Details

Time bar (total: 4.3s)

sample32.0ms

Algorithm
intervals
Results
6.0ms248×body80nan
6.0ms49×body1280valid
4.0ms36×body640valid
3.0ms132×body80valid
2.0ms21×body320valid
1.0ms18×body160valid

simplify4.0ms

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 2 expressions with local error:

0.0b
(sqrt (+ x 1.0))
4.4b
(- (sqrt (+ x 1.0)) (sqrt x))

rewrite15.0ms

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))
12.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

series13.0ms

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

simplify30.0ms

Algorithm
egg-herbie
Counts
41 → 41
Iterations

Useful iterations: 2 (26.0ms)

IterNodesCost
0282318
11037308
25001297

prune74.0ms

Filtered
41 candidates to 31 candidates (24.4%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New38341
Fresh000
Picked011
Done000
Total38442

Merged error: 0.1b

Counts
42 → 4

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.1b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

rewrite26.0ms

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))
9.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
11.0ms
(/ (+ 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

prune159.0ms

Filtered
89 candidates to 59 candidates (33.7%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New81889
Fresh202
Picked011
Done101
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)) (sqrt x)))
0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.1b
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite109.0ms

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:
7.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
7.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
13.0ms
(/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
33.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series48.0ms

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))))
9.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify131.0ms

Algorithm
egg-herbie
Counts
559 → 559
Iterations

Useful iterations: 1 (33.0ms)

IterNodesCost
0130411535
150019913

prune644.0ms

Filtered
559 candidates to 153 candidates (72.6%)
Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New5554559
Fresh527
Picked101
Done011
Total5617568

Merged error: 0.0b

Counts
568 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite113.0ms

Algorithm
rewrite-expression-head
Rules
363×sqrt-prod
278×sqrt-div
222×times-frac
220×*-un-lft-identity
114×associate-/r/
103×add-sqr-sqrt
92×flip3-+ flip-+
87×add-cube-cbrt
76×distribute-lft-out
60×frac-times
30×associate-*r/ associate-*l/
20×add-exp-log add-cbrt-cube
18×associate-/l*
17×pow1
15×sqrt-pow1 div-inv
13×associate-/r*
12×associate-*r*
9×pow1/2 associate-*l*
7×cbrt-undiv div-exp
6×pow-prod-up unswap-sqr
4×add-log-exp
3×pow-prod-down prod-exp cbrt-unprod
2×rem-sqrt-square frac-2neg pow3 clear-num
1×sqrt-unprod *-commutative associate-/l/
Counts
4 → 336
Calls
4 calls:
12.0ms
(sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
20.0ms
(/ 1.0 (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
21.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
37.0ms
(/ (/ 1.0 (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

series80.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
35.0ms
(/ 1.0 (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))))
21.0ms
(* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))
10.0ms
(/ (/ 1.0 (* (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify107.0ms

Algorithm
egg-herbie
Counts
348 → 348
Iterations

Useful iterations: 1 (32.0ms)

IterNodesCost
0153610456
150019758

prune1.5s

Filtered
348 candidates to 242 candidates (30.5%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New3471348
Fresh055
Picked011
Done011
Total3478355

Merged error: 0b

Counts
355 → 8

regimes59.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0126
1166
2166

end0.0ms

sample980.0ms

Algorithm
intervals
Results
224.0ms1758×body1280valid
215.0ms8177×body80nan
126.0ms1218×body640valid
112.0ms4057×body80valid
47.0ms625×body320valid
19.0ms342×body160valid

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