Details

Time bar (total: 13.2s)

sample48.0ms

Algorithm
intervals
Results
23.0ms84×body1280valid
9.0ms142×body80valid
4.0ms19×body640valid
2.0ms9×body320valid
0.0ms2×body160valid

simplify21.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.4b

localize40.0ms

Local error

Found 2 expressions with local error:

0.9b
(- (atan (+ N 1)) (atan N))
0.0b
(atan (+ N 1))

rewrite12.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
1×sub-neg flip3-- diff-log diff-atan flip-- distribute-lft-out-- difference-of-squares
Calls
2 calls:
Slowest
9.0ms
(- (atan (+ N 1)) (atan N))
2.0ms
(atan (+ N 1))

series22.0ms

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

simplify243.0ms

Calls
12 calls:
Slowest
69.0ms
(/ (exp (atan (+ N 1))) (exp (atan N)))
30.0ms
(- (+ N 1) N)
28.0ms
(+ 1 (* (+ N 1) N))
20.0ms
(- (atan (+ N 1)) (atan N))
17.0ms
(- (atan (+ N 1)) (atan N))

prune225.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 2 expressions with local error:

0.3b
(atan2 1 (+ 1 (* (+ N 1) N)))
0.0b
(* (+ N 1) N)

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity
4×pow1 add-cbrt-cube associate-*l* add-exp-log add-cube-cbrt
3×associate-*r*
2×associate-*l/ insert-posit16 add-log-exp
1×flip3-+ pow-prod-down prod-exp *-commutative cbrt-unprod flip-+ distribute-lft-out unswap-sqr
Calls
2 calls:
Slowest
23.0ms
(* (+ N 1) N)
0.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

series58.0ms

Calls
2 calls:
Slowest
55.0ms
(* (+ N 1) N)
3.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

simplify837.0ms

Calls
17 calls:
Slowest
369.0ms
(* (* (* (+ N 1) (+ N 1)) (+ N 1)) (* (* N N) N))
106.0ms
(* (+ (pow N 3) (pow 1 3)) N)
104.0ms
(* (- (* N N) (* 1 1)) N)
56.0ms
(atan2 1 (+ N (+ (pow N 2) 1)))
41.0ms
(atan2 1 (+ N (+ (pow N 2) 1)))

prune276.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize28.0ms

Local error

Found 4 expressions with local error:

14.6b
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
14.6b
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.6b
(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
0.3b
(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite12.0ms

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×insert-posit16 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
Calls
4 calls:
Slowest
9.0ms
(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
1.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
1.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
0.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

series40.0ms

Calls
4 calls:
Slowest
20.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
14.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
3.0ms
(* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))
2.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

simplify2.6s

Calls
82 calls:
Slowest
203.0ms
(* (* (* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (* (* (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))))
132.0ms
(* (* (cbrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (cbrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))) (* (cbrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N))))) (cbrt (sqrt (atan2 1 (+ 1 (* (+ N 1) N)))))))
61.0ms
(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
60.0ms
(sqrt (atan2 1 (+ N (+ (pow N 2) 1))))
58.0ms
(atan2 1 (+ N (+ (pow N 2) 1)))

prune927.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize24.0ms

Local error

Found 4 expressions with local error:

8.8b
(cbrt (* (atan2 1 (+ (* (+ N 1) N) 1)) (* (atan2 1 (+ (* (+ N 1) N) 1)) (atan2 1 (+ (* (+ N 1) N) 1)))))
0.5b
(* (atan2 1 (+ (* (+ N 1) N) 1)) (* (atan2 1 (+ (* (+ N 1) N) 1)) (atan2 1 (+ (* (+ N 1) N) 1))))
0.3b
(atan2 1 (+ (* (+ N 1) N) 1))
0.3b
(atan2 1 (+ (* (+ N 1) N) 1))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
41×add-sqr-sqrt
36×associate-*r*
28×cbrt-prod
18×pow1
17×*-un-lft-identity add-cube-cbrt
14×unswap-sqr
12×associate-*l*
9×add-cbrt-cube add-exp-log
8×swap-sqr *-commutative
5×pow-prod-up
4×cube-unmult insert-posit16 add-log-exp
3×pow-prod-down prod-exp cbrt-unprod
2×rem-cbrt-cube
1×pow2 pow-plus pow1/3 pow-sqr
Calls
4 calls:
Slowest
20.0ms
(* (atan2 1 (+ (* (+ N 1) N) 1)) (* (atan2 1 (+ (* (+ N 1) N) 1)) (atan2 1 (+ (* (+ N 1) N) 1))))
15.0ms
(cbrt (* (atan2 1 (+ (* (+ N 1) N) 1)) (* (atan2 1 (+ (* (+ N 1) N) 1)) (atan2 1 (+ (* (+ N 1) N) 1)))))
0.0ms
(atan2 1 (+ (* (+ N 1) N) 1))
0.0ms
(atan2 1 (+ (* (+ N 1) N) 1))

series69.0ms

Calls
4 calls:
Slowest
57.0ms
(* (atan2 1 (+ (* (+ N 1) N) 1)) (* (atan2 1 (+ (* (+ N 1) N) 1)) (atan2 1 (+ (* (+ N 1) N) 1))))
4.0ms
(atan2 1 (+ (* (+ N 1) N) 1))
4.0ms
(atan2 1 (+ (* (+ N 1) N) 1))
4.0ms
(cbrt (* (atan2 1 (+ (* (+ N 1) N) 1)) (* (atan2 1 (+ (* (+ N 1) N) 1)) (atan2 1 (+ (* (+ N 1) N) 1)))))

simplify4.8s

Calls
81 calls:
Slowest
245.0ms
(* (* (* (atan2 1 (+ (* (+ N 1) N) 1)) (atan2 1 (+ (* (+ N 1) N) 1))) (atan2 1 (+ (* (+ N 1) N) 1))) (* (* (* (atan2 1 (+ (* (+ N 1) N) 1)) (atan2 1 (+ (* (+ N 1) N) 1))) (* (atan2 1 (+ (* (+ N 1) N) 1)) (atan2 1 (+ (* (+ N 1) N) 1)))) (* (atan2 1 (+ (* (+ N 1) N) 1)) (atan2 1 (+ (* (+ N 1) N) 1)))))
244.0ms
(cbrt (* (atan2 1 (+ (* (+ N 1) N) 1)) (* (* (cbrt (atan2 1 (+ (* (+ N 1) N) 1))) (cbrt (atan2 1 (+ (* (+ N 1) N) 1)))) (* (cbrt (atan2 1 (+ (* (+ N 1) N) 1))) (cbrt (atan2 1 (+ (* (+ N 1) N) 1)))))))
217.0ms
(* (* (* (atan2 1 (+ (* (+ N 1) N) 1)) (atan2 1 (+ (* (+ N 1) N) 1))) (atan2 1 (+ (* (+ N 1) N) 1))) (* (* (* (atan2 1 (+ (* (+ N 1) N) 1)) (atan2 1 (+ (* (+ N 1) N) 1))) (atan2 1 (+ (* (+ N 1) N) 1))) (* (* (atan2 1 (+ (* (+ N 1) N) 1)) (atan2 1 (+ (* (+ N 1) N) 1))) (atan2 1 (+ (* (+ N 1) N) 1)))))
211.0ms
(pow (atan2 1 (+ N (+ (pow N 2) 1))) 3)
185.0ms
(pow (atan2 1 (+ N (+ (pow N 2) 1))) 3)

prune995.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.3b

regimes26.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.0s2965×body1280valid
375.0ms3943×body80valid
204.0ms636×body640valid
57.0ms302×body320valid
21.0ms154×body160valid