Details

Time bar (total: 2.8s)

analyze2.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%100%0%0
0%100%0%1
50%50%0%2
50%25%25%3
50%12.5%37.5%4
50%6.2%43.8%5
50%3.1%46.9%6
50%1.6%48.5%7
50%0.8%49.2%8
50%0.4%49.6%9
50%0.2%49.8%10
50%0.1%49.9%11
50%0%50%12
50%0%50%13
50%0%50%14

sample22.0ms

Algorithm
intervals
Results
6.0ms53×body1280valid
5.0ms49×body640valid
4.0ms134×body80valid
1.0ms12×body320valid
0.0ms8×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (4.0ms)

IterNodesCost
0777
1777

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.2b

Counts
2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

2.0b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite12.0ms

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 → 18
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))

simplify49.0ms

Algorithm
egg-herbie
Counts
21 → 21
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
04938339
14938339

prune45.0ms

Filtered
15 candidates to 21 candidates (-40.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New19221
Fresh000
Picked101
Done000
Total20222

Merged error: 0.1b

Counts
22 → 2

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)))

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:
8.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
13.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series15.0ms

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)))

simplify48.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
05331976

prune134.0ms

Filtered
46 candidates to 70 candidates (-52.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New64670
Fresh011
Picked011
Done000
Total64872

Merged error: 0.0b

Counts
72 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.0b
(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.1b
(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.2b
(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite94.0ms

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 (+ 1.0 x)) (sqrt x)))
14.0ms
(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
28.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series64.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms
(sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))
18.0ms
(/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x))))
25.0ms
(/ (/ 1.0 (sqrt (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify161.0ms

Algorithm
egg-herbie
Counts
457 → 457
Iterations

Useful iterations: 0 (92.0ms)

IterNodesCost
0489911267
1489911267

prune609.0ms

Filtered
149 candidates to 457 candidates (-206.7%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New4534457
Fresh336
Picked101
Done011
Total4578465

Merged error: 0b

Counts
465 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x))))
0.1b
(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.1b
(/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))
0.3b
(* (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ 1.0 x)) (sqrt x)))))

rewrite85.0ms

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

series49.0ms

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

simplify88.0ms

Algorithm
egg-herbie
Counts
262 → 262
Iterations

Useful iterations: 0 (55.0ms)

IterNodesCost
049644319
149644319

prune469.0ms

Filtered
142 candidates to 262 candidates (-84.5%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New2620262
Fresh066
Picked011
Done011
Total2628270

Merged error: 0b

Counts
270 → 8

regimes116.0ms

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 (1.0ms)

IterNodesCost
0299
1299

end0.0ms

sample613.0ms

Algorithm
intervals
Results
215.0ms1719×body1280valid
124.0ms1256×body640valid
118.0ms4138×body80valid
42.0ms584×body320valid
15.0ms303×body160valid
0.0ms1×body80nan

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