Details

Time bar (total: 5.2s)

sample16.0ms

Algorithm
intervals
Results
7.0ms256×body80valid
2.0ms81×body80nan

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
084
184

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: 0.2b

Counts
2 → 1

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.2b
(/ x (+ 1.0 (sqrt (+ x 1.0))))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
14×add-sqr-sqrt
13×add-cube-cbrt
12×times-frac
6×distribute-lft-out
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 associate-/r* sqrt-prod
3×flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 61
Calls
3 calls:
3.0ms
(sqrt (+ x 1.0))
6.0ms
(+ 1.0 (sqrt (+ x 1.0)))
8.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series213.0ms

Counts
3 → 9
Calls
3 calls:
30.0ms
(sqrt (+ x 1.0))
45.0ms
(+ 1.0 (sqrt (+ x 1.0)))
139.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify37.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0317483
11159435
25001427

prune122.0ms

Filtered
70 candidates to 52 candidates (74.3%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New65570
Fresh000
Picked011
Done000
Total65671

Merged error: 0b

Counts
71 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.0b
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
0.4b
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
0.4b
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
378×times-frac
306×*-un-lft-identity
232×sqrt-prod
192×add-sqr-sqrt
190×add-cube-cbrt
58×distribute-lft-out
30×associate-/l*
24×sqrt-div
20×associate-/r/
14×associate-/r*
12×flip3-+ flip-+
11×add-exp-log add-cbrt-cube
10×div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 317
Calls
4 calls:
6.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
7.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
22.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
9.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

series823.0ms

Counts
4 → 12
Calls
4 calls:
127.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
134.0ms
(sqrt (+ 1.0 (sqrt (+ x 1.0))))
139.0ms
(/ (/ x (sqrt (+ 1.0 (sqrt (+ x 1.0))))) (sqrt (+ 1.0 (sqrt (+ x 1.0)))))
423.0ms
(/ x (sqrt (+ 1.0 (sqrt (+ x 1.0)))))

simplify115.0ms

Algorithm
egg-herbie
Counts
329 → 329
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
08875646
135015039
250014956

prune390.0ms

Filtered
329 candidates to 142 candidates (43.2%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New3290329
Fresh044
Picked011
Done011
Total3296335

Merged error: 0b

Counts
335 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b
(/ 1 (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
0.9b
(cbrt (+ 1.0 (sqrt (+ x 1.0))))
0.9b
(cbrt (+ 1.0 (sqrt (+ x 1.0))))
0.9b
(cbrt (+ 1.0 (sqrt (+ x 1.0))))

rewrite38.0ms

Algorithm
rewrite-expression-head
Rules
18×cbrt-div
15×add-exp-log *-un-lft-identity
12×pow1 cbrt-prod
9×add-sqr-sqrt add-cube-cbrt pow-flip flip3-+ pow1/3 flip-+
8×associate-/r/
7×add-cbrt-cube
4×frac-times div-exp add-log-exp
3×times-frac prod-exp distribute-lft-out associate-/l*
2×cbrt-undiv rec-exp 1-exp associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×pow2 frac-2neg pow-plus clear-num associate-/r* cbrt-unprod div-inv inv-pow
Counts
4 → 85
Calls
4 calls:
17.0ms
(/ 1 (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
6.0ms
(cbrt (+ 1.0 (sqrt (+ x 1.0))))
6.0ms
(cbrt (+ 1.0 (sqrt (+ x 1.0))))
6.0ms
(cbrt (+ 1.0 (sqrt (+ x 1.0))))

series1.8s

Counts
4 → 12
Calls
4 calls:
1.0s
(/ 1 (* (cbrt (+ 1.0 (sqrt (+ x 1.0)))) (cbrt (+ 1.0 (sqrt (+ x 1.0))))))
244.0ms
(cbrt (+ 1.0 (sqrt (+ x 1.0))))
246.0ms
(cbrt (+ 1.0 (sqrt (+ x 1.0))))
245.0ms
(cbrt (+ 1.0 (sqrt (+ x 1.0))))

simplify70.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (58.0ms)

IterNodesCost
05961220
123611083
250011031

prune230.0ms

Filtered
97 candidates to 64 candidates (66.0%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New97097
Fresh033
Picked011
Done022
Total976103

Merged error: 0b

Counts
103 → 6

localize7.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.0b
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
0.1b
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
69×*-un-lft-identity
56×add-sqr-sqrt
52×times-frac
39×add-cube-cbrt sqrt-prod
30×associate-*r*
15×distribute-lft-out
11×add-exp-log add-cbrt-cube
7×pow1
6×associate-*l* associate-/l* add-log-exp unswap-sqr
4×flip3-+ associate-/r* associate-/r/ flip-+
2×cbrt-undiv sqrt-div div-exp prod-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
4 → 132
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
6.0ms
(+ 1.0 (sqrt (+ x 1.0)))
9.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
18.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series518.0ms

Counts
4 → 12
Calls
4 calls:
30.0ms
(sqrt (+ x 1.0))
50.0ms
(+ 1.0 (sqrt (+ x 1.0)))
296.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
141.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify66.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
05291281
122431134
250011107

prune226.0ms

Filtered
144 candidates to 90 candidates (62.5%)
Pruning

6 alts after pruning (2 fresh and 4 done)

PrunedKeptTotal
New1440144
Fresh022
Picked011
Done033
Total1446150

Merged error: 0b

Counts
150 → 6

regimes45.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
084
184

end0.0ms

sample397.0ms

Algorithm
intervals
Results
214.0ms7998×body80valid
65.0ms2746×body80nan
0.0ms2×body1280valid

Profiling

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