Details

Time bar (total: 4.8s)

sample33.0ms

Algorithm
intervals
Results
8.0ms66×body1280valid
7.0ms275×body80nan
4.0ms42×body640valid
3.0ms124×body80valid
1.0ms16×body320valid
0.0ms8×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: 31.7b

Counts
2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

2.5b
(- (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:
8.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series73.0ms

Counts
1 → 3
Calls
1 calls:
73.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify48.0ms

Algorithm
egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 3 (45.0ms)

IterNodesCost
0132175
1400159
21559153
35001149

prune43.0ms

Filtered
22 candidates to 14 candidates (63.6%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New20222
Fresh000
Picked101
Done000
Total21223

Merged error: 0.1b

Counts
23 → 2

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)))

rewrite19.0ms

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:
7.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
10.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

series202.0ms

Counts
2 → 6
Calls
2 calls:
64.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
138.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify36.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0295535
11077482
25002453

prune110.0ms

Filtered
61 candidates to 39 candidates (63.9%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New54761
Fresh101
Picked011
Done000
Total55863

Merged error: 0.0b

Counts
63 → 8

localize9.0ms

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)))
0.3b
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite82.0ms

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:
10.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
10.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
9.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
35.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series794.0ms

Counts
4 → 12
Calls
4 calls:
349.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
144.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
136.0ms
(/ 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)))))

simplify115.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 2 (80.0ms)

IterNodesCost
06472845
131522529
250022489

prune441.0ms

Filtered
262 candidates to 135 candidates (51.5%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New2575262
Fresh426
Picked101
Done011
Total2628270

Merged error: 0.0b

Counts
270 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b
(sqrt (pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 4))
0.1b
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
0.5b
(pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 4)

rewrite61.0ms

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:
11.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
14.0ms
(sqrt (pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 4))
10.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
18.0ms
(pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 4)

series1.3s

Counts
4 → 12
Calls
4 calls:
349.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
170.0ms
(sqrt (pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 4))
139.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
623.0ms
(pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 4)

simplify94.0ms

Algorithm
egg-herbie
Counts
178 → 178
Iterations

Useful iterations: 2 (67.0ms)

IterNodesCost
07752204
129541912
250011846

prune371.0ms

Filtered
178 candidates to 108 candidates (60.7%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1771178
Fresh156
Picked011
Done011
Total1788186

Merged error: 0.0b

Counts
186 → 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

sample917.0ms

Algorithm
intervals
Results
234.0ms1814×body1280valid
207.0ms8056×body80nan
123.0ms1282×body640valid
108.0ms3997×body80valid
44.0ms588×body320valid
16.0ms319×body160valid

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