Details

Time bar (total: 2.3s)

sample35.0ms

Algorithm
intervals
Results
8.0ms63×body1280valid
7.0ms255×body80nan
5.0ms45×body640valid
3.0ms120×body80valid
2.0ms23×body320valid
0.0ms5×body160valid

simplify3.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0107
1107

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 32.7b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
1.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite12.0ms

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))

series13.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(sqrt (+ x 1.0))
10.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify32.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
05141523

prune68.0ms

Filtered
30 candidates to 41 candidates (-36.7%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New39241
Fresh000
Picked101
Done000
Total40242

Merged error: 0.2b

Counts
42 → 2

localize6.0ms

Local error

Found 3 expressions with local error:

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

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
52×*-un-lft-identity
24×sqrt-prod
21×distribute-lft-out
18×times-frac
16×add-sqr-sqrt
15×add-cube-cbrt
6×associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1
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 → 71
Calls
3 calls:
3.0ms
(sqrt (+ x 1.0))
8.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
10.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series18.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(sqrt (+ x 1.0))
5.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify60.0ms

Algorithm
egg-herbie
Counts
80 → 80
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
050701035

prune143.0ms

Filtered
59 candidates to 80 candidates (-35.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New72880
Fresh101
Picked011
Done000
Total73982

Merged error: 0.0b

Counts
82 → 9

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

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 (+ 1.0 x)))
6.0ms
(sqrt (sqrt (+ 1.0 x)))
15.0ms
(/ 1.0 (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x)))
15.0ms
(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

series24.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(sqrt (sqrt (+ 1.0 x)))
6.0ms
(sqrt (sqrt (+ 1.0 x)))
9.0ms
(/ 1.0 (+ (* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x)))) (sqrt x)))
4.0ms
(* (sqrt (sqrt (+ 1.0 x))) (sqrt (sqrt (+ 1.0 x))))

simplify50.0ms

Algorithm
egg-herbie
Counts
173 → 173
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
049201732
149201732

prune225.0ms

Filtered
89 candidates to 173 candidates (-94.4%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1730173
Fresh077
Picked011
Done011
Total1739182

Merged error: 0.0b

Counts
182 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 1.0 (+ (* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x)))) (sqrt x)))
0.2b
(* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x))))
0.3b
(cbrt (+ 1.0 x))
0.3b
(cbrt (+ 1.0 x))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt *-un-lft-identity
18×add-cube-cbrt
13×cbrt-prod
10×associate-*r*
9×times-frac sqrt-prod
8×add-exp-log add-cbrt-cube
6×pow1 cbrt-div
4×flip3-+ flip-+ add-log-exp
3×associate-*l* associate-/r* distribute-lft-out associate-/l* unswap-sqr
2×pow1/3 sqrt-div associate-*r/ associate-/r/
1×cbrt-undiv frac-2neg div-exp pow-prod-down prod-exp clear-num *-commutative cbrt-unprod div-inv
Counts
4 → 86
Calls
4 calls:
13.0ms
(/ 1.0 (+ (* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x)))) (sqrt x)))
8.0ms
(* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x))))
3.0ms
(cbrt (+ 1.0 x))
3.0ms
(cbrt (+ 1.0 x))

series64.0ms

Counts
4 → 12
Calls
4 calls:
42.0ms
(/ 1.0 (+ (* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x)))) (sqrt x)))
10.0ms
(* (fabs (cbrt (+ 1.0 x))) (sqrt (cbrt (+ 1.0 x))))
6.0ms
(cbrt (+ 1.0 x))
6.0ms
(cbrt (+ 1.0 x))

simplify69.0ms

Algorithm
egg-herbie
Counts
98 → 98
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
048512085
148512085

prune267.0ms

Filtered
80 candidates to 98 candidates (-22.5%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New96298
Fresh156
Picked101
Done022
Total989107

Merged error: 0.0b

Counts
107 → 9

regimes54.0ms

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
099
199

end0.0ms

sample997.0ms

Algorithm
intervals
Results
230.0ms1715×body1280valid
217.0ms8049×body80nan
127.0ms1243×body640valid
114.0ms4079×body80valid
52.0ms651×body320valid
16.0ms312×body160valid

Profiling

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