Details

Time bar (total: 7.1s)

sample37.0ms

Algorithm
intervals
Results
21.0ms95×body1280valid
6.0ms133×body80valid
3.0ms17×body640valid
1.0ms7×body160valid
1.0ms4×body320valid

simplify11.0ms

Calls
1 calls:
Slowest
11.0ms
(- (atan (+ N 1)) (atan N))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.8b

localize10.0ms

Local error

Found 1 expressions with local error:

2.0b
(- (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))

series12.0ms

Calls
1 calls:
Slowest
12.0ms
(- (atan (+ N 1)) (atan N))

simplify875.0ms

Calls
29 calls:
Slowest
77.0ms
(fma 1 (atan (+ N 1)) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
63.0ms
(fma (* (cbrt (atan (+ N 1))) (cbrt (atan (+ N 1)))) (cbrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
56.0ms
(fma (sqrt (atan (+ N 1))) (sqrt (atan (+ N 1))) (- (* (sqrt (atan N)) (sqrt (atan N)))))
56.0ms
(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))
51.0ms
(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))

prune258.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.6b

localize13.0ms

Local error

Found 1 expressions with local error:

0.6b
(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
Calls
1 calls:
Slowest
0.0ms
(atan2 1 (fma N (+ N 1) 1))

series4.0ms

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

simplify69.0ms

Calls
3 calls:
Slowest
32.0ms
(atan2 1 (fma N (+ N 1) 1))
18.0ms
(atan2 1 (fma N (+ N 1) 1))
18.0ms
(atan2 1 (fma N (+ N 1) 1))

prune92.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.6b

localize6.0ms

Local error

Found 4 expressions with local error:

15.0b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
15.0b
(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))))
0.6b
(atan2 1 (fma N (+ N 1) 1))

rewrite16.0ms

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
12.0ms
(* (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))

series41.0ms

Calls
4 calls:
Slowest
18.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
18.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
3.0ms
(* (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))

simplify1.2s

Calls
42 calls:
Slowest
105.0ms
(* (* (* (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)))))
41.0ms
(+ (log (sqrt (atan2 1 (fma N (+ N 1) 1)))) (log (sqrt (atan2 1 (fma N (+ N 1) 1)))))
40.0ms
(sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))
38.0ms
(sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))
37.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))

prune861.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.5b

localize15.0ms

Local error

Found 4 expressions with local error:

15.4b
(cbrt (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
15.4b
(cbrt (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
15.4b
(cbrt (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
15.0b
(sqrt (atan2 1 (fma N (+ N 1) 1)))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×*-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×cbrt-prod pow1/3 sqrt-prod
1×rem-sqrt-square pow1/2
Calls
4 calls:
Slowest
3.0ms
(cbrt (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
3.0ms
(cbrt (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
3.0ms
(cbrt (* (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)))

series521.0ms

Calls
4 calls:
Slowest
187.0ms
(cbrt (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
177.0ms
(cbrt (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
140.0ms
(cbrt (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
17.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))

simplify448.0ms

Calls
19 calls:
Slowest
38.0ms
(cbrt (sqrt (atan2 1 (fma N (+ N 1) 1))))
37.0ms
(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)
33.0ms
(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)
27.0ms
(sqrt (* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1)))))
27.0ms
(cbrt (sqrt (atan2 1 (fma N (+ N 1) 1))))

prune766.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 0.5b

regimes83.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.0s2864×body1280valid
305.0ms4048×body80valid
202.0ms632×body640valid
61.0ms302×body320valid
59.0ms154×body160valid