Details

Time bar (total: 8.2s)

sample35.0ms

Algorithm
intervals
Results
18.0ms95×body1280valid
6.0ms132×body80valid
2.0ms15×body640valid
1.0ms10×body320valid
0.0ms4×body160valid

simplify20.0ms

Counts
1 → 1
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: 13.3b

localize21.0ms

Local error

Found 1 expressions with local error:

1.5b
(- (atan (+ N 1)) (atan N))

rewrite8.0ms

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
8.0ms
(- (atan (+ N 1)) (atan N))

series24.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
24.0ms
(- (atan (+ N 1)) (atan N))

simplify1.4s

Counts
29 → 33
Calls
29 calls:
Slowest
201.0ms
(fma (* (cbrt (atan (+ N 1))) (cbrt (atan (+ N 1)))) (cbrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
149.0ms
(fma (sqrt (atan (+ N 1))) (sqrt (atan (+ N 1))) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
142.0ms
(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))
111.0ms
(fma 1 (atan (+ N 1)) (- (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N))))))
111.0ms
(fma (- (cbrt (atan N))) (* (cbrt (atan N)) (cbrt (atan N))) (* (cbrt (atan N)) (* (cbrt (atan N)) (cbrt (atan N)))))

prune203.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 1 expressions with local error:

0.2b
(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
Counts
1 → 10
Calls
1 calls:
Slowest
1.0ms
(atan2 1 (fma N (+ N 1) 1))

series3.0ms

Counts
1 → 3
Calls
1 calls:
Slowest
3.0ms
(atan2 1 (fma N (+ N 1) 1))

simplify85.0ms

Counts
3 → 13
Calls
3 calls:
Slowest
31.0ms
(atan2 1 (fma N (+ N 1) 1))
31.0ms
(atan2 1 (fma N (+ N 1) 1))
21.0ms
(atan2 1 (fma N (+ N 1) 1))

prune91.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

16.3b
(sqrt (atan2 1 (fma N (+ N 1) 1)))
16.3b
(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))))
0.2b
(atan2 1 (fma N (+ N 1) 1))

rewrite15.0ms

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 (fma N (+ N 1) 1))) (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))

series35.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
13.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
12.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
5.0ms
(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))))

simplify1.7s

Counts
82 → 106
Calls
82 calls:
Slowest
142.0ms
(* (* (* (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)))))
86.0ms
(* (* (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))))))
37.0ms
(sqrt (sqrt (atan2 1 (fma N (+ N 1) 1))))
33.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))
32.0ms
(* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1))))

prune796.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

16.8b
(cbrt (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
16.8b
(cbrt (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
16.8b
(cbrt (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
16.3b
(sqrt (atan2 1 (fma N (+ N 1) 1)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt
5×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×cbrt-prod pow1/3 sqrt-prod
1×rem-sqrt-square sqrt-pow1 pow1/2
Counts
4 → 52
Calls
4 calls:
Slowest
5.0ms
(cbrt (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
5.0ms
(cbrt (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
5.0ms
(cbrt (* (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)))

series411.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
143.0ms
(cbrt (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
128.0ms
(cbrt (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
126.0ms
(cbrt (* (sqrt (atan2 1 (fma N (+ N 1) 1))) (sqrt (atan2 1 (fma N (+ N 1) 1)))))
13.0ms
(sqrt (atan2 1 (fma N (+ N 1) 1)))

simplify1.0s

Counts
20 → 64
Calls
20 calls:
Slowest
105.0ms
(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)
94.0ms
(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)
90.0ms
(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)
87.0ms
(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)
86.0ms
(pow (atan2 1 (fma N (+ N 1) 1)) 1/3)

prune645.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.1b

regimes57.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.4s

Algorithm
intervals
Results
883.0ms2903×body1280valid
247.0ms4040×body80valid
148.0ms613×body640valid
47.0ms306×body320valid
15.0ms138×body160valid