Details

Time bar (total: 2.7s)

analyze2.0ms

Algorithm
search

sample25.0ms

Algorithm
intervals
Results
7.0ms51×body1280valid
5.0ms18×body320valid
4.0ms141×body80valid
3.0ms34×body640valid
1.0ms12×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.2b

Counts
2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

2.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite8.0ms

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:
8.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series10.0ms

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

simplify121.0ms

Algorithm
egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 2 (23.0ms)

IterNodesCost
0203216
1808206
24153197
35001197

prune43.0ms

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

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New21122
Fresh000
Picked011
Done000
Total21223

Merged error: 0.2b

Counts
23 → 2

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite23.0ms

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)))

series15.0ms

Counts
2 → 6
Calls
2 calls:
6.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify63.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (52.0ms)

IterNodesCost
0435698
11872651
25001615

prune119.0ms

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

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New64670
Fresh000
Picked011
Done101
Total65772

Merged error: 0.0b

Counts
72 → 7

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

rewrite123.0ms

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)))
19.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
51.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series51.0ms

Counts
4 → 12
Calls
4 calls:
20.0ms
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
9.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
9.0ms
(/ (+ 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)))))

simplify164.0ms

Algorithm
egg-herbie
Counts
328 → 328
Iterations

Useful iterations: 2 (121.0ms)

IterNodesCost
08273981
145313471
250013422

prune574.0ms

Filtered
152 candidates to 328 candidates (-115.8%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New3226328
Fresh415
Picked011
Done011
Total3269335

Merged error: 0.0b

Counts
335 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm
rewrite-expression-head
Rules
142×*-un-lft-identity
96×sqrt-prod
61×distribute-lft-out
58×times-frac
36×add-sqr-sqrt
32×add-cube-cbrt
15×associate-/r*
11×add-exp-log add-cbrt-cube
6×pow1 sqrt-div associate-/r/
5×flip3-+ flip-+ associate-/l*
4×add-log-exp
3×cbrt-undiv rem-sqrt-square div-exp div-inv associate-/l/
2×frac-2neg sqrt-pow1 pow1/2 clear-num
1×sqrt-undiv sqrt-unprod associate-*l/ prod-exp cbrt-unprod
Counts
4 → 147
Calls
4 calls:
12.0ms
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
10.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
13.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
26.0ms
(/ (* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series55.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
10.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
9.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
12.0ms
(/ (* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify127.0ms

Algorithm
egg-herbie
Counts
159 → 159
Iterations

Useful iterations: 2 (107.0ms)

IterNodesCost
09522241
145762057
250021968

prune363.0ms

Filtered
97 candidates to 159 candidates (-63.9%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New1581159
Fresh156
Picked011
Done022
Total1599168

Merged error: 0.0b

Counts
168 → 9

regimes62.0ms

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
0126
1166
2166

end0.0ms

analyze2.0ms

Algorithm
search

sample634.0ms

Algorithm
intervals
Results
232.0ms1756×body1280valid
133.0ms1234×body640valid
113.0ms4114×body80valid
46.0ms600×body320valid
15.0ms296×body160valid
0.0ms1×body80nan

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