Details

Time bar (total: 37.4s)

sample283.0ms

Algorithm
intervals
Results
113.0ms79×body1280valid
85.0ms25×body2560valid
28.0ms49×body640valid
12.0ms33×body320valid
10.0ms111×body80valid
5.0ms67×body80nan
3.0ms12×body160valid

simplify3.6s

Counts
1 → 1
Iterations
IterNodes
done5003
63444
5877
4318
3139
260
125
010

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.4b

localize23.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.0b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.4b
(pow (+ 1.0 (/ i n)) n)
8.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite1.2s

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:
446.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
273.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
16.0ms
(pow (+ 1.0 (/ i n)) n)
441.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.9s

Counts
4 → 12
Calls
4 calls:
562.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
391.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
338.0ms
(pow (+ 1.0 (/ i n)) n)
609.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify2.5s

Counts
333 → 333
Iterations
IterNodes
done5000
11492
0479

prune2.3s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 20.6b

localize41.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
0.3b
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
1.0b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.4b
(pow (+ 1.0 (/ i n)) n)

rewrite1.6s

Algorithm
rewrite-expression-head
Rules
340×times-frac
330×add-sqr-sqrt
230×*-un-lft-identity
162×add-cube-cbrt
96×associate-*r*
84×difference-of-squares
49×add-exp-log
48×unpow-prod-down
33×sqr-pow
30×add-cbrt-cube
28×distribute-lft-out--
24×prod-diff
23×div-exp
18×div-inv
13×associate-/r* associate-*l*
12×cbrt-undiv
10×prod-exp
8×fma-neg unswap-sqr
7×pow1 associate-/l*
6×cbrt-unprod add-log-exp
5×distribute-lft-out
4×expm1-log1p-u log1p-expm1-u
3×rec-exp pow-unpow 1-exp
2×flip3-- associate-/r/ flip-- associate-/l/
1×frac-times pow-to-exp clear-num sub-neg pow-pow frac-2neg diff-log div-sub pow-prod-down associate-*l/ pow-exp associate-*r/ *-commutative
Counts
4 → 350
Calls
4 calls:
451.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
450.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
224.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
419.0ms
(pow (+ 1.0 (/ i n)) n)

series1.6s

Counts
4 → 12
Calls
4 calls:
373.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n))
537.0ms
(* (/ 100.0 i) (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ 1 n)))
372.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
312.0ms
(pow (+ 1.0 (/ i n)) n)

simplify2.9s

Counts
362 → 362
Iterations
IterNodes
done5000
24800
11720
0509

prune1.8s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.1b

localize60.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (* 0.5 i) i) (- (* i 1.0) (* (* (* 0.5 i) i) (log 1.0))))
2.3b
(/ (fma (log 1.0) n (+ (* (* 0.5 i) i) (- (* i 1.0) (* (* (* 0.5 i) i) (log 1.0))))) (/ 1 n))
11.9b
(* (* (* 0.5 i) i) (log 1.0))
16.7b
(* (/ 100.0 i) (/ (fma (log 1.0) n (+ (* (* 0.5 i) i) (- (* i 1.0) (* (* (* 0.5 i) i) (log 1.0))))) (/ 1 n)))

rewrite169.0ms

Algorithm
rewrite-expression-head
Rules
164×times-frac
119×add-sqr-sqrt
93×*-un-lft-identity
91×add-cube-cbrt
57×add-exp-log
48×associate-*r*
39×add-cbrt-cube
23×div-exp
16×pow1 prod-exp
14×associate-*l*
13×associate-/r*
12×cbrt-undiv cbrt-unprod
10×div-inv
9×add-log-exp
8×unswap-sqr
7×pow-prod-down
6×log-prod
4×expm1-log1p-u log1p-expm1-u
3×distribute-rgt-in rec-exp associate-+r+ distribute-lft-in 1-exp associate-/l*
2×sum-log associate-/r/ *-commutative
1×frac-times +-commutative clear-num associate-+r- sub-neg fma-def frac-2neg flip3-+ diff-log prod-diff associate-*l/ associate-*r/ log-pow flip-+
Counts
4 → 218
Calls
4 calls:
21.0ms
(+ (* (* 0.5 i) i) (- (* i 1.0) (* (* (* 0.5 i) i) (log 1.0))))
11.0ms
(/ (fma (log 1.0) n (+ (* (* 0.5 i) i) (- (* i 1.0) (* (* (* 0.5 i) i) (log 1.0))))) (/ 1 n))
59.0ms
(* (* (* 0.5 i) i) (log 1.0))
68.0ms
(* (/ 100.0 i) (/ (fma (log 1.0) n (+ (* (* 0.5 i) i) (- (* i 1.0) (* (* (* 0.5 i) i) (log 1.0))))) (/ 1 n)))

series1.1s

Counts
4 → 12
Calls
4 calls:
433.0ms
(+ (* (* 0.5 i) i) (- (* i 1.0) (* (* (* 0.5 i) i) (log 1.0))))
181.0ms
(/ (fma (log 1.0) n (+ (* (* 0.5 i) i) (- (* i 1.0) (* (* (* 0.5 i) i) (log 1.0))))) (/ 1 n))
258.0ms
(* (* (* 0.5 i) i) (log 1.0))
270.0ms
(* (/ 100.0 i) (/ (fma (log 1.0) n (+ (* (* 0.5 i) i) (- (* i 1.0) (* (* (* 0.5 i) i) (log 1.0))))) (/ 1 n)))

simplify2.2s

Counts
230 → 230
Iterations
IterNodes
done5001
23415
11198
0386

prune1.6s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 11.8b

localize66.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt i)
2.2b
(* (fma n (log 1.0) (fma (* i i) (- 0.5 (* 0.5 (log 1.0))) (* 1.0 i))) n)
6.8b
(/ (* 100.0 (* (fma n (log 1.0) (fma (* i i) (- 0.5 (* 0.5 (log 1.0))) (* 1.0 i))) n)) (cbrt i))
9.6b
(* (/ 1 (* (cbrt i) (cbrt i))) (/ (* 100.0 (* (fma n (log 1.0) (fma (* i i) (- 0.5 (* 0.5 (log 1.0))) (* 1.0 i))) n)) (cbrt i)))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
133×add-exp-log
65×prod-exp
49×add-cbrt-cube
40×div-exp
29×cbrt-unprod
23×add-sqr-sqrt
20×cbrt-undiv
17×*-un-lft-identity times-frac
16×add-cube-cbrt
13×associate-*r*
12×cbrt-prod
10×associate-*l*
8×pow1 rec-exp 1-exp
6×associate-/r*
4×expm1-log1p-u log1p-expm1-u add-log-exp unswap-sqr
3×div-inv
2×pow-prod-down *-commutative
1×frac-times clear-num frac-2neg pow1/3 associate-*l/ associate-*r/ associate-/l*
Counts
4 → 138
Calls
4 calls:
1.0ms
(cbrt i)
9.0ms
(* (fma n (log 1.0) (fma (* i i) (- 0.5 (* 0.5 (log 1.0))) (* 1.0 i))) n)
27.0ms
(/ (* 100.0 (* (fma n (log 1.0) (fma (* i i) (- 0.5 (* 0.5 (log 1.0))) (* 1.0 i))) n)) (cbrt i))
102.0ms
(* (/ 1 (* (cbrt i) (cbrt i))) (/ (* 100.0 (* (fma n (log 1.0) (fma (* i i) (- 0.5 (* 0.5 (log 1.0))) (* 1.0 i))) n)) (cbrt i)))

series1.6s

Counts
4 → 12
Calls
4 calls:
274.0ms
(cbrt i)
203.0ms
(* (fma n (log 1.0) (fma (* i i) (- 0.5 (* 0.5 (log 1.0))) (* 1.0 i))) n)
705.0ms
(/ (* 100.0 (* (fma n (log 1.0) (fma (* i i) (- 0.5 (* 0.5 (log 1.0))) (* 1.0 i))) n)) (cbrt i))
368.0ms
(* (/ 1 (* (cbrt i) (cbrt i))) (/ (* 100.0 (* (fma n (log 1.0) (fma (* i i) (- 0.5 (* 0.5 (log 1.0))) (* 1.0 i))) n)) (cbrt i)))

simplify2.6s

Counts
150 → 150
Iterations
IterNodes
done5014
22937
1792
0270

prune727.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.8b

regimes417.0ms

Accuracy

41.7% (13.1b remaining)

Error of 23.7b against oracle of 10.6b and baseline of 33.1b

bsearch566.0ms

Steps
ItersRangePoint
7
5.680956200681059e-225
8.96171128476665e-223
8.76599642872152e-223
6
-3.052506018274348e-266
-2.3564052050298823e-267
-4.586926552796908e-267
7
-8.1353853441046
-0.1501579911863904
-1.995072885870678
9
-1.1388694309263412e+60
-6.092716108791962e+53
-1.4219894413191279e+58
5
-5.900767996836685e+175
-2.667336073769385e+175
-2.8131143936191375e+175

simplify35.0ms

Iterations
IterNodes
done84
184
070

end0.0ms

sample6.4s

Algorithm
intervals
Results
2.3s2498×body1280valid
2.1s957×body2560valid
971.0ms1594×body640valid
295.0ms875×body320valid
183.0ms3121×body80valid
175.0ms2279×body80nan
62.0ms466×body160valid
23.0ms6×body5120valid