Details

Time bar (total: 2.8s)

sample36.0ms

Algorithm
intervals
Results
7.0ms269×body80nan
7.0ms52×body1280valid
4.0ms140×body80valid
3.0ms33×body640valid
1.0ms19×body320valid
1.0ms12×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
094
1104
2104

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 27.7b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
3.6b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
12×add-sqr-sqrt *-un-lft-identity sqrt-prod
4×add-log-exp difference-of-squares
3×pow1 add-cube-cbrt distribute-lft-out--
2×add-exp-log sqrt-div add-cbrt-cube distribute-lft-out
1×sub-neg rem-sqrt-square flip3-- sqrt-pow1 flip3-+ pow1/2 diff-log flip-- flip-+
Counts
2 → 35
Calls
2 calls:
3.0ms
(sqrt (+ x 1.0))
7.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series14.0ms

Counts
2 → 6
Calls
2 calls:
3.0ms
(sqrt (+ x 1.0))
10.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify32.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
0282318
11037308
25001297

prune75.0ms

Filtered
31 candidates to 41 candidates (-32.3%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New37441
Fresh000
Picked101
Done000
Total38442

Merged error: 0.1b

Counts
42 → 4

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
74×*-un-lft-identity
32×distribute-lft-out
28×sqrt-prod
24×times-frac
17×add-sqr-sqrt
16×add-cube-cbrt
6×associate-/r*
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/ associate-/l/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 80
Calls
3 calls:
3.0ms
(sqrt (+ x 1.0))
8.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
12.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series18.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(sqrt (+ x 1.0))
5.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
9.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify66.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (57.0ms)

IterNodesCost
0514800
12206753
25001721

prune156.0ms

Filtered
59 candidates to 89 candidates (-50.8%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New81889
Fresh303
Picked011
Done000
Total84993

Merged error: 0.0b

Counts
93 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b
(sqrt (sqrt (+ x 1.0)))
0.1b
(sqrt (sqrt (+ x 1.0)))
0.2b
(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
0.2b
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
106×sqrt-prod
63×add-sqr-sqrt
55×*-un-lft-identity
40×sqrt-pow1
32×sqrt-div
31×pow1
29×add-cube-cbrt
20×pow1/2
18×swap-sqr
12×times-frac distribute-lft-out
10×flip3-+ associate-*r* associate-*l* flip-+
9×pow-prod-up unswap-sqr
8×add-exp-log add-cbrt-cube
5×pow-prod-down pow-sqr
4×frac-times rem-sqrt-square associate-/l* add-log-exp
3×associate-/r*
2×associate-*r/ associate-*l/ associate-/r/ associate-/l/
1×cbrt-undiv pow2 frac-2neg pow-plus sqrt-unprod div-exp prod-exp clear-num rem-square-sqrt *-commutative cbrt-unprod div-inv
Counts
4 → 167
Calls
4 calls:
4.0ms
(sqrt (sqrt (+ x 1.0)))
4.0ms
(sqrt (sqrt (+ x 1.0)))
17.0ms
(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
16.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

series25.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(sqrt (sqrt (+ x 1.0)))
6.0ms
(sqrt (sqrt (+ x 1.0)))
9.0ms
(/ (+ 1.0 0) (+ (* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0)))) (sqrt x)))
4.0ms
(* (sqrt (sqrt (+ x 1.0))) (sqrt (sqrt (+ x 1.0))))

simplify110.0ms

Algorithm
egg-herbie
Counts
179 → 179
Iterations

Useful iterations: 2 (89.0ms)

IterNodesCost
06791539
133011371
250021347

prune284.0ms

Filtered
96 candidates to 179 candidates (-86.5%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1772179
Fresh257
Picked011
Done011
Total1799188

Merged error: 0.0b

Counts
188 → 9

localize10.0ms

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 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite103.0ms

Algorithm
rewrite-expression-head
Rules
1122×*-un-lft-identity
900×sqrt-prod
774×times-frac
460×distribute-lft-out
294×add-sqr-sqrt
292×add-cube-cbrt
46×associate-/l*
28×sqrt-div
24×associate-/r/
18×associate-/r*
15×flip3-+ flip-+
12×div-inv
11×add-exp-log add-cbrt-cube
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×associate-/l/
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num
Counts
4 → 547
Calls
4 calls:
10.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
7.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
12.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
30.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series56.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
10.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
18.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
17.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify122.0ms

Algorithm
egg-herbie
Counts
559 → 559
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0130411535
150019913

prune604.0ms

Filtered
154 candidates to 559 candidates (-263.0%)
Pruning

9 alts after pruning (6 fresh and 3 done)

PrunedKeptTotal
New5590559
Fresh066
Picked011
Done022
Total5599568

Merged error: 0.0b

Counts
568 → 9

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
0126
1166
2166

end0.0ms

sample955.0ms

Algorithm
intervals
Results
219.0ms1710×body1280valid
205.0ms7902×body80nan
119.0ms1161×body640valid
114.0ms4192×body80valid
46.0ms630×body320valid
15.0ms307×body160valid

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