Details

Time bar (total: 4.4s)

sample35.0ms

Algorithm
intervals
Results
9.0ms49×body1280valid
7.0ms281×body80nan
4.0ms42×body640valid
4.0ms133×body80valid
1.0ms19×body320valid
1.0ms13×body160valid

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: 29.4b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.3b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
61×sqrt-prod
54×*-un-lft-identity
42×add-sqr-sqrt prod-diff
31×add-cube-cbrt
9×distribute-lft-out
7×fma-neg
4×add-log-exp difference-of-squares
3×pow1 distribute-lft-out--
2×add-exp-log expm1-log1p-u sqrt-div add-cbrt-cube log1p-expm1-u
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+ hypot-def
Counts
2 → 89
Calls
2 calls:
3.0ms
(sqrt (+ x 1.0))
9.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series99.0ms

Counts
2 → 6
Calls
2 calls:
29.0ms
(sqrt (+ x 1.0))
70.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify40.0ms

Algorithm
egg-herbie
Counts
95 → 95
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
02991161
1921822
25001744

prune127.0ms

Filtered
95 candidates to 44 candidates (46.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New91495
Fresh000
Picked101
Done000
Total92496

Merged error: 0.2b

Counts
96 → 4

localize7.0ms

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 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
78×*-un-lft-identity
33×distribute-lft-out
32×sqrt-prod
24×times-frac
21×add-sqr-sqrt
18×add-cube-cbrt
7×fma-def
6×associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 flip3-+ flip-+ associate-/l*
3×expm1-log1p-u log1p-expm1-u
2×sqrt-div associate-/r/ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log hypot-def div-inv
Counts
3 → 94
Calls
3 calls:
4.0ms
(sqrt (+ x 1.0))
8.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
15.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series240.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(sqrt (+ x 1.0))
62.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
142.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify49.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 2 (40.0ms)

IterNodesCost
0409789
11675716
25001675

prune201.0ms

Filtered
103 candidates to 68 candidates (66.0%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New967103
Fresh213
Picked011
Done000
Total989107

Merged error: 0.0b

Counts
107 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite114.0ms

Algorithm
rewrite-expression-head
Rules
597×*-un-lft-identity
420×sqrt-prod
256×distribute-lft-out
247×times-frac
130×add-sqr-sqrt
99×add-cube-cbrt
71×swap-sqr
33×associate-*r* associate-*l*
20×pow1
14×associate-/r/
12×associate-/r*
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 flip3-+ pow1/2 flip-+ unswap-sqr
8×associate-/l*
7×div-inv
5×sqrt-div pow-prod-up
4×expm1-log1p-u log1p-expm1-u associate-/l/ 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 → 324
Calls
4 calls:
12.0ms
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
12.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
12.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
48.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series799.0ms

Counts
4 → 12
Calls
4 calls:
348.0ms
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
144.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
137.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
169.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify136.0ms

Algorithm
egg-herbie
Counts
336 → 336
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
07233905
138853364
250023360

prune540.0ms

Filtered
336 candidates to 156 candidates (46.4%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New3315336
Fresh347
Picked011
Done101
Total33510345

Merged error: 0.0b

Counts
345 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ (+ 1.0 0) (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
0.3b
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
90×sqrt-prod
78×*-un-lft-identity
46×add-sqr-sqrt
34×distribute-lft-out
28×sqrt-div
21×pow1
16×add-cube-cbrt
15×flip3-+ swap-sqr flip-+
11×add-exp-log add-cbrt-cube
10×sqrt-pow1 pow1/2
9×associate-*r* associate-*l*
8×frac-times associate-/r/ hypot-def
5×pow-prod-up
4×expm1-log1p-u times-frac associate-*r/ associate-*l/ log1p-expm1-u associate-/l* add-log-exp unswap-sqr
3×pow-prod-down pow-sqr
2×cbrt-undiv rem-sqrt-square div-exp prod-exp cbrt-unprod associate-/l/
1×pow2 frac-2neg pow-plus sqrt-unprod clear-num associate-/r* rem-square-sqrt *-commutative div-inv
Counts
4 → 155
Calls
4 calls:
8.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
27.0ms
(/ (+ 1.0 0) (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
20.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series526.0ms

Counts
4 → 12
Calls
4 calls:
155.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
159.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
142.0ms
(/ (+ 1.0 0) (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
69.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify89.0ms

Algorithm
egg-herbie
Counts
167 → 167
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
05801748
128081508
250011484

prune289.0ms

Filtered
167 candidates to 92 candidates (55.1%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1643167
Fresh268
Picked101
Done011
Total16710177

Merged error: 0.0b

Counts
177 → 10

regimes42.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01415
11815
21815

end0.0ms

sample951.0ms

Algorithm
intervals
Results
239.0ms1791×body1280valid
221.0ms8286×body80nan
132.0ms1225×body640valid
115.0ms4107×body80valid
46.0ms596×body320valid
15.0ms281×body160valid