Details

Time bar (total: 14.2s)

sample90.0ms

Algorithm
intervals
Results
27.0ms61×body1280valid
14.0ms49×body640valid
14.0ms282×body80nan
9.0ms123×body80valid
3.0ms17×body320valid
1.0ms6×body160valid

simplify8.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune30.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.4b

localize22.0ms

Local error

Found 2 expressions with local error:

1.5b
(- (log (+ N 1.0)) (log N))
3.1b
(log (+ N 1.0))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
16×add-sqr-sqrt pow1 prod-diff
14×log-pow add-cube-cbrt
11×log-prod
4×log-div fma-neg associate--l+ distribute-lft-out--
3×add-exp-log associate--r+
2×associate--l- expm1-log1p-u flip3-+ add-cbrt-cube flip-+ log1p-expm1-u distribute-lft-out add-log-exp
1×sub-neg flip3-- diff-log rem-log-exp flip-- difference-of-squares
Counts
2 → 65
Calls
2 calls:
12.0ms
(- (log (+ N 1.0)) (log N))
5.0ms
(log (+ N 1.0))

series621.0ms

Counts
2 → 6
Calls
2 calls:
121.0ms
(- (log (+ N 1.0)) (log N))
500.0ms
(log (+ N 1.0))

simplify1.5s

Counts
71 → 71
Iterations
IterNodes
done5001
21090
1287
0127

prune253.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5)))
0.1b
(* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))
0.1b
(/ (/ 1 N) N)

rewrite142.0ms

Algorithm
rewrite-expression-head
Rules
201×times-frac
167×add-sqr-sqrt
152×*-un-lft-identity
149×add-cube-cbrt
78×prod-diff
43×associate-*l*
41×distribute-rgt-in distribute-lft-in
27×add-exp-log
17×add-cbrt-cube
16×div-inv
13×associate-/l*
12×div-exp
8×pow1
6×cbrt-undiv associate-*r*
5×prod-exp unswap-sqr
3×expm1-log1p-u associate-/r* cbrt-unprod log1p-expm1-u add-log-exp
2×frac-times rec-exp sub-neg flip3-- 1-exp associate-*r/ flip-- difference-of-squares pow-div
1×clear-num frac-2neg pow-prod-down associate-*l/ *-commutative fma-udef pow-flip distribute-lft-out-- inv-pow associate-/l/
Counts
3 → 246
Calls
3 calls:
0.0ms
(fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5)))
107.0ms
(* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))
19.0ms
(/ (/ 1 N) N)

series189.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(fma (/ 1 N) 1.0 (* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5)))
104.0ms
(* (/ (/ 1 N) N) (- (/ 0.3333333333333333 N) 0.5))
30.0ms
(/ (/ 1 N) N)

simplify1.2s

Counts
255 → 255
Iterations
IterNodes
done5001
11227
0416

prune1.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize36.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* N N) N)
0.4b
(/ 0.3333333333333333 (* (* N N) N))
0.4b
(/ 0.5 (* N N))
12.8b
(+ (/ 0.3333333333333333 (* (* N N) N)) (- (/ 1.0 N) (/ 0.5 (* N N))))

rewrite205.0ms

Algorithm
rewrite-expression-head
Rules
111×times-frac
93×associate-+r+
91×*-un-lft-identity prod-diff
87×add-sqr-sqrt
86×add-cube-cbrt
23×pow1 add-cbrt-cube add-exp-log div-inv
9×add-log-exp
7×fma-def prod-exp cbrt-unprod
6×pow-plus pow-prod-up associate-/l*
5×cbrt-undiv div-exp
4×expm1-log1p-u log1p-expm1-u
3×associate-*r* pow-prod-down frac-add
2×pow2 clear-num associate-/r* sum-log frac-2neg pow-sqr distribute-lft-out
1×+-commutative associate-+r- sub-neg flip3-+ flip3-- diff-log associate-*l* pow3 *-commutative frac-sub flip-+ flip-- distribute-lft-out-- unswap-sqr
Counts
4 → 198
Calls
4 calls:
20.0ms
(* (* N N) N)
28.0ms
(/ 0.3333333333333333 (* (* N N) N))
12.0ms
(/ 0.5 (* N N))
137.0ms
(+ (/ 0.3333333333333333 (* (* N N) N)) (- (/ 1.0 N) (/ 0.5 (* N N))))

series190.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (* N N) N)
66.0ms
(/ 0.3333333333333333 (* (* N N) N))
36.0ms
(/ 0.5 (* N N))
41.0ms
(+ (/ 0.3333333333333333 (* (* N N) N)) (- (/ 1.0 N) (/ 0.5 (* N N))))

simplify1.2s

Counts
210 → 210
Iterations
IterNodes
done5000
1985
0385

prune1.0s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize93.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (/ 1.0 N))
0.6b
(cbrt (/ 1.0 N))
12.8b
(+ (/ 0.3333333333333333 (* (* N N) N)) (fma (* (cbrt (/ 1.0 N)) (cbrt (/ 1.0 N))) (cbrt (/ 1.0 N)) (- (* (/ 1 (* N N)) 0.5))))
15.8b
(fma (- (/ 1 (* N N))) 0.5 (* (/ 1 (* N N)) 0.5))

rewrite60.0ms

Algorithm
rewrite-expression-head
Rules
26×cbrt-prod
22×*-un-lft-identity
21×times-frac
20×add-sqr-sqrt add-cube-cbrt
7×fma-def
6×add-log-exp
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log log1p-expm1-u
3×div-inv
2×cbrt-div pow1/3 fma-udef
1×+-commutative associate-+r+ sum-log flip3-+ flip-+ distribute-lft-out
Counts
4 → 80
Calls
4 calls:
3.0ms
(cbrt (/ 1.0 N))
4.0ms
(cbrt (/ 1.0 N))
48.0ms
(+ (/ 0.3333333333333333 (* (* N N) N)) (fma (* (cbrt (/ 1.0 N)) (cbrt (/ 1.0 N))) (cbrt (/ 1.0 N)) (- (* (/ 1 (* N N)) 0.5))))
1.0ms
(fma (- (/ 1 (* N N))) 0.5 (* (/ 1 (* N N)) 0.5))

series856.0ms

Counts
4 → 12
Calls
4 calls:
316.0ms
(cbrt (/ 1.0 N))
279.0ms
(cbrt (/ 1.0 N))
173.0ms
(+ (/ 0.3333333333333333 (* (* N N) N)) (fma (* (cbrt (/ 1.0 N)) (cbrt (/ 1.0 N))) (cbrt (/ 1.0 N)) (- (* (/ 1 (* N N)) 0.5))))
87.0ms
(fma (- (/ 1 (* N N))) 0.5 (* (/ 1 (* N N)) 0.5))

simplify1.3s

Counts
92 → 92
Iterations
IterNodes
done5001
2900
1244
0126

prune703.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes37.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.5b

bsearch28.0ms

Steps
ItersRangePoint
7
1126.7541422477805
58098.925141855936
8023.454188180856

simplify2.0ms

Iterations
IterNodes
done20
120
017

end0.0ms

sample2.9s

Algorithm
intervals
Results
1.2s1747×body1280valid
420.0ms1272×body640valid
414.0ms4055×body80valid
383.0ms7994×body80nan
148.0ms624×body320valid
33.0ms302×body160valid