Details

Time bar (total: 9.9s)

sample254.0ms

Algorithm
intervals
Results
78.0ms142×body1280valid
51.0ms44×body1280nan
22.0ms47×body640valid
21.0ms30×body640nan
21.0ms137×body80overflowed
9.0ms95×body80valid
9.0ms173×body80nan
8.0ms19×body320nan
7.0ms22×body320valid
2.0ms10×body160valid
2.0ms7×body160nan

simplify44.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (42.0ms)

IterNodesCost
0497813
1497813

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 31.5b

Counts
2 → 1

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(pow (+ x 1.0) (/ 1.0 n))
0.0b
(pow x (/ 1.0 n))
1.6b
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
31×add-sqr-sqrt
28×*-un-lft-identity
26×pow-unpow
19×add-cube-cbrt
18×times-frac
17×unpow-prod-down
9×difference-of-squares
8×sqr-pow
5×pow1 add-exp-log add-log-exp
3×add-cbrt-cube distribute-lft-out--
2×pow-to-exp pow-pow pow-exp div-inv distribute-lft-out
1×sub-neg flip3-- diff-log flip--
Counts
3 → 79
Calls
3 calls:
5.0ms
(pow (+ x 1.0) (/ 1.0 n))
3.0ms
(pow x (/ 1.0 n))
9.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

series72.0ms

Counts
3 → 9
Calls
3 calls:
17.0ms
(pow (+ x 1.0) (/ 1.0 n))
12.0ms
(pow x (/ 1.0 n))
43.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

simplify40.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
049801256
149801256

prune190.0ms

Filtered
71 candidates to 88 candidates (-23.9%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New81788
Fresh000
Picked101
Done000
Total82789

Merged error: 20.9b

Counts
89 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
0.0b
(pow x (/ 1.0 n))
0.0b
(pow x (/ 1.0 n))
3.3b
(- (pow (+ x 1.0) (/ 1.0 n)) (* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
62×add-sqr-sqrt
54×sqrt-prod
32×add-cube-cbrt *-un-lft-identity
27×unpow-prod-down
26×pow-unpow
18×times-frac
16×unswap-sqr
15×sqr-pow
13×pow1
12×swap-sqr
10×associate-*r* associate-*l*
8×add-exp-log
6×sqrt-pow1 pow1/2 add-cbrt-cube add-log-exp
3×pow-prod-down pow-sqr pow-prod-up difference-of-squares
2×pow-to-exp pow-pow pow-exp div-inv
1×pow2 sub-neg flip3-- pow-plus sqrt-unprod diff-log prod-exp rem-square-sqrt *-commutative flip-- cbrt-unprod
Counts
4 → 140
Calls
4 calls:
9.0ms
(* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
3.0ms
(pow x (/ 1.0 n))
3.0ms
(pow x (/ 1.0 n))
6.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))

series75.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n))))
12.0ms
(pow x (/ 1.0 n))
12.0ms
(pow x (/ 1.0 n))
40.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (* (sqrt (pow x (/ 1.0 n))) (sqrt (pow x (/ 1.0 n)))))

simplify49.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 0 (36.0ms)

IterNodesCost
061661867

prune277.0ms

Filtered
96 candidates to 152 candidates (-58.3%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1493152
Fresh156
Picked011
Done000
Total1509159

Merged error: 20.6b

Counts
159 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow x (/ 1.0 n))
0.0b
(pow x (/ 1.0 n))
0.0b
(pow x (/ 1.0 n))
1.8b
(- (pow (+ x 1.0) (/ 1.0 n)) (* (* (sqrt (pow x (/ 1.0 n))) (fabs (cbrt (pow x (/ 1.0 n))))) (sqrt (cbrt (pow x (/ 1.0 n))))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
39×pow-unpow
28×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
27×times-frac
9×unpow-prod-down
7×pow1 add-exp-log
6×add-log-exp
4×add-cbrt-cube
3×pow-to-exp pow-pow pow-exp div-inv sqr-pow
1×sub-neg flip3-- diff-log flip--
Counts
4 → 93
Calls
4 calls:
3.0ms
(pow x (/ 1.0 n))
3.0ms
(pow x (/ 1.0 n))
3.0ms
(pow x (/ 1.0 n))
6.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (* (* (sqrt (pow x (/ 1.0 n))) (fabs (cbrt (pow x (/ 1.0 n))))) (sqrt (cbrt (pow x (/ 1.0 n))))))

series89.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(pow x (/ 1.0 n))
11.0ms
(pow x (/ 1.0 n))
12.0ms
(pow x (/ 1.0 n))
54.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (* (* (sqrt (pow x (/ 1.0 n))) (fabs (cbrt (pow x (/ 1.0 n))))) (sqrt (cbrt (pow x (/ 1.0 n))))))

simplify40.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 0 (30.0ms)

IterNodesCost
049821501
149821501

prune374.0ms

Filtered
85 candidates to 105 candidates (-23.5%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1023105
Fresh167
Picked101
Done011
Total10410114

Merged error: 20.6b

Counts
114 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(pow x (/ 1.0 n))
0.0b
(pow x (/ 1.0 n))
0.1b
(pow (pow x (/ 1.0 n)) 2/3)
2.3b
(- (pow (+ x 1.0) (/ 1.0 n)) (* (* (sqrt (* (pow (pow x (/ 1.0 n)) 2/3) (cbrt (pow x (/ 1.0 n))))) (fabs (cbrt (pow x (/ 1.0 n))))) (sqrt (cbrt (pow x (/ 1.0 n))))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
29×pow-unpow
23×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
18×times-frac
16×unpow-prod-down
8×add-exp-log
6×pow1 pow-exp add-log-exp
4×pow-to-exp add-cbrt-cube sqr-pow
3×pow-pow
2×div-inv
1×sub-neg flip3-- diff-log flip--
Counts
4 → 89
Calls
4 calls:
3.0ms
(pow x (/ 1.0 n))
3.0ms
(pow x (/ 1.0 n))
4.0ms
(pow (pow x (/ 1.0 n)) 2/3)
6.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (* (* (sqrt (* (pow (pow x (/ 1.0 n)) 2/3) (cbrt (pow x (/ 1.0 n))))) (fabs (cbrt (pow x (/ 1.0 n))))) (sqrt (cbrt (pow x (/ 1.0 n))))))

series95.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(pow x (/ 1.0 n))
12.0ms
(pow x (/ 1.0 n))
17.0ms
(pow (pow x (/ 1.0 n)) 2/3)
54.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (* (* (sqrt (* (pow (pow x (/ 1.0 n)) 2/3) (cbrt (pow x (/ 1.0 n))))) (fabs (cbrt (pow x (/ 1.0 n))))) (sqrt (cbrt (pow x (/ 1.0 n))))))

simplify44.0ms

Algorithm
egg-herbie
Counts
101 → 101
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
049791519
149791519

prune379.0ms

Filtered
80 candidates to 101 candidates (-26.3%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1001101
Fresh088
Picked101
Done011
Total10110111

Merged error: 20.6b

Counts
111 → 10

regimes400.0ms

Accuracy

89.2% (1.1b remaining)

Error of 22.4b against oracle of 21.2b and baseline of 31.9b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03886
13886

end0.0ms

sample7.3s

Algorithm
intervals
Results
2.3s3976×body1280valid
1.2s1088×body1280nan
798.0ms1686×body640valid
617.0ms902×body640nan
591.0ms4093×body80overflowed
334.0ms3215×body80valid
323.0ms6124×body80nan
275.0ms847×body320valid
185.0ms441×body320nan
92.0ms446×body160valid
48.0ms217×body160nan

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