Details

Time bar (total: 18.6s)

sample90.0ms

Algorithm
intervals
Results
29.0ms55×body1280valid
15.0ms249×body80nan
14.0ms43×body640valid
11.0ms121×body80valid
5.0ms21×body320valid
2.0ms16×body160valid

simplify16.0ms

Counts
1 → 1
Iterations
IterNodes
313
213
111
06

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.7b

localize17.0ms

Local error

Found 1 expressions with local error:

4.5b
(- (log1p N) (log N))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×add-sqr-sqrt prod-diff
10×add-cube-cbrt
5×pow1
4×log-pow
3×log-prod fma-neg associate--r+
2×diff-log distribute-lft-out-- add-log-exp
1×expm1-log1p-u log1p-udef sub-neg flip3-- add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u flip-- difference-of-squares
Counts
1 → 37
Calls
1 calls:
7.0ms
(- (log1p N) (log N))

series76.0ms

Counts
1 → 3
Calls
1 calls:
76.0ms
(- (log1p N) (log N))

simplify2.1s

Counts
40 → 40
Iterations
IterNodes
42841
3991
2370
1185
083

prune369.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize42.0ms

Local error

Found 4 expressions with local error:

0.1b
(fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))
0.1b
(/ (/ 1 N) (* N N))
0.1b
(/ (/ 1 N) N)
12.2b
(fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
106×times-frac
60×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
35×add-exp-log
26×associate-/l*
21×pow1 add-cbrt-cube
18×div-exp
10×pow-div
9×cbrt-undiv
8×div-inv
5×pow-flip inv-pow
4×expm1-log1p-u associate-/r* prod-exp insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp 1-exp
2×pow2 clear-num frac-2neg pow-plus pow-sqr pow-prod-up cbrt-unprod fma-udef associate-/l/
Counts
4 → 160
Calls
4 calls:
0.0ms
(fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))
11.0ms
(/ (/ 1 N) (* N N))
9.0ms
(/ (/ 1 N) N)
1.0ms
(fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N)))

series222.0ms

Counts
4 → 12
Calls
4 calls:
112.0ms
(fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))
40.0ms
(/ (/ 1 N) (* N N))
40.0ms
(/ (/ 1 N) N)
29.0ms
(fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N)))

simplify4.3s

Counts
172 → 172
Iterations
IterNodes
36178
21396
1522
0235

prune1.7s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize46.0ms

Local error

Found 4 expressions with local error:

9.0b
(sqrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))))
9.0b
(sqrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))))
12.2b
(fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N)))
12.2b
(fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N)))

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
8×add-sqr-sqrt
6×pow1 *-un-lft-identity add-cube-cbrt sqrt-prod
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×rem-sqrt-square sqrt-pow1 pow1/2 fma-udef
Counts
4 → 54
Calls
4 calls:
2.0ms
(sqrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))))
2.0ms
(sqrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))))
0.0ms
(fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N)))
1.0ms
(fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N)))

series201.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(sqrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))))
73.0ms
(sqrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))))
27.0ms
(fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N)))
41.0ms
(fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N)))

simplify2.4s

Counts
66 → 66
Iterations
IterNodes
43860
31024
2320
1135
063

prune665.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize105.0ms

Local error

Found 4 expressions with local error:

14.4b
(sqrt (* (cbrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N)))) (cbrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))))))
18.6b
(cbrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))))
18.6b
(cbrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))))
18.6b
(cbrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
12×pow1
9×cbrt-prod sqrt-pow1 pow1/3
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
2×pow-prod-down pow-sqr pow-prod-up
1×pow2 rem-sqrt-square pow-plus pow1/2 sqrt-prod
Counts
4 → 64
Calls
4 calls:
11.0ms
(sqrt (* (cbrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N)))) (cbrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))))))
1.0ms
(cbrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))))
1.0ms
(cbrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))))
2.0ms
(cbrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))))

series393.0ms

Counts
4 → 12
Calls
4 calls:
99.0ms
(sqrt (* (cbrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N)))) (cbrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))))))
94.0ms
(cbrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))))
95.0ms
(cbrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))))
105.0ms
(cbrt (fma (/ (/ 1 N) N) -1/2 (fma (/ (/ 1 N) (* N N)) 1/3 (/ 1 N))))

simplify1.4s

Counts
76 → 76
Iterations
IterNodes
42391
3954
2399
1177
092

prune999.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes38.0ms

Accuracy

100% (0.0b remaining)

Error of 0.0b against oracle of 0.0b and baseline of 31.1b

bsearch33.0ms

Steps
ItersRangePoint
8
13.774552749451386
335086.0623706297
7336.587493395303

simplify4.0ms

Iterations
IterNodes
219
119
016

end0.0ms

sample3.4s

Algorithm
intervals
Results
1.5s1747×body1280valid
553.0ms1250×body640valid
464.0ms7978×body80nan
400.0ms4101×body80valid
177.0ms605×body320valid
89.0ms297×body160valid