Details

Time bar (total: 52.7s)

sample287.0ms

Algorithm
intervals
Results
117.0ms39×body2560valid
87.0ms75×body1280valid
25.0ms47×body640valid
7.0ms105×body80valid
6.0ms20×body320valid
4.0ms71×body80nan
4.0ms20×body160valid

simplify7.2s

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

prune19.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 45.6b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.0b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
7.9b
(pow (+ 1.0 (/ i n)) n)
12.6b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite2.0s

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 insert-posit16 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 → 325
Calls
4 calls:
659.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
415.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
42.0ms
(pow (+ 1.0 (/ i n)) n)
748.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series2.7s

Counts
4 → 12
Calls
4 calls:
926.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
548.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
469.0ms
(pow (+ 1.0 (/ i n)) n)
750.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify4.3s

Counts
337 → 337
Iterations
IterNodes
done5000
11493
0483

prune3.6s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 24.3b

localize77.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma (* i i) 0.5 (* 1.0 i))
0.1b
(* 100.0 (/ (+ (* (- (* 0.5 (log 1.0))) (* i i)) (fma (log 1.0) n (fma (* i i) 0.5 (* 1.0 i)))) (/ i n)))
10.4b
(* (- (* 0.5 (log 1.0))) (* i i))
21.2b
(/ (+ (* (- (* 0.5 (log 1.0))) (* i i)) (fma (log 1.0) n (fma (* i i) 0.5 (* 1.0 i)))) (/ i n))

rewrite296.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
93×add-sqr-sqrt
83×*-un-lft-identity add-cube-cbrt
45×associate-*r*
23×add-cbrt-cube add-exp-log
13×associate-/r*
11×pow1
9×associate-*l* div-inv
6×cbrt-undiv div-exp prod-exp cbrt-unprod
4×expm1-log1p-u pow-prod-down insert-posit16 log1p-expm1-u add-log-exp unswap-sqr
3×associate-/l*
2×associate-/r/ *-commutative associate-/l/
1×distribute-lft-neg-out distribute-lft-neg-in clear-num neg-mul-1 distribute-rgt-neg-in frac-2neg flip3-+ associate-*r/ flip-+ fma-udef
Counts
4 → 181
Calls
4 calls:
1.0ms
(fma (* i i) 0.5 (* 1.0 i))
110.0ms
(* 100.0 (/ (+ (* (- (* 0.5 (log 1.0))) (* i i)) (fma (log 1.0) n (fma (* i i) 0.5 (* 1.0 i)))) (/ i n)))
49.0ms
(* (- (* 0.5 (log 1.0))) (* i i))
120.0ms
(/ (+ (* (- (* 0.5 (log 1.0))) (* i i)) (fma (log 1.0) n (fma (* i i) 0.5 (* 1.0 i)))) (/ i n))

series1.1s

Counts
4 → 12
Calls
4 calls:
116.0ms
(fma (* i i) 0.5 (* 1.0 i))
373.0ms
(* 100.0 (/ (+ (* (- (* 0.5 (log 1.0))) (* i i)) (fma (log 1.0) n (fma (* i i) 0.5 (* 1.0 i)))) (/ i n)))
268.0ms
(* (- (* 0.5 (log 1.0))) (* i i))
336.0ms
(/ (+ (* (- (* 0.5 (log 1.0))) (* i i)) (fma (log 1.0) n (fma (* i i) 0.5 (* 1.0 i)))) (/ i n))

simplify5.7s

Counts
193 → 193
Iterations
IterNodes
done5000
23391
1891
0314

prune2.5s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 11.3b

localize68.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (/ (fma (* (* i 0.5) (- (log 1.0))) i (fma n (log 1.0) (* i (fma 0.5 i 1.0)))) i) n)
0.0b
(* i (fma 0.5 i 1.0))
0.1b
(* 100.0 (* (/ (fma (* (* i 0.5) (- (log 1.0))) i (fma n (log 1.0) (* i (fma 0.5 i 1.0)))) i) n))
9.9b
(/ (fma (* (* i 0.5) (- (log 1.0))) i (fma n (log 1.0) (* i (fma 0.5 i 1.0)))) i)

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
23×*-un-lft-identity add-cube-cbrt
22×add-cbrt-cube add-exp-log
19×times-frac associate-*l*
13×pow1
8×prod-exp cbrt-unprod
7×associate-*r*
5×pow-prod-down
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×cbrt-undiv associate-/r* div-exp *-commutative associate-/l* unswap-sqr
2×associate-*l/ fma-udef div-inv
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in associate-*r/
Counts
4 → 112
Calls
4 calls:
25.0ms
(* (/ (fma (* (* i 0.5) (- (log 1.0))) i (fma n (log 1.0) (* i (fma 0.5 i 1.0)))) i) n)
10.0ms
(* i (fma 0.5 i 1.0))
59.0ms
(* 100.0 (* (/ (fma (* (* i 0.5) (- (log 1.0))) i (fma n (log 1.0) (* i (fma 0.5 i 1.0)))) i) n))
14.0ms
(/ (fma (* (* i 0.5) (- (log 1.0))) i (fma n (log 1.0) (* i (fma 0.5 i 1.0)))) i)

series1.1s

Counts
4 → 12
Calls
4 calls:
367.0ms
(* (/ (fma (* (* i 0.5) (- (log 1.0))) i (fma n (log 1.0) (* i (fma 0.5 i 1.0)))) i) n)
99.0ms
(* i (fma 0.5 i 1.0))
330.0ms
(* 100.0 (* (/ (fma (* (* i 0.5) (- (log 1.0))) i (fma n (log 1.0) (* i (fma 0.5 i 1.0)))) i) n))
260.0ms
(/ (fma (* (* i 0.5) (- (log 1.0))) i (fma n (log 1.0) (* i (fma 0.5 i 1.0)))) i)

simplify3.1s

Counts
124 → 124
Iterations
IterNodes
done5000
21462
1467
0192

prune1.6s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 11.3b

localize69.0ms

Local error

Found 4 expressions with local error:

0.0b
(* i (fma 0.5 i 1.0))
0.1b
(* 100.0 (* (posit16->real (real->posit16 (/ (fma (* (* i 0.5) (- (log 1.0))) i (fma n (log 1.0) (* i (fma 0.5 i 1.0)))) i))) n))
9.9b
(/ (fma (* (* i 0.5) (- (log 1.0))) i (fma n (log 1.0) (* i (fma 0.5 i 1.0)))) i)
20.9b
(posit16->real (real->posit16 (/ (fma (* (* i 0.5) (- (log 1.0))) i (fma n (log 1.0) (* i (fma 0.5 i 1.0)))) i)))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
15×*-un-lft-identity add-cube-cbrt
13×add-cbrt-cube add-exp-log
11×pow1
9×times-frac
6×associate-*l*
4×expm1-log1p-u associate-*r* pow-prod-down prod-exp cbrt-unprod insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* associate-/l*
2×*-commutative fma-udef
1×distribute-rgt-in cbrt-undiv clear-num frac-2neg distribute-lft-in div-exp div-inv remove-posit16 unswap-sqr
Counts
4 → 85
Calls
4 calls:
10.0ms
(* i (fma 0.5 i 1.0))
36.0ms
(* 100.0 (* (posit16->real (real->posit16 (/ (fma (* (* i 0.5) (- (log 1.0))) i (fma n (log 1.0) (* i (fma 0.5 i 1.0)))) i))) n))
11.0ms
(/ (fma (* (* i 0.5) (- (log 1.0))) i (fma n (log 1.0) (* i (fma 0.5 i 1.0)))) i)
1.0ms
(posit16->real (real->posit16 (/ (fma (* (* i 0.5) (- (log 1.0))) i (fma n (log 1.0) (* i (fma 0.5 i 1.0)))) i)))

series876.0ms

Counts
4 → 12
Calls
4 calls:
107.0ms
(* i (fma 0.5 i 1.0))
312.0ms
(* 100.0 (* (posit16->real (real->posit16 (/ (fma (* (* i 0.5) (- (log 1.0))) i (fma n (log 1.0) (* i (fma 0.5 i 1.0)))) i))) n))
243.0ms
(/ (fma (* (* i 0.5) (- (log 1.0))) i (fma n (log 1.0) (* i (fma 0.5 i 1.0)))) i)
213.0ms
(posit16->real (real->posit16 (/ (fma (* (* i 0.5) (- (log 1.0))) i (fma n (log 1.0) (* i (fma 0.5 i 1.0)))) i)))

simplify6.1s

Counts
97 → 97
Iterations
IterNodes
done5000
34293
21032
1349
0162

prune1.7s

Pruning

23 alts after pruning (22 fresh and 1 done)

Merged error: 11.3b

regimes959.0ms

Accuracy

50.2% (11.5b remaining)

Error of 22.1b against oracle of 10.6b and baseline of 33.7b

bsearch741.0ms

Steps
ItersRangePoint
7
4.844052074247226e-103
1.4804481956603392e-101
4.930404890743995e-103
7
-1.903881763283314e-306
-7.036936607564605e-308
-3.388139377181462e-307
10
-524937.0299516014
-3.8822111449762154e-05
-2.4617384878412216
9
-6.999589544614527e+61
-8.353436009901676e+53
-3.0859985436646373e+59
9
-2.4334994185842963e+101
-8.921734026293468e+92
-1.4968988971170808e+97

simplify50.0ms

Iterations
IterNodes
done74
374
267
163
049

end0.0ms

sample6.4s

Algorithm
intervals
Results
2.3s999×body2560valid
2.2s2496×body1280valid
991.0ms1571×body640valid
205.0ms3075×body80valid
180.0ms859×body320valid
98.0ms2226×body80nan
83.0ms417×body160valid
27.0ms7×body5120valid