Details

Time bar (total: 2.9s)

analyze2.0ms

Algorithm
search

sample21.0ms

Algorithm
intervals
Results
6.0ms47×body1280valid
4.0ms41×body640valid
4.0ms139×body80valid
1.0ms17×body320valid
1.0ms12×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.2b

Counts
2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

3.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
9×add-sqr-sqrt
8×*-un-lft-identity sqrt-prod
4×difference-of-squares
3×distribute-lft-out-- add-log-exp
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out
Counts
1 → 19
Calls
1 calls:
12.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series10.0ms

Counts
1 → 3
Calls
1 calls:
10.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify118.0ms

Algorithm
egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0203216
1808206
24153197
35001197

prune45.0ms

Filtered
15 candidates to 22 candidates (-46.7%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New19322
Fresh000
Picked101
Done000
Total20323

Merged error: 0.1b

Counts
23 → 3

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
70×*-un-lft-identity
31×distribute-lft-out
24×times-frac sqrt-prod
14×add-sqr-sqrt add-cube-cbrt
6×associate-/r*
4×add-exp-log add-cbrt-cube associate-/l* add-log-exp
3×flip3-+ flip-+
2×pow1 associate-/r/ associate-/l/
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 64
Calls
2 calls:
7.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
12.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series14.0ms

Counts
2 → 6
Calls
2 calls:
5.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify58.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
0435698
11872651
25001615

prune117.0ms

Filtered
44 candidates to 70 candidates (-59.1%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New65570
Fresh112
Picked011
Done000
Total66773

Merged error: 0.0b

Counts
73 → 7

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(/ (+ 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)))))

rewrite98.0ms

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×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 → 316
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)))
14.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
40.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series53.0ms

Counts
4 → 12
Calls
4 calls:
19.0ms
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
9.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
14.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
12.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify165.0ms

Algorithm
egg-herbie
Counts
328 → 328
Iterations

Useful iterations: 2 (123.0ms)

IterNodesCost
08273981
145313471
250013422

prune545.0ms

Filtered
151 candidates to 328 candidates (-117.2%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New3262328
Fresh055
Picked011
Done011
Total3269335

Merged error: 0b

Counts
335 → 9

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)))
0.1b
(/ (+ 1.0 0) (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))))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
1122×*-un-lft-identity
900×sqrt-prod
774×times-frac
460×distribute-lft-out
294×add-sqr-sqrt
292×add-cube-cbrt
46×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
15×flip3-+ flip-+
12×div-inv
11×add-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 547
Calls
4 calls:
7.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
7.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
13.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
34.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series54.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
24.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
9.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify125.0ms

Algorithm
egg-herbie
Counts
559 → 559
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0130411535
150019913

prune648.0ms

Filtered
154 candidates to 559 candidates (-263.0%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New5572559
Fresh336
Picked011
Done022
Total5608568

Merged error: 0b

Counts
568 → 8

regimes54.0ms

Accuracy

0% (0.1b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0126
1166
2166

end0.0ms

analyze2.0ms

Algorithm
search

sample605.0ms

Algorithm
intervals
Results
217.0ms1714×body1280valid
121.0ms1221×body640valid
110.0ms4109×body80valid
52.0ms646×body320valid
15.0ms310×body160valid
0.0ms2×body80nan

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