Details

Time bar (total: 12.7s)

sample70.0ms

Algorithm
intervals
Results
37.0ms94×body1280valid
11.0ms125×body80valid
6.0ms19×body640valid
3.0ms12×body320valid
1.0ms6×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: 17.2b

localize39.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
4×add-sqr-sqrt *-un-lft-identity add-log-exp
2×pow1 add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
1×sub-neg flip3-- diff-log diff-atan flip-- distribute-lft-out-- difference-of-squares
Counts
2 → 24
Calls
2 calls:
Slowest
8.0ms
(- (atan (+ N 1)) (atan N))
2.0ms
(atan (+ N 1))

series23.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
20.0ms
(- (atan (+ N 1)) (atan N))
3.0ms
(atan (+ N 1))

simplify1.3s

Counts
34 → 30
Calls
34 calls:
Slowest
353.0ms
(* (* (- (atan (+ N 1)) (atan N)) (- (atan (+ N 1)) (atan N))) (- (atan (+ N 1)) (atan N)))
241.0ms
(- (pow (atan (+ N 1)) 3) (pow (atan N) 3))
113.0ms
(- (* (atan (+ N 1)) (atan (+ N 1))) (* (atan N) (atan N)))
64.0ms
(/ (exp (atan (+ N 1))) (exp (atan N)))
61.0ms
(* (* (atan (+ N 1)) (atan (+ N 1))) (atan (+ N 1)))

prune202.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 1 expressions with local error:

0.2b
(atan2 1 (+ 1 (* (+ N 1) N)))

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
1×add-sqr-sqrt pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
Counts
1 → 8
Calls
1 calls:
Slowest
0.0ms
(atan2 1 (+ 1 (* (+ N 1) N)))

series2.0ms

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

simplify500.0ms

Counts
11 → 11
Calls
11 calls:
Slowest
82.0ms
(* (* (atan2 1 (+ 1 (* (+ N 1) N))) (atan2 1 (+ 1 (* (+ N 1) N)))) (atan2 1 (+ 1 (* (+ N 1) N))))
59.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
49.0ms
(* (cbrt (atan2 1 (+ 1 (* (+ N 1) N)))) (cbrt (atan2 1 (+ 1 (* (+ N 1) N)))))
45.0ms
(sqrt (atan2 1 (+ 1 (* (+ N 1) N))))
42.0ms
(real->posit16 (atan2 1 (+ 1 (* (+ N 1) N))))

prune120.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize26.0ms

Local error

Found 2 expressions with local error:

0.2b
(atan2 1 (+ N (+ (* N N) 1)))
0.0b
(+ N (+ (* N N) 1))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
7×add-log-exp
4×*-un-lft-identity
3×sum-log
2×add-sqr-sqrt pow1 add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16
1×+-commutative associate-+r+ flip3-+ flip-+ distribute-lft-out
Counts
2 → 23
Calls
2 calls:
Slowest
26.0ms
(+ N (+ (* N N) 1))
1.0ms
(atan2 1 (+ N (+ (* N N) 1)))

series31.0ms

Counts
2 → 6
Calls
2 calls:
Slowest
26.0ms
(+ N (+ (* N N) 1))
5.0ms
(atan2 1 (+ N (+ (* N N) 1)))

simplify2.6s

Counts
30 → 29
Calls
30 calls:
Slowest
441.0ms
(* (exp N) (* (exp (* N N)) (exp 1)))
316.0ms
(+ (pow N 3) (pow (+ (* N N) 1) 3))
274.0ms
(+ (* N N) (- (* (+ (* N N) 1) (+ (* N N) 1)) (* N (+ (* N N) 1))))
197.0ms
(- (* N N) (* (+ (* N N) 1) (+ (* N N) 1)))
163.0ms
(* (exp N) (exp (+ (* N N) 1)))

prune192.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

localize33.0ms

Local error

Found 4 expressions with local error:

13.9b
(sqrt (atan2 1 (+ N (+ (* N N) 1))))
13.9b
(sqrt (atan2 1 (+ N (+ (* N N) 1))))
0.6b
(* (sqrt (atan2 1 (+ N (+ (* N N) 1)))) (sqrt (atan2 1 (+ N (+ (* N N) 1)))))
0.2b
(atan2 1 (+ N (+ (* N N) 1)))

rewrite12.0ms

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×insert-posit16 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 → 86
Calls
4 calls:
Slowest
9.0ms
(* (sqrt (atan2 1 (+ N (+ (* N N) 1)))) (sqrt (atan2 1 (+ N (+ (* N N) 1)))))
1.0ms
(sqrt (atan2 1 (+ N (+ (* N N) 1))))
1.0ms
(sqrt (atan2 1 (+ N (+ (* N N) 1))))
0.0ms
(atan2 1 (+ N (+ (* N N) 1)))

series44.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
21.0ms
(sqrt (atan2 1 (+ N (+ (* N N) 1))))
15.0ms
(sqrt (atan2 1 (+ N (+ (* N N) 1))))
4.0ms
(* (sqrt (atan2 1 (+ N (+ (* N N) 1)))) (sqrt (atan2 1 (+ N (+ (* N N) 1)))))
4.0ms
(atan2 1 (+ N (+ (* N N) 1)))

simplify4.9s

Counts
109 → 98
Calls
109 calls:
Slowest
217.0ms
(* (* (* (sqrt (atan2 1 (+ N (+ (* N N) 1)))) (sqrt (atan2 1 (+ N (+ (* N N) 1))))) (* (sqrt (atan2 1 (+ N (+ (* N N) 1)))) (sqrt (atan2 1 (+ N (+ (* N N) 1)))))) (* (sqrt (atan2 1 (+ N (+ (* N N) 1)))) (sqrt (atan2 1 (+ N (+ (* N N) 1))))))
168.0ms
(* (* (* (sqrt (atan2 1 (+ N (+ (* N N) 1)))) (sqrt (atan2 1 (+ N (+ (* N N) 1))))) (sqrt (atan2 1 (+ N (+ (* N N) 1))))) (* (* (sqrt (atan2 1 (+ N (+ (* N N) 1)))) (sqrt (atan2 1 (+ N (+ (* N N) 1))))) (sqrt (atan2 1 (+ N (+ (* N N) 1))))))
156.0ms
(* (* (cbrt (sqrt (atan2 1 (+ N (+ (* N N) 1))))) (cbrt (sqrt (atan2 1 (+ N (+ (* N N) 1)))))) (* (cbrt (sqrt (atan2 1 (+ N (+ (* N N) 1))))) (cbrt (sqrt (atan2 1 (+ N (+ (* N N) 1)))))))
154.0ms
(exp (* (sqrt (atan2 1 (+ N (+ (* N N) 1)))) (sqrt (atan2 1 (+ N (+ (* N N) 1))))))
105.0ms
(* (* (sqrt (atan2 1 (+ N (+ (* N N) 1)))) (sqrt (atan2 1 (+ N (+ (* N N) 1))))) (sqrt (atan2 1 (+ N (+ (* N N) 1)))))

prune794.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.2b

regimes33.0ms

Accuracy

0% (0.0b remaining)

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

bsearch1.0ms

end0.0ms

sample1.8s

Algorithm
intervals
Results
1.1s2826×body1280valid
318.0ms4092×body80valid
154.0ms632×body640valid
60.0ms314×body320valid
19.0ms136×body160valid