Details

Time bar (total: 12.2s)

sample51.0ms

Algorithm
intervals
Results
28.0ms88×body1280valid
8.0ms128×body80valid
5.0ms22×body640valid
2.0ms12×body320valid
1.0ms6×body160valid

simplify18.0ms

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.6b

localize21.0ms

Local error

Found 1 expressions with local error:

1.8b
(- (atan (+ N 1)) (atan N))

rewrite12.0ms

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
11.0ms
(- (atan (+ N 1)) (atan N))

series23.0ms

Calls
1 calls:
Slowest
23.0ms
(- (atan (+ N 1)) (atan N))

simplify1.8s

Calls
29 calls:
Slowest
216.0ms
(fma (sqrt (atan (+ N 1))) (sqrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
202.0ms
(fma (* (cbrt (atan (+ N 1))) (cbrt (atan (+ N 1)))) (cbrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
171.0ms
(fma 1 (atan (+ N 1)) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
151.0ms
(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))
149.0ms
(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))

prune268.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 1 expressions with local error:

0.1b
(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
1.0ms
(atan2 1 (fma N (+ N 1) 1))

series3.0ms

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

simplify68.0ms

Calls
3 calls:
Slowest
35.0ms
(atan2 1 (fma N (+ N 1) 1))
16.0ms
(atan2 1 (fma N (+ N 1) 1))
16.0ms
(atan2 1 (fma N (+ N 1) 1))

prune91.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

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))))
0.1b
(atan2 1 (fma N (+ N 1) 1))

rewrite13.0ms

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×expm1-log1p-u insert-posit16 log1p-expm1-u 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 (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))

series34.0ms

Calls
4 calls:
Slowest
14.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
13.0ms
(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))))
3.0ms
(atan2 1 (fma N (+ N 1) 1))

simplify2.3s

Calls
82 calls:
Slowest
191.0ms
(* (* (* (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)))))
146.0ms
(* (* (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1))))) (* (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1))))))
45.0ms
(* (sqrt (* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1))))) (sqrt (* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1))))))
44.0ms
(+ (log (sqrt (atan2 1 (fma N (+ N 1) 1)))) (log (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)))))

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.0b

localize22.0ms

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)))
15.0b
(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))))

rewrite52.0ms

Algorithm
rewrite-expression-head
Rules
60×sqrt-pow1
51×pow1
36×pow1/2
34×pow-prod-up
16×add-sqr-sqrt
14×sqrt-prod
9×*-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
8×pow-sqr
7×pow-prod-down
6×pow-plus associate-*r*
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square prod-exp cbrt-unprod
2×sqrt-unprod swap-sqr unswap-sqr
1×associate-*l* *-commutative
Calls
4 calls:
Slowest
37.0ms
(* (* (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))))
8.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
3.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
2.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))

series72.0ms

Calls
4 calls:
Slowest
22.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
21.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
21.0ms
(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))))

simplify3.7s

Calls
94 calls:
Slowest
502.0ms
(* (* (* (* (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)))))
397.0ms
(* (* (* (* (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)))))
152.0ms
(* (* (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))))
141.0ms
(* (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))) (atan2 1 (fma N (+ N 1) 1)))
136.0ms
(* (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))) (atan2 1 (fma N (+ N 1) 1)))

prune905.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.0b

regimes32.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.5s

Algorithm
intervals
Results
851.0ms2887×body1280valid
391.0ms4045×body80valid
136.0ms641×body640valid
47.0ms280×body320valid
17.0ms147×body160valid