Details

Time bar (total: 14.7s)

sample205.0ms

Algorithm
intervals
Results
78.0ms34×body2560valid
63.0ms72×body1280valid
26.0ms63×body640valid
8.0ms100×body80valid
6.0ms25×body320valid
5.0ms66×body80nan
3.0ms1×body5120valid
3.0ms16×body160valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
0257
1607
21457
33647
412487
550017

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 40.8b

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
1.3b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
3.9b
(pow (+ 1.0 (/ i n)) n)
10.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite615.0ms

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:
230.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
128.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)
227.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

series1.2s

Counts
4 → 12
Calls
4 calls:
371.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
251.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
217.0ms
(pow (+ 1.0 (/ i n)) n)
358.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify64.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (30.0ms)

IterNodesCost
013193734
150023446

prune904.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 21.5b

localize14.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
3.9b
(pow (+ 1.0 (/ i n)) n)
3.9b
(pow (+ 1.0 (/ i n)) n)
3.9b
(pow (+ 1.0 (/ i n)) n)

rewrite165.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
31×add-sqr-sqrt
29×unpow-prod-down
26×add-cube-cbrt
24×prod-diff
9×pow-unpow
8×fma-neg sqr-pow
7×pow1 add-exp-log distribute-lft-out
6×add-log-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×pow-to-exp pow-pow pow-exp difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 110
Calls
4 calls:
127.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)
11.0ms
(pow (+ 1.0 (/ i n)) n)
12.0ms
(pow (+ 1.0 (/ i n)) n)

series915.0ms

Counts
4 → 12
Calls
4 calls:
258.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
218.0ms
(pow (+ 1.0 (/ i n)) n)
223.0ms
(pow (+ 1.0 (/ i n)) n)
216.0ms
(pow (+ 1.0 (/ i n)) n)

simplify145.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 3 (135.0ms)

IterNodesCost
0277905
1898707
24735678
35001657

prune369.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.5b

localize18.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
3.9b
(pow (+ 1.0 (/ i n)) n)
3.9b
(pow (+ 1.0 (/ i n)) n)
3.9b
(pow (+ 1.0 (/ i n)) n)

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
31×add-sqr-sqrt
29×unpow-prod-down
26×add-cube-cbrt
24×prod-diff
9×pow-unpow
8×fma-neg sqr-pow
7×pow1 add-exp-log distribute-lft-out
6×add-log-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u
3×pow-to-exp pow-pow pow-exp difference-of-squares
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 110
Calls
4 calls:
128.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)
11.0ms
(pow (+ 1.0 (/ i n)) n)
11.0ms
(pow (+ 1.0 (/ i n)) n)

series930.0ms

Counts
4 → 12
Calls
4 calls:
265.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
222.0ms
(pow (+ 1.0 (/ i n)) n)
223.0ms
(pow (+ 1.0 (/ i n)) n)
219.0ms
(pow (+ 1.0 (/ i n)) n)

simplify144.0ms

Algorithm
egg-herbie
Counts
122 → 122
Iterations

Useful iterations: 3 (133.0ms)

IterNodesCost
0277905
1898707
24735678
35001657

prune444.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 21.5b

localize20.0ms

Local error

Found 4 expressions with local error:

1.3b
(- (cbrt (pow (pow (+ 1.0 (/ i n)) n) 3)) 1.0)
3.9b
(pow (+ 1.0 (/ i n)) n)
3.9b
(pow (+ 1.0 (/ i n)) n)
3.9b
(pow (+ 1.0 (/ i n)) n)

rewrite329.0ms

Algorithm
rewrite-expression-head
Rules
96×cbrt-prod
83×*-un-lft-identity
81×unpow-prod-down
75×prod-diff
74×add-sqr-sqrt
59×add-cube-cbrt
35×cube-prod
25×fma-neg
18×sqr-pow
11×distribute-lft-out
9×pow-unpow difference-of-squares
7×pow1 add-exp-log
6×add-log-exp
4×expm1-log1p-u cube-mult unpow3 add-cbrt-cube log1p-expm1-u
3×pow-to-exp pow-pow pow-exp
1×sub-neg flip3-- diff-log flip-- distribute-lft-out--
Counts
4 → 184
Calls
4 calls:
286.0ms
(- (cbrt (pow (pow (+ 1.0 (/ i n)) n) 3)) 1.0)
11.0ms
(pow (+ 1.0 (/ i n)) n)
11.0ms
(pow (+ 1.0 (/ i n)) n)
11.0ms
(pow (+ 1.0 (/ i n)) n)

series933.0ms

Counts
4 → 12
Calls
4 calls:
263.0ms
(- (cbrt (pow (pow (+ 1.0 (/ i n)) n) 3)) 1.0)
226.0ms
(pow (+ 1.0 (/ i n)) n)
217.0ms
(pow (+ 1.0 (/ i n)) n)
228.0ms
(pow (+ 1.0 (/ i n)) n)

simplify57.0ms

Algorithm
egg-herbie
Counts
196 → 196
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
04351985
114161210
250021174

prune498.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 21.5b

regimes127.0ms

Accuracy

42.7% (12.1b remaining)

Error of 34.1b against oracle of 21.9b and baseline of 43.1b

bsearch496.0ms

Steps
ItersRangePoint
10
2.3615105478400983e-198
6.60627199456594e-181
8.197984982050091e-194
8
-1043668.381521804
-3875.060168488945
-15831.586444589748
5
-7.694465996572546e+56
-2.740847179348341e+56
-4.530611506849831e+56
9
-1.1922796481491573e+84
-8.789057739707999e+77
-8.046837769241036e+81

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06070
16070

end0.0ms

sample5.8s

Algorithm
intervals
Results
2.2s2499×body1280valid
2.0s985×body2560valid
700.0ms1670×body640valid
236.0ms846×body320valid
230.0ms3001×body80valid
126.0ms2251×body80nan
73.0ms439×body160valid
41.0ms11×body5120valid