Details

Time bar (total: 13.7s)

sample184.0ms

Algorithm
intervals
Results
74.0ms85×body1280valid
56.0ms27×body2560valid
20.0ms52×body640valid
8.0ms96×body80valid
7.0ms26×body320valid
4.0ms64×body80nan
3.0ms19×body160valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1607
21457
33647
412487
550017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 44.8b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.3b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
5.8b
(pow (+ 1.0 (/ i n)) n)
9.2b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite624.0ms

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 sub-neg pow-pow frac-2neg diff-log div-sub associate-*r/ pow-prod-down pow-exp clear-num *-commutative
Counts
4 → 321
Calls
4 calls:
236.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
130.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)
228.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
370.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
257.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
213.0ms
(pow (+ 1.0 (/ i n)) n)
353.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify66.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (29.0ms)

IterNodesCost
013193734
150023446

prune884.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 20.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
0.1b
(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
10.9b
(* (pow i 2) (log 1.0))
18.4b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
144×times-frac
102×add-sqr-sqrt
87×add-cube-cbrt *-un-lft-identity
48×associate-*r*
23×add-exp-log
20×add-cbrt-cube
13×associate-/r*
11×associate-*l*
9×div-inv
7×pow1 unswap-sqr
6×cbrt-undiv log-prod div-exp prod-exp
4×expm1-log1p-u unpow-prod-down cbrt-unprod log1p-expm1-u add-log-exp
3×distribute-rgt-in distribute-lft-in associate-/l*
2×associate-/r/ *-commutative unpow2 sqr-pow
1×pow-to-exp frac-2neg associate-*r/ pow-prod-down pow-exp clear-num log-pow fma-udef
Counts
4 → 186
Calls
4 calls:
0.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
19.0ms
(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
7.0ms
(* (pow i 2) (log 1.0))
5.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

series669.0ms

Counts
4 → 12
Calls
4 calls:
98.0ms
(fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0)))))
226.0ms
(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n)))
143.0ms
(* (pow i 2) (log 1.0))
201.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) (/ i n))

simplify115.0ms

Algorithm
egg-herbie
Counts
198 → 198
Iterations

Useful iterations: 1 (19.0ms)

IterNodesCost
07343209
137502968
250012968

prune758.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 10.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i))
0.1b
(* (* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)) n)
10.3b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
10.9b
(* (pow i 2) (log 1.0))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
26×add-cube-cbrt *-un-lft-identity
25×add-exp-log
22×add-cbrt-cube
20×associate-*r*
19×times-frac
12×pow1 associate-*l*
10×prod-exp
8×cbrt-unprod
6×log-prod unswap-sqr
4×expm1-log1p-u unpow-prod-down pow-prod-down log1p-expm1-u add-log-exp
3×cbrt-undiv distribute-rgt-in distribute-lft-in div-exp associate-/r* *-commutative associate-/l*
2×associate-*r/ div-inv unpow2 sqr-pow
1×pow-to-exp frac-2neg associate-*l/ pow-exp clear-num log-pow
Counts
4 → 122
Calls
4 calls:
7.0ms
(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i))
11.0ms
(* (* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)) n)
2.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
7.0ms
(* (pow i 2) (log 1.0))

series668.0ms

Counts
4 → 12
Calls
4 calls:
153.0ms
(* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i))
227.0ms
(* (* 100.0 (/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)) n)
150.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
138.0ms
(* (pow i 2) (log 1.0))

simplify77.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
04891793
122591525
250011522

prune449.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 10.1b

localize18.0ms

Local error

Found 4 expressions with local error:

10.3b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
10.3b
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
10.9b
(* (pow i 2) (log 1.0))
10.9b
(* (pow i 2) (log 1.0))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
30×add-cube-cbrt *-un-lft-identity
18×add-exp-log times-frac
16×associate-*l*
12×log-prod add-cbrt-cube
8×unpow-prod-down associate-*r* unswap-sqr
6×pow1 distribute-rgt-in distribute-lft-in prod-exp associate-/r* associate-/l*
4×expm1-log1p-u log1p-expm1-u unpow2 add-log-exp sqr-pow
2×cbrt-undiv pow-to-exp frac-2neg div-exp pow-exp clear-num log-pow *-commutative cbrt-unprod div-inv
Counts
4 → 130
Calls
4 calls:
2.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
2.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
7.0ms
(* (pow i 2) (log 1.0))
7.0ms
(* (pow i 2) (log 1.0))

series575.0ms

Counts
4 → 12
Calls
4 calls:
141.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
147.0ms
(/ (fma i 1.0 (- (fma 0.5 (pow i 2) (* (log 1.0) n)) (* 0.5 (* (pow i 2) (log 1.0))))) i)
144.0ms
(* (pow i 2) (log 1.0))
143.0ms
(* (pow i 2) (log 1.0))

simplify49.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
02381480
18681334
250011320

prune579.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 10.1b

regimes407.0ms

Accuracy

49.4% (11.5b remaining)

Error of 22.2b against oracle of 10.8b and baseline of 33.4b

bsearch552.0ms

Steps
ItersRangePoint
8
9.905379659133977e-173
2.410908475436866e-169
2.0850330521039454e-172
10
-1.308610303336602e-202
-1.224995290711999e-214
-1.2431085101949388e-214
9
-8.085901714425178e+20
-317207061041.6537
-3.514216942264821e+16
5
-1.8966346348049942e+86
-4.88873892774292e+85
-1.0958004164778634e+86
9
-2.601267202579393e+142
-2.2079686958706775e+136
-2.2308731815162504e+136

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
062104
162104

end0.0ms

sample5.6s

Algorithm
intervals
Results
2.0s2434×body1280valid
2.0s1008×body2560valid
635.0ms1594×body640valid
261.0ms3083×body80valid
224.0ms892×body320valid
135.0ms2193×body80nan
74.0ms444×body160valid
16.0ms5×body5120valid