Details

Time bar (total: 28.2s)

sample300.0ms

Algorithm
intervals
Results
116.0ms35×body2560valid
94.0ms69×body1280valid
40.0ms44×body640valid
10.0ms33×body320valid
10.0ms110×body80valid
5.0ms76×body80nan
3.0ms15×body160valid

simplify2.0s

Counts
1 → 1
Iterations
IterNodes
done5000
51593
4364
3144
260
125
010

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 42.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
8.8b
(pow (+ 1.0 (/ i n)) n)
10.4b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.0s

Algorithm
rewrite-expression-head
Rules
320×times-frac
305×add-sqr-sqrt
222×*-un-lft-identity
156×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
48×unpow-prod-down
33×sqr-pow
28×distribute-lft-out--
24×prod-diff
19×add-exp-log
18×add-cbrt-cube
17×div-inv
13×associate-/r*
8×fma-neg
7×pow1 associate-/l*
6×cbrt-undiv div-exp add-log-exp
5×distribute-lft-out
4×expm1-log1p-u log1p-expm1-u
3×pow-unpow associate-*l* prod-exp cbrt-unprod unswap-sqr
2×flip3-- associate-/r/ flip-- associate-/l/
1×pow-to-exp clear-num sub-neg pow-pow frac-2neg diff-log div-sub pow-prod-down pow-exp associate-*r/ *-commutative
Counts
4 → 321
Calls
4 calls:
418.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
205.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
20.0ms
(pow (+ 1.0 (/ i n)) n)
374.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.7s

Counts
4 → 12
Calls
4 calls:
571.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
356.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
311.0ms
(pow (+ 1.0 (/ i n)) n)
466.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify1.9s

Counts
333 → 333
Iterations
IterNodes
done5001
11521
0479

prune2.1s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 22.6b

localize76.0ms

Local error

Found 4 expressions with local error:

7.1b
(cbrt (+ 1.0 (/ i n)))
7.1b
(cbrt (+ 1.0 (/ i n)))
7.1b
(cbrt (+ 1.0 (/ i n)))
10.4b
(/ (fma (pow (* (cbrt (+ 1.0 (/ i n))) (cbrt (+ 1.0 (/ i n)))) n) (pow (cbrt (+ 1.0 (/ i n))) n) (- 1.0)) (/ i n))

rewrite49.0ms

Algorithm
rewrite-expression-head
Rules
75×times-frac
55×*-un-lft-identity
49×add-sqr-sqrt add-cube-cbrt
13×associate-/r*
12×cbrt-prod
9×add-cbrt-cube add-exp-log
6×cbrt-div
5×div-inv
4×expm1-log1p-u pow1 log1p-expm1-u add-log-exp
3×cbrt-undiv flip3-+ pow1/3 div-exp flip-+ distribute-lft-out associate-/l*
1×clear-num frac-2neg associate-/r/
Counts
4 → 120
Calls
4 calls:
12.0ms
(cbrt (+ 1.0 (/ i n)))
7.0ms
(cbrt (+ 1.0 (/ i n)))
11.0ms
(cbrt (+ 1.0 (/ i n)))
15.0ms
(/ (fma (pow (* (cbrt (+ 1.0 (/ i n))) (cbrt (+ 1.0 (/ i n)))) n) (pow (cbrt (+ 1.0 (/ i n))) n) (- 1.0)) (/ i n))

series2.0s

Counts
4 → 12
Calls
4 calls:
330.0ms
(cbrt (+ 1.0 (/ i n)))
308.0ms
(cbrt (+ 1.0 (/ i n)))
317.0ms
(cbrt (+ 1.0 (/ i n)))
1.0s
(/ (fma (pow (* (cbrt (+ 1.0 (/ i n))) (cbrt (+ 1.0 (/ i n)))) n) (pow (cbrt (+ 1.0 (/ i n))) n) (- 1.0)) (/ i n))

simplify2.0s

Counts
132 → 132
Iterations
IterNodes
done5001
22789
1599
0241

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 20.5b

localize46.0ms

Local error

Found 4 expressions with local error:

8.8b
(pow (+ 1.0 (/ i n)) n)
17.8b
(cbrt (/ i n))
17.8b
(cbrt (/ i n))
17.8b
(cbrt (/ i n))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
29×*-un-lft-identity
27×add-sqr-sqrt times-frac add-cube-cbrt
5×pow1 add-exp-log
4×expm1-log1p-u unpow-prod-down add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-unpow cbrt-div pow1/3 div-inv
1×pow-to-exp pow-pow pow-exp distribute-lft-out sqr-pow
Counts
4 → 92
Calls
4 calls:
14.0ms
(pow (+ 1.0 (/ i n)) n)
2.0ms
(cbrt (/ i n))
3.0ms
(cbrt (/ i n))
4.0ms
(cbrt (/ i n))

series488.0ms

Counts
4 → 12
Calls
4 calls:
265.0ms
(pow (+ 1.0 (/ i n)) n)
66.0ms
(cbrt (/ i n))
87.0ms
(cbrt (/ i n))
69.0ms
(cbrt (/ i n))

simplify894.0ms

Counts
104 → 104
Iterations
IterNodes
done5001
31619
2493
1215
0115

prune554.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 20.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
1.8b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
8.8b
(pow (+ 1.0 (/ i n)) n)

rewrite936.0ms

Algorithm
rewrite-expression-head
Rules
60×add-sqr-sqrt
53×*-un-lft-identity
35×add-cube-cbrt
28×associate-*r*
24×unpow-prod-down prod-diff
22×times-frac
19×add-exp-log
18×add-cbrt-cube
12×pow1 difference-of-squares
9×sqr-pow
8×fma-neg
7×prod-exp cbrt-unprod
6×add-log-exp
5×distribute-lft-out
4×expm1-log1p-u associate-*l* pow-prod-down log1p-expm1-u distribute-lft-out--
3×pow-unpow
2×cbrt-undiv div-exp associate-*r/ *-commutative unswap-sqr
1×pow-to-exp sub-neg pow-pow flip3-- diff-log associate-*l/ pow-exp div-inv flip--
Counts
4 → 139
Calls
4 calls:
388.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
288.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
224.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
25.0ms
(pow (+ 1.0 (/ i n)) n)

series1.2s

Counts
4 → 12
Calls
4 calls:
465.0ms
(* (* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i)) n)
203.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) i))
302.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
273.0ms
(pow (+ 1.0 (/ i n)) n)

simplify2.1s

Counts
151 → 151
Iterations
IterNodes
done5001
23368
1729
0266

prune520.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 9.8b

regimes196.0ms

Accuracy

39.5% (15.3b remaining)

Error of 24.0b against oracle of 8.6b and baseline of 34.0b

bsearch637.0ms

Steps
ItersRangePoint
8
3.819465148456978e-152
2.729984996487058e-148
4.674985157503464e-152
8
-8.158615695703151e-255
-1.3439850512764193e-257
-3.513107364644464e-256
9
-6.3860482886760424e+47
-2.1008172754670125e+42
-7.520459214308253e+45
6
-1.8354728977064109e+78
-2.1456788011981848e+77
-1.7675524289928927e+78
8
-1.0244940928580636e+218
-4.079775224398851e+214
-4.1271893865869047e+214

simplify21.0ms

Iterations
IterNodes
done76
376
272
166
049

end0.0ms

sample6.3s

Algorithm
intervals
Results
2.5s2473×body1280valid
2.1s990×body2560valid
673.0ms1606×body640valid
250.0ms867×body320valid
233.0ms3039×body80valid
97.0ms2281×body80nan
60.0ms451×body160valid
8.0ms2×body5120valid