Details

Time bar (total: 4.7s)

sample24.0ms

Algorithm
intervals
Results
4.0ms248×body80nan
4.0ms39×body1280valid
3.0ms46×body640valid
3.0ms149×body80valid
1.0ms19×body320valid
0.0ms3×body160valid

simplify7.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (2.0ms)

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: 25.8b

Counts
2 → 1

localize6.0ms

Local error

Found 1 expressions with local error:

1.2b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite10.0ms

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:
9.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series87.0ms

Counts
1 → 3
Calls
1 calls:
86.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify62.0ms

Algorithm
egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 3 (58.0ms)

IterNodesCost
0132175
1400159
21559153
35001149

prune46.0ms

Filtered
22 candidates to 14 candidates (63.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New20222
Fresh000
Picked011
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 (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
20×sqrt-prod distribute-lft-out
18×times-frac
13×add-sqr-sqrt add-cube-cbrt
6×associate-/r*
4×add-exp-log add-cbrt-cube add-log-exp
3×associate-/l*
2×pow1 flip3-+ associate-/r/ flip-+
1×cbrt-undiv +-commutative frac-2neg div-exp clear-num sum-log div-inv
Counts
2 → 55
Calls
2 calls:
8.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
10.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series234.0ms

Counts
2 → 6
Calls
2 calls:
76.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
158.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify51.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0295535
11077482
25001453

prune133.0ms

Filtered
61 candidates to 39 candidates (63.9%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New56561
Fresh011
Picked011
Done101
Total57764

Merged error: 0.0b

Counts
64 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite88.0ms

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:
11.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
11.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
36.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series900.0ms

Counts
4 → 12
Calls
4 calls:
382.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
166.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
158.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
193.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify125.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 2 (86.0ms)

IterNodesCost
06472845
131522529
250022489

prune496.0ms

Filtered
262 candidates to 137 candidates (52.3%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New2593262
Fresh145
Picked011
Done011
Total2609269

Merged error: 0.0b

Counts
269 → 9

localize14.0ms

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

rewrite98.0ms

Algorithm
rewrite-expression-head
Rules
742×*-un-lft-identity
700×sqrt-prod
594×times-frac
280×distribute-lft-out
254×add-sqr-sqrt
252×add-cube-cbrt
36×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
14×flip3-+ flip-+
12×div-inv
11×add-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv div-exp add-log-exp
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
1×associate-/l/
Counts
4 → 445
Calls
4 calls:
8.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
8.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
11.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
29.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series882.0ms

Counts
4 → 12
Calls
4 calls:
176.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
188.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
360.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
157.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify157.0ms

Algorithm
egg-herbie
Counts
457 → 457
Iterations

Useful iterations: 2 (77.0ms)

IterNodesCost
010338862
141207704
250017681

prune534.0ms

Filtered
457 candidates to 147 candidates (32.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New4543457
Fresh246
Picked101
Done112
Total4588466

Merged error: 0b

Counts
466 → 8

regimes36.0ms

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

sample680.0ms

Algorithm
intervals
Results
158.0ms1688×body1280valid
134.0ms7900×body80nan
86.0ms1248×body640valid
80.0ms4119×body80valid
33.0ms641×body320valid
13.0ms304×body160valid