Details

Time bar (total: 5.0s)

sample34.0ms

Algorithm
intervals
Results
7.0ms56×body1280valid
7.0ms243×body80nan
4.0ms40×body640valid
3.0ms118×body80valid
2.0ms29×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: 32.6b

Counts
2 → 1

localize9.0ms

Local error

Found 1 expressions with local error:

3.9b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite9.0ms

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))

series67.0ms

Counts
1 → 3
Calls
1 calls:
67.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify52.0ms

Algorithm
egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 3 (43.0ms)

IterNodesCost
0132175
1400159
21559153
35001149

prune44.0ms

Filtered
22 candidates to 14 candidates (63.6%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New19322
Fresh000
Picked101
Done000
Total20323

Merged error: 0.2b

Counts
23 → 3

localize6.0ms

Local error

Found 2 expressions with local error:

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

series200.0ms

Counts
2 → 6
Calls
2 calls:
65.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
135.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify36.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (30.0ms)

IterNodesCost
0295535
11077482
25001453

prune123.0ms

Filtered
61 candidates to 39 candidates (63.9%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New53861
Fresh112
Picked011
Done000
Total541064

Merged error: 0.0b

Counts
64 → 10

localize9.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b
(* (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))))
10.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
41.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series793.0ms

Counts
4 → 12
Calls
4 calls:
344.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
143.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
141.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
165.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify113.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 2 (78.0ms)

IterNodesCost
06472845
131522529
250022489

prune466.0ms

Filtered
262 candidates to 133 candidates (50.8%)
Pruning

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New2575262
Fresh358
Picked101
Done011
Total26111272

Merged error: 0.0b

Counts
272 → 11

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 4))
0.1b
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.6b
(pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 4)

rewrite65.0ms

Algorithm
rewrite-expression-head
Rules
157×sqrt-prod
140×*-un-lft-identity
74×times-frac
57×add-sqr-sqrt unpow-prod-down
52×distribute-lft-out
49×add-cube-cbrt
8×associate-/r/
7×pow1 add-exp-log rem-sqrt-square
6×associate-/r* add-cbrt-cube
4×flip3-+ flip-+ div-inv add-log-exp
3×pow-unpow pow-pow sqrt-pow1 pow1/2 associate-/l* sqr-pow
1×cbrt-undiv pow-to-exp frac-2neg sqrt-div div-exp pow-exp clear-num sqrt-pow2
Counts
4 → 166
Calls
4 calls:
16.0ms
(sqrt (pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 4))
11.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
15.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
14.0ms
(pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 4)

series1.3s

Counts
4 → 12
Calls
4 calls:
170.0ms
(sqrt (pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 4))
348.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
138.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
604.0ms
(pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 4)

simplify94.0ms

Algorithm
egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
07752204
129541912
250011846

prune404.0ms

Filtered
178 candidates to 108 candidates (60.7%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1753178
Fresh279
Picked011
Done011
Total17712189

Merged error: 0.0b

Counts
189 → 12

regimes51.0ms

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

sample985.0ms

Algorithm
intervals
Results
234.0ms8097×body80nan
232.0ms1770×body1280valid
123.0ms1197×body640valid
118.0ms4102×body80valid
48.0ms621×body320valid
16.0ms310×body160valid