Details

Time bar (total: 6.3s)

sample210.0ms

Algorithm
intervals
Results
51.0ms113×body1280valid
50.0ms84×body1280nan
26.0ms56×body640nan
19.0ms54×body640valid
12.0ms43×body10240exit
8.0ms34×body320nan
8.0ms194×body80nan
6.0ms125×body80valid
5.0ms24×body320valid
3.0ms21×body160valid
2.0ms17×body160nan

simplify35.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0176
1356
2856
32496
49116
550016

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 33.5b

Counts
2 → 1

localize8.0ms

Local error

Found 1 expressions with local error:

3.2b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
66×unpow-prod-down
56×*-un-lft-identity prod-diff
45×add-sqr-sqrt
33×add-cube-cbrt
22×sqr-pow
9×distribute-lft-out difference-of-squares
8×fma-neg
3×distribute-lft-out-- add-log-exp
1×pow1 add-exp-log expm1-log1p-u sub-neg flip3-- diff-log add-cbrt-cube flip-- log1p-expm1-u
Counts
1 → 90
Calls
1 calls:
11.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series282.0ms

Counts
1 → 3
Calls
1 calls:
282.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify56.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (34.0ms)

IterNodesCost
04131840
111821320
250021316

prune134.0ms

Filtered
93 candidates to 44 candidates (47.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New90393
Fresh000
Picked101
Done000
Total91394

Merged error: 22.2b

Counts
94 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(cbrt (+ x 1.0))
0.2b
(cbrt (+ x 1.0))
0.3b
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
4.7b
(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
32×cbrt-prod *-un-lft-identity
22×add-sqr-sqrt
16×cbrt-div
14×add-cube-cbrt
11×pow1
9×swap-sqr
8×flip3-+ pow1/3 flip-+ distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log
4×expm1-log1p-u frac-times add-cbrt-cube log1p-expm1-u add-log-exp unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 pow-plus prod-exp *-commutative cbrt-unprod fma-udef
Counts
4 → 97
Calls
4 calls:
3.0ms
(cbrt (+ x 1.0))
3.0ms
(cbrt (+ x 1.0))
10.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
1.0ms
(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

series1.2s

Counts
4 → 12
Calls
4 calls:
90.0ms
(cbrt (+ x 1.0))
90.0ms
(cbrt (+ x 1.0))
112.0ms
(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
874.0ms
(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))

simplify59.0ms

Algorithm
egg-herbie
Counts
109 → 109
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05961015
12175941
25001893

prune344.0ms

Filtered
109 candidates to 80 candidates (73.4%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New1063109
Fresh022
Picked101
Done000
Total1075112

Merged error: 21.9b

Counts
112 → 5

localize40.0ms

Local error

Found 4 expressions with local error:

4.9b
(pow (fma (pow (/ 1 x) 1/3) 0.6666666666666666 (- (pow (/ 1 x) -2/3) (* 0.1111111111111111 (pow (/ 1 (pow x 4)) 1/3)))) (/ 1.0 n))
5.1b
(pow (/ 1 x) 1/3)
6.1b
(pow (/ 1 x) -2/3)
33.6b
(pow (/ 1 (pow x 4)) 1/3)

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
63×unpow-prod-down
48×times-frac
43×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
25×add-exp-log
22×pow-unpow pow-exp
10×pow1 pow-pow div-exp
7×pow-to-exp sqr-pow
5×rec-exp 1-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u div-inv add-log-exp
3×pow-flip inv-pow
2×unpow1/3
Counts
4 → 151
Calls
4 calls:
4.0ms
(pow (fma (pow (/ 1 x) 1/3) 0.6666666666666666 (- (pow (/ 1 x) -2/3) (* 0.1111111111111111 (pow (/ 1 (pow x 4)) 1/3)))) (/ 1.0 n))
5.0ms
(pow (/ 1 x) 1/3)
5.0ms
(pow (/ 1 x) -2/3)
12.0ms
(pow (/ 1 (pow x 4)) 1/3)

series828.0ms

Counts
4 → 12
Calls
4 calls:
272.0ms
(pow (fma (pow (/ 1 x) 1/3) 0.6666666666666666 (- (pow (/ 1 x) -2/3) (* 0.1111111111111111 (pow (/ 1 (pow x 4)) 1/3)))) (/ 1.0 n))
179.0ms
(pow (/ 1 x) 1/3)
184.0ms
(pow (/ 1 x) -2/3)
193.0ms
(pow (/ 1 (pow x 4)) 1/3)

simplify71.0ms

Algorithm
egg-herbie
Counts
163 → 163
Iterations

Useful iterations: 2 (54.0ms)

IterNodesCost
08241136
129301026
250011011

prune543.0ms

Filtered
163 candidates to 84 candidates (51.5%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New1621163
Fresh134
Picked101
Done000
Total1644168

Merged error: 21.9b

Counts
168 → 4

localize42.0ms

Local error

Found 4 expressions with local error:

1.4b
(fma (pow (fma (pow (/ 1 x) 1/3) 0.6666666666666666 (- (pow (/ 1 x) -2/3) (* 0.1111111111111111 (log1p (expm1 (pow (/ 1 (pow x 4)) 1/3)))))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))
5.1b
(pow (/ 1 x) 1/3)
6.1b
(pow (/ 1 x) -2/3)
33.6b
(pow (/ 1 (pow x 4)) 1/3)

rewrite26.0ms

Algorithm
rewrite-expression-head
Rules
60×unpow-prod-down
39×times-frac
35×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
24×add-exp-log
21×pow-exp
10×div-exp
9×pow1 pow-unpow pow-pow
6×pow-to-exp sqr-pow
5×rec-exp 1-exp
4×expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow-flip div-inv inv-pow
2×unpow1/3
1×fma-udef
Counts
4 → 132
Calls
4 calls:
1.0ms
(fma (pow (fma (pow (/ 1 x) 1/3) 0.6666666666666666 (- (pow (/ 1 x) -2/3) (* 0.1111111111111111 (log1p (expm1 (pow (/ 1 (pow x 4)) 1/3)))))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))
8.0ms
(pow (/ 1 x) 1/3)
5.0ms
(pow (/ 1 x) -2/3)
8.0ms
(pow (/ 1 (pow x 4)) 1/3)

series1.5s

Counts
4 → 12
Calls
4 calls:
957.0ms
(fma (pow (fma (pow (/ 1 x) 1/3) 0.6666666666666666 (- (pow (/ 1 x) -2/3) (* 0.1111111111111111 (log1p (expm1 (pow (/ 1 (pow x 4)) 1/3)))))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (pow x (/ 1.0 n))))
183.0ms
(pow (/ 1 x) 1/3)
177.0ms
(pow (/ 1 x) -2/3)
190.0ms
(pow (/ 1 (pow x 4)) 1/3)

simplify77.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (61.0ms)

IterNodesCost
09291116
13243972
25002957

prune495.0ms

Filtered
144 candidates to 71 candidates (49.3%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1440144
Fresh033
Picked011
Done000
Total1444148

Merged error: 21.9b

Counts
148 → 4

regimes177.0ms

bsearch157.0ms

Steps
ItersRangePoint
9
-35960.30255326699
-0.0014566459989916651
-393.5929326446645

Profiling

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