Details

Time bar (total: 17.6s)

sample156.0ms

Algorithm
intervals
Results
59.0ms82×body1280valid
58.0ms32×body2560valid
13.0ms46×body640valid
5.0ms31×body320valid
4.0ms107×body80valid
2.0ms62×body80nan
1.0ms9×body160valid

simplify43.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1607
21457
33647
412487
550017

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 39.6b

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
0.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b
(pow (+ 1.0 (/ i n)) n)
10.7b
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

rewrite623.0ms

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:
233.0ms
(* 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:
377.0ms
(* 100.0 (/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n)))
252.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
217.0ms
(pow (+ 1.0 (/ i n)) n)
357.0ms
(/ (- (pow (+ 1.0 (/ i n)) n) 1.0) (/ i n))

simplify62.0ms

Algorithm
egg-herbie
Counts
333 → 333
Iterations

Useful iterations: 1 (28.0ms)

IterNodesCost
013193734
150023446

prune864.0ms

Filtered
333 candidates to 242 candidates (72.7%)
Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 19.5b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
0.9b
(- (pow (+ 1.0 (/ i n)) n) 1.0)
6.8b
(pow (+ 1.0 (/ i n)) n)
10.7b
(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

rewrite522.0ms

Algorithm
rewrite-expression-head
Rules
92×*-un-lft-identity
78×add-sqr-sqrt
72×prod-diff
66×add-cube-cbrt
46×unpow-prod-down
31×times-frac
26×distribute-rgt-in distribute-lft-in
19×add-exp-log
18×add-cbrt-cube
13×associate-/r* sqr-pow
11×distribute-lft-out
8×fma-neg
7×pow1 associate-*r*
6×cbrt-undiv div-exp add-log-exp difference-of-squares
4×expm1-log1p-u associate-*r/ log1p-expm1-u
3×sub-neg pow-unpow flip3-- associate-*l* prod-exp flip-- cbrt-unprod div-inv
2×associate-/l/ distribute-lft-out--
1×pow-to-exp pow-pow frac-2neg diff-log pow-prod-down pow-exp clear-num associate-/r/ *-commutative associate-/l* unswap-sqr
Counts
4 → 198
Calls
4 calls:
224.0ms
(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
129.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
12.0ms
(pow (+ 1.0 (/ i n)) n)
148.0ms
(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

series1.1s

Counts
4 → 12
Calls
4 calls:
281.0ms
(* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0))
261.0ms
(- (pow (+ 1.0 (/ i n)) n) 1.0)
225.0ms
(pow (+ 1.0 (/ i n)) n)
379.0ms
(/ (* 100.0 (- (pow (+ 1.0 (/ i n)) n) 1.0)) (/ i n))

simplify111.0ms

Algorithm
egg-herbie
Counts
210 → 210
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
07922367
139171720
250021708

prune371.0ms

Filtered
210 candidates to 113 candidates (53.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.7b

localize16.0ms

Local error

Found 4 expressions with local error:

0.9b
(fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n)))
6.8b
(pow (+ 1.0 (/ i n)) (* 2 n))
6.8b
(pow (+ 1.0 (/ i n)) n)
10.7b
(/ (* 100.0 (/ (fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n))) (+ (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
27×add-exp-log
25×*-un-lft-identity add-cbrt-cube
21×add-sqr-sqrt add-cube-cbrt
13×associate-/r*
11×cbrt-undiv div-exp
8×unpow-prod-down
6×pow1
4×expm1-log1p-u pow-unpow prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×div-inv
2×pow-to-exp pow-pow pow-exp distribute-lft-out sqr-pow
1×frac-2neg associate-*r/ clear-num associate-/r/ fma-udef associate-/l/ associate-/l*
Counts
4 → 101
Calls
4 calls:
0.0ms
(fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n)))
11.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
11.0ms
(pow (+ 1.0 (/ i n)) n)
53.0ms
(/ (* 100.0 (/ (fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n))) (+ (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

series2.9s

Counts
4 → 12
Calls
4 calls:
286.0ms
(fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n)))
238.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
231.0ms
(pow (+ 1.0 (/ i n)) n)
2.1s
(/ (* 100.0 (/ (fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n))) (+ (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

simplify87.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (73.0ms)

IterNodesCost
06971446
137441215
250031205

prune376.0ms

Filtered
113 candidates to 87 candidates (77.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 17.6b

localize18.0ms

Local error

Found 4 expressions with local error:

0.9b
(fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n)))
6.8b
(pow (+ 1.0 (/ i n)) (* 2 n))
6.8b
(pow (+ 1.0 (/ i n)) n)
10.7b
(/ (* 100.0 (/ (log (exp (fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n))))) (+ (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
31×times-frac
27×add-exp-log
25×*-un-lft-identity add-cbrt-cube
21×add-sqr-sqrt add-cube-cbrt
13×associate-/r*
11×cbrt-undiv div-exp
8×unpow-prod-down
6×pow1
4×expm1-log1p-u pow-unpow prod-exp cbrt-unprod log1p-expm1-u add-log-exp
3×div-inv
2×pow-to-exp pow-pow pow-exp distribute-lft-out sqr-pow
1×frac-2neg associate-*r/ clear-num associate-/r/ fma-udef associate-/l/ associate-/l*
Counts
4 → 101
Calls
4 calls:
0.0ms
(fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n)))
13.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
11.0ms
(pow (+ 1.0 (/ i n)) n)
57.0ms
(/ (* 100.0 (/ (log (exp (fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n))))) (+ (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

series3.1s

Counts
4 → 12
Calls
4 calls:
484.0ms
(fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n)))
235.0ms
(pow (+ 1.0 (/ i n)) (* 2 n))
226.0ms
(pow (+ 1.0 (/ i n)) n)
2.1s
(/ (* 100.0 (/ (log (exp (fma (- 1.0) 1.0 (pow (+ 1.0 (/ i n)) (* 2 n))))) (+ (pow (+ 1.0 (/ i n)) n) 1.0))) (/ i n))

simplify86.0ms

Algorithm
egg-herbie
Counts
113 → 113
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
07021506
137881252
250011226

prune371.0ms

Filtered
113 candidates to 88 candidates (77.9%)
Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 17.6b

regimes135.0ms

Accuracy

46.7% (12.9b remaining)

Error of 31.4b against oracle of 18.5b and baseline of 42.7b

bsearch568.0ms

Steps
ItersRangePoint
8
2.6233364391768453e+215
7.559003031217257e+219
7.395559138739582e+219
7
8.449789709258891e+21
1.927335547477129e+23
8.532543483832935e+21
6
3.1399496998840866e-125
3.7800925651486635e-124
6.02622510223327e-125
7
1.4967481787327182e-161
2.5387026277821525e-160
2.515912909264607e-160
8
-1.4252965457371644e-10
-5.035330346103121e-14
-1.3992561866449662e-10
8
-1.6450582212898727e+137
-4.094290472995023e+133
-2.561401665352169e+135

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07685
17685

end0.0ms

sample4.6s

Algorithm
intervals
Results
1.8s2560×body1280valid
1.7s942×body2560valid
466.0ms1643×body640valid
139.0ms871×body320valid
130.0ms3062×body80valid
69.0ms2190×body80nan
39.0ms396×body160valid
29.0ms8×body5120valid