Details

Time bar (total: 8.2s)

sample73.0ms

Algorithm
intervals
Results
35.0ms92×body1280valid
17.0ms127×body80valid
6.0ms19×body640valid
3.0ms13×body320valid
1.0ms5×body160valid

simplify20.0ms

Counts
1 → 1

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.2b

localize22.0ms

Local error

Found 2 expressions with local error:

1.6b
(- (atan (+ N 1)) (atan N))
0.0b
(atan (+ N 1))

rewrite13.0ms

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))

series14.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
12.0ms
(- (atan (+ N 1)) (atan N))
2.0ms
(atan (+ N 1))

simplify920.0ms

Counts
46 → 46

prune247.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.4b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
5×*-un-lft-identity
4×add-log-exp
3×add-sqr-sqrt fma-def add-cube-cbrt
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
1×+-commutative associate-+r+ sum-log flip3-+ flip-+ fma-udef distribute-lft-out
Counts
2 → 29
Calls
2 calls:
Slowest
4.0ms
(+ 1 (fma N N N))
0.0ms
(atan2 1 (+ 1 (fma N N N)))

series21.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
19.0ms
(+ 1 (fma N N N))
2.0ms
(atan2 1 (+ 1 (fma N N N)))

simplify1.3s

Counts
35 → 35

prune208.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
5×*-un-lft-identity
4×add-log-exp
3×add-sqr-sqrt fma-def add-cube-cbrt
2×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
1×+-commutative associate-+l+ sum-log flip3-+ flip-+ fma-udef distribute-lft-out
Counts
2 → 29
Calls
2 calls:
Slowest
5.0ms
(+ (fma N N 1) N)
0.0ms
(atan2 1 (+ (fma N N 1) N))

series22.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
20.0ms
(+ (fma N N 1) N)
2.0ms
(atan2 1 (+ (fma N N 1) N))

simplify1.2s

Counts
35 → 35

prune206.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

localize15.0ms

Local error

Found 4 expressions with local error:

15.5b
(sqrt (atan2 1 (+ 1 (fma N N N))))
15.5b
(sqrt (atan2 1 (+ 1 (fma N N N))))
0.6b
(* (sqrt (atan2 1 (+ 1 (fma N N N)))) (sqrt (atan2 1 (+ 1 (fma N N N)))))
0.4b
(atan2 1 (+ 1 (fma N N N)))

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
9.0ms
(* (sqrt (atan2 1 (+ 1 (fma N N N)))) (sqrt (atan2 1 (+ 1 (fma N N N)))))
4.0ms
(sqrt (atan2 1 (+ 1 (fma N N N))))
1.0ms
(sqrt (atan2 1 (+ 1 (fma N N N))))
0.0ms
(atan2 1 (+ 1 (fma N N N)))

series31.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
14.0ms
(sqrt (atan2 1 (+ 1 (fma N N N))))
12.0ms
(sqrt (atan2 1 (+ 1 (fma N N N))))
3.0ms
(* (sqrt (atan2 1 (+ 1 (fma N N N)))) (sqrt (atan2 1 (+ 1 (fma N N N)))))
2.0ms
(atan2 1 (+ 1 (fma N N N)))

simplify2.0s

Counts
106 → 106

prune648.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.3b

regimes34.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.2s

Algorithm
intervals
Results
725.0ms2849×body1280valid
208.0ms4070×body80valid
111.0ms638×body640valid
68.0ms300×body320valid
14.0ms143×body160valid