log1p (atan2 1 (fma N (+ N 1) 1)))
0.0ms
(expm1 (log1p (atan2 1 (fma N (+ N 1) 1))))
0.0ms
(atan2 1 (fma N (+ N 1) 1))

series215.0ms

Counts
3 → 9
Calls
3 calls:
Slowest
130.0ms
(expm1 (log1p (atan2 1 (fma N (+ N 1) 1))))
82.0ms
(log1p (atan2 1 (fma N (+ N 1) 1)))
3.0ms
(atan2 1 (fma N (+ N 1) 1))

simplify254.0ms

Counts
10 → 43
Calls
10 calls:
Slowest
42.0ms
(log (+ (atan2 1 (fma N (+ N 1) 1)) 1))
32.0ms
(atan2 1 (fma N (+ N 1) 1))
29.0ms
(log (+ (atan2 1 (fma N (+ N 1) 1)) 1))
27.0ms
(atan2 1 (fma N (+ N 1) 1))
27.0ms
(atan2 1 (fma N (+ N 1) 1))

prune379.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

16.5b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
16.5b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
0.6b
(* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1))))
0.4b
(expm1 (log1p (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1))))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
24×sqrt-prod
21×pow1
14×*-un-lft-identity add-cube-cbrt
10×sqrt-pow1 pow1/2
8×swap-sqr
6×add-cbrt-cube associate-*r* associate-*l* add-exp-log
5×pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×rem-sqrt-square
1×pow2 expm1-log1p rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod expm1-udef
Counts
4 → 96
Calls
4 calls:
Slowest
10.0ms
(* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1))))
3.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
2.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
0.0ms
(expm1 (log1p (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1))))))

series152.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
120.0ms
(expm1 (log1p (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1))))))
18.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
12.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
2.0ms
(* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1))))

simplify1.9s

Counts
83 → 108
Calls
83 calls:
Slowest
133.0ms
(* (* (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (atan2 1 (fma N (+ N 1) 1)))) (* (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
92.0ms
(* (* (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1))))) (* (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1))))))
43.0ms
(sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))
43.0ms
(sqrt (* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1)))))
40.0ms
(sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))

prune1.0s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

0% (0.5b remaining)

Error of 0.8b against oracle of 0.3b and baseline of 0.8b

bsearch1.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
915.0ms2885×body1280valid
479.0ms320×body320valid
269.0ms4033×body80valid
140.0ms613×body640valid
18.0ms149×body160valid