Details

Time bar (total: 7.9s)

sample67.0ms

Algorithm
intervals
Results
36.0ms93×body1280valid
11.0ms125×body80valid
8.0ms24×body640valid
2.0ms8×body320valid
1.0ms6×body160valid

simplify19.0ms

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

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.3b

localize21.0ms

Local error

Found 1 expressions with local error:

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

rewrite10.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt *-un-lft-identity
9×prod-diff
8×add-cube-cbrt
3×fma-neg add-log-exp
1×expm1-log1p-u pow1 sub-neg flip3-- add-cbrt-cube diff-log diff-atan add-exp-log insert-posit16 log1p-expm1-u flip-- distribute-lft-out-- difference-of-squares
Calls
1 calls:
Slowest
9.0ms
(- (atan (+ N 1)) (atan N))

series18.0ms

Calls
1 calls:
Slowest
18.0ms
(- (atan (+ N 1)) (atan N))

simplify910.0ms

Calls
29 calls:
Slowest
62.0ms
(fma (* (cbrt (atan (+ N 1))) (cbrt (atan (+ N 1)))) (cbrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
59.0ms
(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))
59.0ms
(fma 1 (atan (+ N 1)) (- (* (sqrt (atan N)) (sqrt (atan N)))))
58.0ms
(fma 1 (atan (+ N 1)) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
52.0ms
(/ (exp (atan (+ N 1))) (exp (atan N)))

prune262.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize7.0ms

Local error

Found 1 expressions with local error:

0.2b
(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
Calls
1 calls:
Slowest
0.0ms
(atan2 1 (fma N (+ N 1) 1))

series2.0ms

Calls
1 calls:
Slowest
2.0ms
(atan2 1 (fma N (+ N 1) 1))

simplify59.0ms

Calls
3 calls:
Slowest
22.0ms
(atan2 1 (fma N (+ N 1) 1))
20.0ms
(atan2 1 (fma N (+ N 1) 1))
16.0ms
(atan2 1 (fma N (+ N 1) 1))

prune124.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize9.0ms

Local error

Found 4 expressions with local error:

16.7b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
16.7b
(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))))
0.2b
(atan2 1 (fma N (+ N 1) 1))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
10×*-un-lft-identity add-cube-cbrt
9×pow1
6×add-cbrt-cube pow1/2 associate-*r* associate-*l* add-exp-log
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square pow-prod-down pow-prod-up
1×pow2 rem-square-sqrt pow-plus sqrt-unprod prod-exp *-commutative cbrt-unprod
Calls
4 calls:
Slowest
6.0ms
(* (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))

series31.0ms

Calls
4 calls:
Slowest
13.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
13.0ms
(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))))
2.0ms
(atan2 1 (fma N (+ N 1) 1))

simplify1.1s

Calls
42 calls:
Slowest
77.0ms
(* (* (* (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)))))
42.0ms
(sqrt (* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1)))))
42.0ms
(+ (log (sqrt (atan2 1 (fma N (+ N 1) 1)))) (log (sqrt (atan2 1 (fma N (+ N 1) 1)))))
41.0ms
(* (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1)))))
39.0ms
(sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))

prune812.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 0.1b

localize12.0ms

Local error

Found 4 expressions with local error:

16.7b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
16.7b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
16.7b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
0.6b
(* (* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))) (sqrt (atan2 1 (fma N (+ N 1) 1))))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt sqrt-prod
10×pow1 pow1/2
9×*-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
6×associate-*r*
5×pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square prod-exp pow-prod-up cbrt-unprod
2×sqrt-unprod
1×pow-plus associate-*l* *-commutative
Calls
4 calls:
Slowest
19.0ms
(* (* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (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)))
1.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))

series64.0ms

Calls
4 calls:
Slowest
21.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
21.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
20.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
2.0ms
(* (* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))) (sqrt (atan2 1 (fma N (+ N 1) 1))))

simplify1.6s

Calls
42 calls:
Slowest
227.0ms
(* (* (* (* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))) (* (* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))) (sqrt (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)))))
188.0ms
(* (* (* (* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))) (* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))))) (* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (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)))))
64.0ms
(* (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))) (atan2 1 (fma N (+ N 1) 1)))
60.0ms
(* (* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))) (sqrt (atan2 1 (fma N (+ N 1) 1))))
58.0ms
(+ (log (* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))))) (log (sqrt (atan2 1 (fma N (+ N 1) 1)))))

prune979.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.1b

regimes51.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.1s2837×body1280valid
303.0ms4085×body80valid
154.0ms616×body640valid
58.0ms305×body320valid
21.0ms157×body160valid