Details

Time bar (total: 5.4s)

sample25.0ms

Algorithm
intervals
Results
6.0ms229×body80nan
4.0ms52×body1280valid
3.0ms46×body640valid
2.0ms135×body80valid
1.0ms17×body320valid
0.0ms6×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 (100.0%)
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:

1.9b
(- (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))

series77.0ms

Counts
1 → 3
Calls
1 calls:
76.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify48.0ms

Algorithm
egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 3 (44.0ms)

IterNodesCost
0129175
1383159
21492153
35002149

prune37.0ms

Filtered
22 candidates to 14 candidates (36.4%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New20222
Fresh000
Picked101
Done000
Total21223

Merged error: 0.1b

Counts
23 → 2

localize6.0ms

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)))

rewrite20.0ms

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)))

series222.0ms

Counts
2 → 6
Calls
2 calls:
69.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
153.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify35.0ms

Algorithm
egg-herbie
Counts
61 → 61
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0292535
11048482
25001453

prune98.0ms

Filtered
61 candidates to 39 candidates (36.1%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New55661
Fresh101
Picked011
Done000
Total56763

Merged error: 0.0b

Counts
63 → 7

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)))))

rewrite115.0ms

Algorithm
rewrite-expression-head
Rules
540×*-un-lft-identity
382×sqrt-prod
324×sqrt-div
224×distribute-lft-out
174×associate-/r*
173×add-sqr-sqrt
157×times-frac
144×frac-times
142×add-cube-cbrt
87×associate-/l*
41×swap-sqr
29×frac-2neg clear-num
27×associate-*r* associate-*l*
20×pow1
14×associate-/r/
12×associate-*r/ associate-*l/
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 pow1/2 unswap-sqr
7×flip3-+ flip-+ div-inv
5×pow-prod-up
4×add-log-exp
3×pow-prod-down pow-sqr
2×cbrt-undiv rem-sqrt-square div-exp
1×pow2 pow-plus sqrt-unprod prod-exp rem-square-sqrt *-commutative cbrt-unprod
Counts
4 → 426
Calls
4 calls:
11.0ms
(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)))
45.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

series820.0ms

Counts
4 → 12
Calls
4 calls:
352.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
146.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
145.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
177.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify139.0ms

Algorithm
egg-herbie
Counts
438 → 438
Iterations

Useful iterations: 2 (84.0ms)

IterNodesCost
07935700
136235087
250015004

prune534.0ms

Filtered
438 candidates to 174 candidates (60.3%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New4344438
Fresh325
Picked011
Done011
Total4378445

Merged error: 0.0b

Counts
445 → 8

localize11.0ms

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)))
0.2b
(/ 1 (sqrt (/ (+ (sqrt (+ x 1.0)) (sqrt x)) 1.0)))
0.3b
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1 (sqrt (/ (+ (sqrt (+ x 1.0)) (sqrt x)) 1.0))))

rewrite207.0ms

Algorithm
rewrite-expression-head
Rules
1136×*-un-lft-identity
934×sqrt-prod
596×times-frac
560×associate-/r*
458×add-sqr-sqrt
424×sqrt-div
420×distribute-lft-out
391×add-cube-cbrt
372×frac-times
157×associate-/l*
93×associate-*r*
51×clear-num
50×frac-2neg
34×associate-/r/
31×associate-*r/
27×associate-*l*
25×div-inv
21×unswap-sqr
19×add-exp-log
13×add-cbrt-cube
12×associate-*l/
9×pow1
5×flip3-+ div-exp flip-+
4×prod-exp associate-/l/ add-log-exp
3×cbrt-undiv pow-flip un-div-inv
2×rem-sqrt-square rec-exp sqrt-pow1 pow1/2 1-exp cbrt-unprod
1×pow-prod-down *-commutative inv-pow
Counts
4 → 797
Calls
4 calls:
11.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
10.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
21.0ms
(/ 1 (sqrt (/ (+ (sqrt (+ x 1.0)) (sqrt x)) 1.0)))
83.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1 (sqrt (/ (+ (sqrt (+ x 1.0)) (sqrt x)) 1.0))))

series1.0s

Counts
4 → 12
Calls
4 calls:
354.0ms
(sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x))))
146.0ms
(/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))
384.0ms
(/ 1 (sqrt (/ (+ (sqrt (+ x 1.0)) (sqrt x)) 1.0)))
147.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (/ 1 (sqrt (/ (+ (sqrt (+ x 1.0)) (sqrt x)) 1.0))))

simplify162.0ms

Algorithm
egg-herbie
Counts
809 → 809
Iterations

Useful iterations: 1 (44.0ms)

IterNodesCost
0201614153
1500113262

prune1.1s

Filtered
809 candidates to 332 candidates (59.0%)
Pruning

7 alts after pruning (5 fresh and 2 done)

PrunedKeptTotal
New8081809
Fresh145
Picked101
Done022
Total8107817

Merged error: 0.0b

Counts
817 → 7

regimes32.0ms

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

sample634.0ms

Algorithm
intervals
Results
134.0ms1679×body1280valid
125.0ms7872×body80nan
89.0ms1255×body640valid
75.0ms4148×body80valid
30.0ms625×body320valid
9.0ms293×body160valid