Details

Time bar (total: 17.6s)

sample70.0ms

Algorithm
intervals
Results
41.0ms89×body1280valid
11.0ms134×body80valid
6.0ms17×body640valid
3.0ms12×body320valid
1.0ms4×body160valid

simplify11.0ms

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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.1b

localize11.0ms

Local error

Found 1 expressions with local error:

0.9b
(- (atan (+ N 1)) (atan N))

rewrite6.0ms

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
Counts
1 → 30
Calls
1 calls:
Slowest
5.0ms
(- (atan (+ N 1)) (atan N))

series12.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
12.0ms
(- (atan (+ N 1)) (atan N))

simplify3.1s

Counts
46 → 33
Calls
46 calls:
Slowest
502.0ms
(* (* (- (atan (+ N 1)) (atan N)) (- (atan (+ N 1)) (atan N))) (- (atan (+ N 1)) (atan N)))
229.0ms
(- (pow (atan (+ N 1)) 3) (pow (atan N) 3))
217.0ms
(fma (* (cbrt (atan (+ N 1))) (cbrt (atan (+ N 1)))) (cbrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
198.0ms
(fma (sqrt (atan (+ N 1))) (sqrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
186.0ms
(fma 1 (atan (+ N 1)) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))

prune279.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize13.0ms

Local error

Found 2 expressions with local error:

0.4b
(atan2 1 (fma N (+ N 1) 1))
0.0b
(fma N (+ N 1) 1)

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
2×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
1×fma-udef
Counts
2 → 21
Calls
2 calls:
Slowest
0.0ms
(atan2 1 (fma N (+ N 1) 1))
0.0ms
(fma N (+ N 1) 1)

series31.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
29.0ms
(fma N (+ N 1) 1)
2.0ms
(atan2 1 (fma N (+ N 1) 1))

simplify1.6s

Counts
27 → 27
Calls
27 calls:
Slowest
663.0ms
(* (* (fma N (+ N 1) 1) (fma N (+ N 1) 1)) (fma N (+ N 1) 1))
88.0ms
(* (* (atan2 1 (fma N (+ N 1) 1)) (atan2 1 (fma N (+ N 1) 1))) (atan2 1 (fma N (+ N 1) 1)))
57.0ms
(* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1))))
54.0ms
(+ N (+ (pow N 2) 1))
53.0ms
(log (atan2 1 (fma N (+ N 1) 1)))

prune247.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

localize35.0ms

Local error

Found 4 expressions with local error:

14.2b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
14.2b
(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))

rewrite14.0ms

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
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)))
1.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
0.0ms
(atan2 1 (fma N (+ N 1) 1))

series42.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
22.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
14.0ms
(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))

simplify5.3s

Counts
117 → 106
Calls
117 calls:
Slowest
209.0ms
(* (* (* (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)))))
201.0ms
(* (* (* (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)))))
134.0ms
(exp (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
132.0ms
(* (* (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))))))
75.0ms
(sqrt (* (cbrt (atan2 1 (fma N (+ N 1) 1))) (cbrt (atan2 1 (fma N (+ N 1) 1)))))

prune1.0s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.4b

localize34.0ms

Local error

Found 4 expressions with local error:

14.2b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
14.2b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
14.2b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
0.4b
(atan2 1 (fma N (+ N 1) 1))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×sqrt-prod
7×pow1 *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 58
Calls
4 calls:
Slowest
2.0ms
(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))

series66.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
22.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
21.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
20.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
3.0ms
(atan2 1 (fma N (+ N 1) 1))

simplify3.0s

Counts
73 → 70
Calls
73 calls:
Slowest
90.0ms
(* (* (atan2 1 (fma N (+ N 1) 1)) (atan2 1 (fma N (+ N 1) 1))) (atan2 1 (fma N (+ N 1) 1)))
84.0ms
(* (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (atan2 1 (fma N (+ N 1) 1))))
75.0ms
(* (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (atan2 1 (fma N (+ N 1) 1))))
75.0ms
(* (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))) (sqrt (atan2 1 (fma N (+ N 1) 1))))
73.0ms
(expm1 (sqrt (atan2 1 (fma N (+ N 1) 1))))

prune674.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 0.4b

regimes113.0ms

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
923.0ms2839×body1280valid
491.0ms323×body320valid
243.0ms4066×body80valid
136.0ms627×body640valid
18.0ms145×body160valid