Details

Time bar (total: 7.8s)

sample56.0ms

Algorithm
intervals
Results
28.0ms79×body1280valid
10.0ms142×body80valid
6.0ms21×body640valid
2.0ms7×body320valid
1.0ms7×body160valid

simplify21.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.7b

localize21.0ms

Local error

Found 2 expressions with local error:

1.9b
(- (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))

series14.0ms

Calls
2 calls:
Slowest
11.0ms
(- (atan (+ N 1)) (atan N))
2.0ms
(atan (+ N 1))

simplify1.0s

Calls
32 calls:
Slowest
73.0ms
(fma (* (cbrt (atan (+ N 1))) (cbrt (atan (+ N 1)))) (cbrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
66.0ms
(fma (* (cbrt (atan (+ N 1))) (cbrt (atan (+ N 1)))) (cbrt (atan (+ N 1))) (- (* (sqrt (atan N)) (sqrt (atan N)))))
65.0ms
(fma (* (cbrt (atan (+ N 1))) (cbrt (atan (+ N 1)))) (cbrt (atan (+ N 1))) (- (* (atan N) 1)))
65.0ms
(fma 1 (atan (+ N 1)) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
61.0ms
(fma 1 (atan (+ N 1)) (- (* (atan N) 1)))

prune403.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.3b

localize15.0ms

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))

simplify68.0ms

Calls
3 calls:
Slowest
30.0ms
(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))

prune151.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize5.0ms

Local error

Found 4 expressions with local error:

13.5b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
13.5b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
0.7b
(* (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))

rewrite12.0ms

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
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))

series31.0ms

Calls
4 calls:
Slowest
12.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
11.0ms
(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))))
4.0ms
(atan2 1 (fma N (+ N 1) 1))

simplify1.0s

Calls
42 calls:
Slowest
103.0ms
(* (* (* (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)))))
40.0ms
(sqrt (* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1)))))
37.0ms
(sqrt (cbrt (atan2 1 (fma N (+ N 1) 1))))
37.0ms
(+ (log (sqrt (atan2 1 (fma N (+ N 1) 1)))) (log (sqrt (atan2 1 (fma N (+ N 1) 1)))))
37.0ms
(sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))

prune842.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

localize8.0ms

Local error

Found 4 expressions with local error:

13.5b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
13.5b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
13.5b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
0.7b
(* (* (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))))

rewrite25.0ms

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
20.0ms
(* (* (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)))

series65.0ms

Calls
4 calls:
Slowest
19.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
19.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
18.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
8.0ms
(* (* (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))))

simplify1.3s

Calls
42 calls:
Slowest
146.0ms
(* (* (* (* (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)))))
142.0ms
(* (* (* (* (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)))))
62.0ms
(* (* (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)))))
43.0ms
(* (* (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))))

prune786.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 0.3b

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

sample1.9s

Algorithm
intervals
Results
851.0ms2814×body1280valid
507.0ms662×body640valid
266.0ms4035×body80valid
95.0ms190×body160valid
49.0ms299×body320valid