Details

Time bar (total: 3.9s)

sample37.0ms

Algorithm
intervals
Results
9.0ms70×body1280valid
6.0ms246×body80nan
5.0ms49×body640valid
5.0ms4×body160valid
3.0ms118×body80valid
1.0ms15×body320valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

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: 33.2b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
2.1b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity sqrt-prod
4×add-log-exp difference-of-squares
3×pow1 add-cube-cbrt distribute-lft-out--
2×add-exp-log sqrt-div add-cbrt-cube distribute-lft-out
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+
Counts
2 → 35
Calls
2 calls:
3.0ms
(sqrt (+ x 1.0))
8.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series100.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(sqrt (+ x 1.0))
71.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify56.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 3 (52.0ms)

IterNodesCost
0182265
1544243
22020233
35002230

prune69.0ms

Filtered
41 candidates to 28 candidates (68.3%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New39241
Fresh000
Picked101
Done000
Total40242

Merged error: 0.1b

Counts
42 → 2

localize6.0ms

Local error

Found 2 expressions with local error:

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

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
44×*-un-lft-identity
20×sqrt-prod
18×times-frac
17×distribute-lft-out
15×add-sqr-sqrt
14×add-cube-cbrt
6×associate-/r*
4×add-exp-log add-cbrt-cube
3×pow1 associate-/l*
2×flip3-+ sqrt-div associate-/r/ flip-+ add-log-exp
1×cbrt-undiv rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num div-inv
Counts
2 → 57
Calls
2 calls:
3.0ms
(sqrt (+ x 1.0))
9.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series172.0ms

Counts
2 → 6
Calls
2 calls:
35.0ms
(sqrt (+ x 1.0))
137.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify35.0ms

Algorithm
egg-herbie
Counts
63 → 63
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0309501
11128459
25002430

prune120.0ms

Filtered
63 candidates to 40 candidates (63.5%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New55863
Fresh011
Picked011
Done000
Total551065

Merged error: 0.0b

Counts
65 → 10

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ x 1.0)))
0.1b
(sqrt (sqrt (+ x 1.0)))
0.2b
(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
0.3b
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
106×sqrt-prod
62×add-sqr-sqrt
46×*-un-lft-identity
40×sqrt-pow1
32×sqrt-div
31×pow1
28×add-cube-cbrt
20×pow1/2
18×swap-sqr
10×associate-*r* associate-*l*
9×flip3-+ times-frac pow-prod-up flip-+ unswap-sqr
8×add-exp-log add-cbrt-cube distribute-lft-out
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square add-log-exp
3×associate-/r* associate-/l*
2×associate-*r/ associate-*l/ associate-/r/
1×cbrt-undiv pow2 frac-2neg pow-plus sqrt-unprod div-exp prod-exp clear-num rem-square-sqrt *-commutative cbrt-unprod div-inv
Counts
4 → 161
Calls
4 calls:
4.0ms
(sqrt (sqrt (+ x 1.0)))
4.0ms
(sqrt (sqrt (+ x 1.0)))
15.0ms
(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
15.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series359.0ms

Counts
4 → 12
Calls
4 calls:
90.0ms
(sqrt (sqrt (+ x 1.0)))
90.0ms
(sqrt (sqrt (+ x 1.0)))
144.0ms
(/ 1.0 (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
36.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify72.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
05251350
123291176
250011152

prune460.0ms

Filtered
173 candidates to 92 candidates (53.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1712173
Fresh268
Picked101
Done011
Total1749183

Merged error: 0.0b

Counts
183 → 9

localize8.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite80.0ms

Algorithm
rewrite-expression-head
Rules
297×*-un-lft-identity
274×sqrt-prod
157×times-frac
119×add-sqr-sqrt
116×distribute-lft-out
88×add-cube-cbrt
41×swap-sqr
27×associate-*r* associate-*l*
20×pow1
14×associate-/r/
12×associate-/r*
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 pow1/2 unswap-sqr
7×flip3-+ flip-+ div-inv
6×associate-/l*
5×sqrt-div pow-prod-up
4×add-log-exp
3×pow-prod-down pow-sqr
2×cbrt-undiv rem-sqrt-square frac-2neg div-exp clear-num
1×pow2 frac-times pow-plus sqrt-unprod associate-*r/ associate-*l/ prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 250
Calls
4 calls:
10.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
9.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
9.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
37.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series775.0ms

Counts
4 → 12
Calls
4 calls:
346.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
136.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
133.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
160.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify104.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
06472845
131522529
250022489

prune409.0ms

Filtered
262 candidates to 136 candidates (51.9%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New2566262
Fresh257
Picked101
Done011
Total25912271

Merged error: 0b

Counts
271 → 12

regimes40.0ms

Accuracy

0% (0.1b 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
095
195

end0.0ms

sample928.0ms

Algorithm
intervals
Results
224.0ms1719×body1280valid
219.0ms8240×body80nan
131.0ms1296×body640valid
111.0ms4058×body80valid
44.0ms595×body320valid
17.0ms332×body160valid

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