Details

Time bar (total: 12.4s)

sample58.0ms

Algorithm
intervals
Results
35.0ms93×body1280valid
9.0ms132×body80valid
4.0ms16×body640valid
1.0ms8×body320valid
1.0ms7×body160valid

simplify15.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
15.0ms
(- (atan (+ N 1)) (atan N))

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.5b

localize22.0ms

Local error

Found 2 expressions with local error:

1.7b
(- (atan (+ N 1)) (atan N))
0.0b
(atan (+ N 1))

rewrite14.0ms

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
Counts
2 → 40
Calls
2 calls:
Slowest
10.0ms
(- (atan (+ N 1)) (atan N))
2.0ms
(atan (+ N 1))

series21.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
19.0ms
(- (atan (+ N 1)) (atan N))
3.0ms
(atan (+ N 1))

simplify1.7s

Counts
32 → 46
Calls
32 calls:
Slowest
217.0ms
(fma (sqrt (atan (+ N 1))) (sqrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
204.0ms
(fma (* (cbrt (atan (+ N 1))) (cbrt (atan (+ N 1)))) (cbrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
195.0ms
(fma 1 (atan (+ N 1)) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
119.0ms
(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))
114.0ms
(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))

prune388.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 1 expressions with local error:

0.4b
(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
Counts
1 → 10
Calls
1 calls:
Slowest
0.0ms
(atan2 1 (fma N (+ N 1) 1))

series2.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
2.0ms
(atan2 1 (fma N (+ N 1) 1))

simplify63.0ms

Counts
3 → 13
Calls
3 calls:
Slowest
24.0ms
(atan2 1 (fma N (+ N 1) 1))
23.0ms
(atan2 1 (fma N (+ N 1) 1))
16.0ms
(atan2 1 (fma N (+ N 1) 1))

prune107.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.3b

localize16.0ms

Local error

Found 4 expressions with local error:

11.7b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
11.7b
(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))))
0.4b
(atan2 1 (fma N (+ N 1) 1))

rewrite16.0ms

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
Counts
4 → 94
Calls
4 calls:
Slowest
11.0ms
(* (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))

series32.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
16.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
12.0ms
(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))

simplify2.3s

Counts
82 → 106
Calls
82 calls:
Slowest
206.0ms
(* (* (* (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)))))
93.0ms
(* (* (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)))))
42.0ms
(* (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (cbrt (sqrt (atan2 1 (fma N (+ N 1) 1)))))
41.0ms
(* (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (sqrt (atan2 1 (fma N (+ N 1) 1)))))

prune995.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

localize42.0ms

Local error

Found 4 expressions with local error:

11.7b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
11.7b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
11.7b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
0.6b
(* (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))))))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
54×sqrt-pow1
45×pow1
30×pow1/2 pow-prod-up
16×add-sqr-sqrt
14×sqrt-prod
9×*-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt
7×pow-prod-down
6×associate-*l* pow-sqr
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-*r* *-commutative
Counts
4 → 97
Calls
4 calls:
Slowest
33.0ms
(* (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))))))
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)))

series52.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
23.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
12.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
12.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
4.0ms
(* (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))))))

simplify3.3s

Counts
87 → 109
Calls
87 calls:
Slowest
481.0ms
(* (* (* (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 (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)))))))
346.0ms
(* (* (* (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 (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)))))))
97.0ms
(* (atan2 1 (fma N (+ N 1) 1)) (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
91.0ms
(* (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))))))
89.0ms
(* (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))))))

prune1.1s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.3b

regimes121.0ms

Accuracy

0% (0.0b remaining)

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

bsearch2.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.0s2883×body1280valid
376.0ms4022×body80valid
221.0ms602×body640valid
68.0ms347×body320valid
21.0ms146×body160valid