Details

Time bar (total: 9.3s)

sample37.0ms

Algorithm
intervals
Results
20.0ms98×body1280valid
5.0ms120×body80valid
3.0ms20×body640valid
1.0ms10×body320valid
1.0ms8×body160valid

simplify21.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
21.0ms
(- (atan (+ N 1)) (atan N))

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

localize14.0ms

Local error

Found 2 expressions with local error:

2.6b
(- (atan (+ N 1)) (atan N))
0.0b
(atan (+ N 1))

rewrite14.0ms

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
10.0ms
(- (atan (+ N 1)) (atan N))
2.0ms
(atan (+ N 1))

series22.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
19.0ms
(- (atan (+ N 1)) (atan N))
3.0ms
(atan (+ N 1))

simplify1.8s

Counts
32 → 46
Calls
32 calls:
Slowest
210.0ms
(fma (* (cbrt (atan (+ N 1))) (cbrt (atan (+ N 1)))) (cbrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
204.0ms
(fma 1 (atan (+ N 1)) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
194.0ms
(fma (sqrt (atan (+ N 1))) (sqrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
156.0ms
(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))
145.0ms
(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))

prune439.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 1 expressions with local error:

0.3b
(atan2 1 (fma N (+ N 1) 1))

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 insert-posit16 log1p-expm1-u add-log-exp
Counts
1 → 10
Calls
1 calls:
Slowest
0.0ms
(atan2 1 (fma N (+ N 1) 1))

series6.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
6.0ms
(atan2 1 (fma N (+ N 1) 1))

simplify70.0ms

Counts
3 → 13
Calls
3 calls:
Slowest
31.0ms
(atan2 1 (fma N (+ N 1) 1))
20.0ms
(atan2 1 (fma N (+ N 1) 1))
17.0ms
(atan2 1 (fma N (+ N 1) 1))

prune117.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

16.3b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
16.3b
(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))))
0.3b
(atan2 1 (fma N (+ N 1) 1))

rewrite13.0ms

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 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Counts
4 → 94
Calls
4 calls:
Slowest
9.0ms
(* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1))))
1.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
1.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
0.0ms
(atan2 1 (fma N (+ N 1) 1))

series51.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
22.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
21.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
4.0ms
(* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1))))
3.0ms
(atan2 1 (fma N (+ N 1) 1))

simplify2.3s

Counts
82 → 106
Calls
82 calls:
Slowest
171.0ms
(* (* (* (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)))))
115.0ms
(* (* (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))))))
47.0ms
(sqrt (* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1)))))
44.0ms
(sqrt (* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1)))))
42.0ms
(* (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1)))))

prune1.0s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

16.3b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
16.3b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
16.3b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
0.3b
(atan2 1 (fma N (+ N 1) 1))

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 insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 58
Calls
4 calls:
Slowest
1.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
1.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
1.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
0.0ms
(atan2 1 (fma N (+ N 1) 1))

series46.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
17.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
14.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
12.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
2.0ms
(atan2 1 (fma N (+ N 1) 1))

simplify714.0ms

Counts
27 → 70
Calls
27 calls:
Slowest
43.0ms
(sqrt (* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1)))))
42.0ms
(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))))
36.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
36.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))

prune749.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.2b

regimes43.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.0s2844×body1280valid
296.0ms4019×body80valid
195.0ms655×body640valid
61.0ms314×body320valid
23.0ms168×body160valid