Details

Time bar (total: 31.8s)

sample106.0ms

Algorithm
intervals
Results
33.0ms62×body1280valid
18.0ms272×body80nan
16.0ms40×body640valid
12.0ms123×body80valid
5.0ms19×body320valid
2.0ms12×body160valid

simplify49.0ms

Counts
1 → 1
Iterations
IterNodes
done10
210
19
06

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.1b

localize45.0ms

Local error

Found 2 expressions with local error:

2.6b
(log (+ N 1.0))
4.4b
(- (log (+ N 1.0)) (log N))

rewrite77.0ms

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-+ insert-posit16 log1p-expm1-u distribute-lft-out add-log-exp
1×sub-neg flip3-- diff-log rem-log-exp flip-- difference-of-squares
Counts
2 → 67
Calls
2 calls:
22.0ms
(log (+ N 1.0))
42.0ms
(- (log (+ N 1.0)) (log N))

series223.0ms

Counts
2 → 6
Calls
2 calls:
66.0ms
(log (+ N 1.0))
157.0ms
(- (log (+ N 1.0)) (log N))

simplify5.1s

Counts
73 → 73
Iterations
IterNodes
done5001
31996
2700
1288
0129

prune594.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize141.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N))) (/ 1.0 N))
0.1b
(/ (/ 0.3333333333333333 N) (* N N))
0.7b
(/ -1 (* N N))
11.4b
(fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N)))

rewrite119.0ms

Algorithm
rewrite-expression-head
Rules
34×times-frac
23×*-un-lft-identity
21×add-sqr-sqrt add-cbrt-cube add-exp-log add-cube-cbrt
16×associate-/l*
8×cbrt-undiv div-exp
6×add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u div-inv
3×fma-def prod-exp cbrt-unprod
2×clear-num associate-/r* frac-2neg fma-udef
1×+-commutative associate-+l+ sum-log flip3-+ flip-+ distribute-lft-out associate-/l/
Counts
4 → 103
Calls
4 calls:
26.0ms
(+ (fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N))) (/ 1.0 N))
62.0ms
(/ (/ 0.3333333333333333 N) (* N N))
24.0ms
(/ -1 (* N N))
1.0ms
(fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N)))

series323.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(+ (fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N))) (/ 1.0 N))
61.0ms
(/ (/ 0.3333333333333333 N) (* N N))
50.0ms
(/ -1 (* N N))
155.0ms
(fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N)))

simplify3.8s

Counts
115 → 115
Iterations
IterNodes
done5002
21511
1437
0185

prune1.2s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize237.0ms

Local error

Found 4 expressions with local error:

11.4b
(fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N)))
20.2b
(cbrt (+ (fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N))) (/ 1.0 N)))
20.2b
(cbrt (+ (fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N))) (/ 1.0 N)))
20.2b
(cbrt (+ (fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N))) (/ 1.0 N)))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ pow1/3 flip-+ distribute-lft-out
1×fma-udef
Counts
4 → 62
Calls
4 calls:
2.0ms
(fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N)))
17.0ms
(cbrt (+ (fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N))) (/ 1.0 N)))
17.0ms
(cbrt (+ (fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N))) (/ 1.0 N)))
23.0ms
(cbrt (+ (fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N))) (/ 1.0 N)))

series960.0ms

Counts
4 → 12
Calls
4 calls:
150.0ms
(fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N)))
302.0ms
(cbrt (+ (fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N))) (/ 1.0 N)))
235.0ms
(cbrt (+ (fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N))) (/ 1.0 N)))
272.0ms
(cbrt (+ (fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N))) (/ 1.0 N)))

simplify5.8s

Counts
74 → 74
Iterations
IterNodes
done5002
33105
2784
1282
0118

prune1.0s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize361.0ms

Local error

Found 4 expressions with local error:

11.4b
(fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N)))
11.4b
(fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N)))
20.2b
(cbrt (+ (fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N))) (/ 1.0 N)))
20.2b
(cbrt (+ (fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N))) (/ 1.0 N)))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
8×cbrt-prod
6×add-sqr-sqrt add-cube-cbrt
4×expm1-log1p-u pow1 cbrt-div add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×flip3-+ pow1/3 flip-+ fma-udef distribute-lft-out
Counts
4 → 56
Calls
4 calls:
1.0ms
(fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N)))
1.0ms
(fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N)))
16.0ms
(cbrt (+ (fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N))) (/ 1.0 N)))
23.0ms
(cbrt (+ (fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N))) (/ 1.0 N)))

series914.0ms

Counts
4 → 12
Calls
4 calls:
195.0ms
(fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N)))
134.0ms
(fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N)))
304.0ms
(cbrt (+ (fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N))) (/ 1.0 N)))
281.0ms
(cbrt (+ (fma (/ -1 (* N N)) 0.5 (/ (/ 0.3333333333333333 N) (* N N))) (/ 1.0 N)))

simplify6.0s

Counts
68 → 68
Iterations
IterNodes
done5002
33105
2784
1282
0118

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

regimes135.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.3b

bsearch55.0ms

Steps
ItersRangePoint
6
3173.18146809654
23716.851585869685
9848.91410832408

simplify15.0ms

Iterations
IterNodes
done20
120
018

end0.0ms

sample3.3s

Algorithm
intervals
Results
1.1s1790×body1280valid
697.0ms8083×body80nan
470.0ms1270×body640valid
413.0ms4031×body80valid
155.0ms606×body320valid
73.0ms303×body160valid