Details

Time bar (total: 8.0s)

sample44.0ms

Algorithm
intervals
Results
24.0ms104×body1280valid
6.0ms121×body80valid
4.0ms19×body640valid
1.0ms8×body320valid
0.0ms4×body160valid

simplify20.0ms

Calls
1 calls:
Slowest
20.0ms
(- (atan (+ N 1)) (atan N))

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.5b

localize21.0ms

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
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
Calls
2 calls:
Slowest
10.0ms
(- (atan (+ N 1)) (atan N))
1.0ms
(atan (+ N 1))

series31.0ms

Calls
2 calls:
Slowest
28.0ms
(- (atan (+ N 1)) (atan N))
3.0ms
(atan (+ N 1))

simplify901.0ms

Calls
32 calls:
Slowest
90.0ms
(fma (sqrt (atan (+ N 1))) (sqrt (atan (+ N 1))) (- (* (sqrt (atan N)) (sqrt (atan N)))))
62.0ms
(fma 1 (atan (+ N 1)) (- (* (sqrt (atan N)) (sqrt (atan N)))))
57.0ms
(fma 1 (atan (+ N 1)) (- (* (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)))))
49.0ms
(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))

prune348.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 1 expressions with local error:

0.3b
(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
4.0ms
(atan2 1 (fma N (+ N 1) 1))

simplify72.0ms

Calls
3 calls:
Slowest
31.0ms
(atan2 1 (fma N (+ N 1) 1))
24.0ms
(atan2 1 (fma N (+ N 1) 1))
15.0ms
(atan2 1 (fma N (+ N 1) 1))

prune132.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

17.5b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
17.5b
(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))))
0.3b
(atan2 1 (fma N (+ N 1) 1))

rewrite15.0ms

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
10.0ms
(* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1))))
2.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
2.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
0.0ms
(atan2 1 (fma N (+ N 1) 1))

series28.0ms

Calls
4 calls:
Slowest
14.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
10.0ms
(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))

simplify987.0ms

Calls
42 calls:
Slowest
68.0ms
(* (* (* (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
(* (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1)))))
36.0ms
(sqrt (* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1)))))
36.0ms
(sqrt (cbrt (atan2 1 (fma N (+ N 1) 1))))
33.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))

prune783.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

17.5b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
17.5b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
17.5b
(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))))

rewrite22.0ms

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
18.0ms
(* (* (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)))

series45.0ms

Calls
4 calls:
Slowest
17.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
13.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
12.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
3.0ms
(* (* (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))))

simplify1.4s

Calls
42 calls:
Slowest
178.0ms
(* (* (* (* (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)))))
139.0ms
(* (* (* (* (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)))))
65.0ms
(* (* (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))))
56.0ms
(* (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))) (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)))))

prune889.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.2b

regimes38.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample2.1s

Algorithm
intervals
Results
1.0s2797×body1280valid
475.0ms303×body320valid
348.0ms4120×body80valid
154.0ms626×body640valid
21.0ms154×body160valid