Details

Time bar (total: 13.5s)

sample77.0ms

Algorithm
intervals
Results
20.0ms58×body1280valid
20.0ms252×body80nan
10.0ms41×body640valid
8.0ms122×body80valid
3.0ms22×body320valid
1.0ms13×body160valid

simplify4.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
2107
done107

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.2b

localize11.0ms

Local error

Found 2 expressions with local error:

3.2b
(- (log (+ N 1.0)) (log N))
3.4b
(log (+ N 1.0))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
22×*-un-lft-identity
16×pow1 add-sqr-sqrt prod-diff
14×add-cube-cbrt log-pow
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:
29.0ms
(- (log (+ N 1.0)) (log N))
10.0ms
(log (+ N 1.0))

series259.0ms

Counts
2 → 6
Calls
2 calls:
172.0ms
(- (log (+ N 1.0)) (log N))
87.0ms
(log (+ N 1.0))

simplify1.3s

Counts
71 → 71
Iterations

Useful iterations: done (1.3s)

IterNodesCost
01271052
1288863
21086705
done5001614

prune224.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (/ 1.0 N) (/ 0.5 (* N N)))
0.2b
(/ 0.3333333333333333 (pow N 3))
0.5b
(/ 0.5 (* N N))
10.8b
(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))

rewrite326.0ms

Algorithm
rewrite-expression-head
Rules
292×times-frac
220×add-sqr-sqrt
217×*-un-lft-identity
210×add-cube-cbrt
182×prod-diff
93×associate-+r+
44×div-inv
40×fma-def
21×unpow-prod-down cube-prod
14×add-exp-log
13×fma-neg associate-/r*
11×add-cbrt-cube add-log-exp
7×cube-mult unpow3 sqr-pow
6×associate-/l*
5×div-exp
4×pow1 expm1-log1p-u log1p-expm1-u difference-of-squares
3×cbrt-undiv frac-add
2×sub-neg flip3-- frac-2neg diff-log clear-num sum-log frac-sub flip-- distribute-lft-out distribute-lft-out--
1×+-commutative pow-to-exp associate-+r- flip3-+ pow-exp prod-exp cbrt-unprod flip-+
Counts
4 → 367
Calls
4 calls:
40.0ms
(- (/ 1.0 N) (/ 0.5 (* N N)))
16.0ms
(/ 0.3333333333333333 (pow N 3))
15.0ms
(/ 0.5 (* N N))
217.0ms
(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))

series289.0ms

Counts
4 → 12
Calls
4 calls:
126.0ms
(- (/ 1.0 N) (/ 0.5 (* N N)))
53.0ms
(/ 0.3333333333333333 (pow N 3))
55.0ms
(/ 0.5 (* N N))
56.0ms
(+ (/ 0.3333333333333333 (pow N 3)) (- (/ 1.0 N) (/ 0.5 (* N N))))

simplify765.0ms

Counts
379 → 379
Iterations

Useful iterations: done (746.0ms)

IterNodesCost
04448644
110617221
done50016378

prune1.5s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize72.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt N)
0.6b
(cbrt N)
10.8b
(+ (/ 0.3333333333333333 (pow N 3)) (fma (/ (sqrt 1.0) (* (cbrt N) (cbrt N))) (/ (sqrt 1.0) (cbrt N)) (- (/ (/ 0.5 N) N))))
45.1b
(fma (- (/ 0.5 N)) (/ 1 N) (* (/ 0.5 N) (/ 1 N)))

rewrite64.0ms

Algorithm
rewrite-expression-head
Rules
40×fma-def
36×times-frac
30×*-un-lft-identity
28×add-sqr-sqrt add-cube-cbrt
9×unpow-prod-down cube-prod
6×cbrt-prod add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×cube-mult unpow3 sqr-pow
2×pow1/3 fma-udef
1×+-commutative associate-+r+ flip3-+ sum-log flip-+ div-inv distribute-lft-out
Counts
4 → 91
Calls
4 calls:
1.0ms
(cbrt N)
2.0ms
(cbrt N)
54.0ms
(+ (/ 0.3333333333333333 (pow N 3)) (fma (/ (sqrt 1.0) (* (cbrt N) (cbrt N))) (/ (sqrt 1.0) (cbrt N)) (- (/ (/ 0.5 N) N))))
1.0ms
(fma (- (/ 0.5 N)) (/ 1 N) (* (/ 0.5 N) (/ 1 N)))

series1.4s

Counts
4 → 12
Calls
4 calls:
316.0ms
(cbrt N)
732.0ms
(cbrt N)
239.0ms
(+ (/ 0.3333333333333333 (pow N 3)) (fma (/ (sqrt 1.0) (* (cbrt N) (cbrt N))) (/ (sqrt 1.0) (cbrt N)) (- (/ (/ 0.5 N) N))))
99.0ms
(fma (- (/ 0.5 N)) (/ 1 N) (* (/ 0.5 N) (/ 1 N)))

simplify795.0ms

Counts
103 → 103
Iterations

Useful iterations: done (792.0ms)

IterNodesCost
090998
1209964
2866781
done5001680

prune671.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

localize48.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt N)
0.6b
(cbrt N)
10.8b
(+ (/ 0.3333333333333333 (pow N 3)) (fma (/ (sqrt 1.0) (* (cbrt N) (* (cbrt (sqrt N)) (cbrt (sqrt N))))) (/ (sqrt 1.0) (cbrt N)) (- (/ (/ 0.5 N) N))))
45.1b
(fma (- (/ 0.5 N)) (/ 1 N) (* (/ 0.5 N) (/ 1 N)))

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
40×fma-def
36×times-frac
30×*-un-lft-identity
28×add-sqr-sqrt add-cube-cbrt
9×unpow-prod-down cube-prod
6×cbrt-prod add-log-exp
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×cube-mult unpow3 sqr-pow
2×pow1/3 fma-udef
1×+-commutative associate-+r+ flip3-+ sum-log flip-+ div-inv distribute-lft-out
Counts
4 → 91
Calls
4 calls:
2.0ms
(cbrt N)
2.0ms
(cbrt N)
82.0ms
(+ (/ 0.3333333333333333 (pow N 3)) (fma (/ (sqrt 1.0) (* (cbrt N) (* (cbrt (sqrt N)) (cbrt (sqrt N))))) (/ (sqrt 1.0) (cbrt N)) (- (/ (/ 0.5 N) N))))
1.0ms
(fma (- (/ 0.5 N)) (/ 1 N) (* (/ 0.5 N) (/ 1 N)))

series952.0ms

Counts
4 → 12
Calls
4 calls:
319.0ms
(cbrt N)
275.0ms
(cbrt N)
251.0ms
(+ (/ 0.3333333333333333 (pow N 3)) (fma (/ (sqrt 1.0) (* (cbrt N) (* (cbrt (sqrt N)) (cbrt (sqrt N))))) (/ (sqrt 1.0) (cbrt N)) (- (/ (/ 0.5 N) N))))
107.0ms
(fma (- (/ 0.5 N)) (/ 1 N) (* (/ 0.5 N) (/ 1 N)))

simplify869.0ms

Counts
103 → 103
Iterations

Useful iterations: done (861.0ms)

IterNodesCost
01211184
13111141
21340888
done5000877

prune835.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes82.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 31.4b

bsearch1.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02131
12331
done2331

end0.0ms

sample2.8s

Algorithm
intervals
Results
892.0ms1782×body1280valid
473.0ms8028×body80nan
446.0ms4057×body80valid
346.0ms1228×body640valid
115.0ms606×body320valid
38.0ms327×body160valid