Details

Time bar (total: 6.0s)

sample32.0ms

Algorithm
intervals
Results
7.0ms59×body1280valid
7.0ms278×body80nan
4.0ms46×body640valid
3.0ms125×body80valid
1.0ms16×body320valid
0.0ms10×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: 31.3b

Counts
2 → 1

localize5.0ms

Local error

Found 1 expressions with local error:

2.9b
(- (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))

series177.0ms

Counts
1 → 3
Calls
1 calls:
177.0ms
(- (sqrt (+ x 1.0)) (sqrt x))

simplify117.0ms

Algorithm
egg-herbie
Counts
22 → 22
Iterations

Useful iterations: 2 (22.0ms)

IterNodesCost
0203216
1808206
24153197
35001197

prune54.0ms

Filtered
22 candidates to 15 candidates (68.2%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New19322
Fresh000
Picked011
Done000
Total19423

Merged error: 0.2b

Counts
23 → 4

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(+ (sqrt (+ x 1.0)) (sqrt x))
0.2b
(/ (+ 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:
7.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
13.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

series441.0ms

Counts
2 → 6
Calls
2 calls:
96.0ms
(+ (sqrt (+ x 1.0)) (sqrt x))
345.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))

simplify63.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (55.0ms)

IterNodesCost
0435698
11872651
25001615

prune141.0ms

Filtered
70 candidates to 44 candidates (62.9%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New64670
Fresh022
Picked011
Done101
Total65974

Merged error: 0.0b

Counts
74 → 9

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.3b
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

rewrite110.0ms

Algorithm
rewrite-expression-head
Rules
597×*-un-lft-identity
420×sqrt-prod
256×distribute-lft-out
247×times-frac
130×add-sqr-sqrt
99×add-cube-cbrt
71×swap-sqr
33×associate-*r* associate-*l*
20×pow1
14×associate-/r/
12×associate-/r*
10×add-exp-log add-cbrt-cube
9×sqrt-pow1 flip3-+ pow1/2 flip-+ unswap-sqr
8×associate-/l*
7×div-inv
5×sqrt-div pow-prod-up
4×associate-/l/ 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 → 316
Calls
4 calls:
15.0ms
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
13.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
14.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
44.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

series1.2s

Counts
4 → 12
Calls
4 calls:
559.0ms
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
217.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
206.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
245.0ms
(* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))))

simplify165.0ms

Algorithm
egg-herbie
Counts
328 → 328
Iterations

Useful iterations: 2 (126.0ms)

IterNodesCost
08273981
145313471
250013422

prune544.0ms

Filtered
328 candidates to 150 candidates (45.7%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New3226328
Fresh437
Picked101
Done011
Total32710337

Merged error: 0.0b

Counts
337 → 10

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
0.1b
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
0.2b
(/ (* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
142×*-un-lft-identity
96×sqrt-prod
61×distribute-lft-out
58×times-frac
36×add-sqr-sqrt
32×add-cube-cbrt
15×associate-/r*
11×add-exp-log add-cbrt-cube
6×pow1 sqrt-div associate-/r/
5×flip3-+ flip-+ associate-/l*
4×add-log-exp
3×cbrt-undiv rem-sqrt-square div-exp div-inv associate-/l/
2×frac-2neg sqrt-pow1 pow1/2 clear-num
1×sqrt-undiv sqrt-unprod associate-*l/ prod-exp cbrt-unprod
Counts
4 → 147
Calls
4 calls:
12.0ms
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
8.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
13.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
31.0ms
(/ (* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

series1.3s

Counts
4 → 12
Calls
4 calls:
556.0ms
(sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x))))
252.0ms
(sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))
214.0ms
(/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))
246.0ms
(/ (* (sqrt (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt 1.0)) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))

simplify141.0ms

Algorithm
egg-herbie
Counts
159 → 159
Iterations

Useful iterations: 2 (113.0ms)

IterNodesCost
09522241
145762057
250022050

prune426.0ms

Filtered
159 candidates to 111 candidates (69.8%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1572159
Fresh178
Picked101
Done011
Total15910169

Merged error: 0b

Counts
169 → 10

regimes43.0ms

Accuracy

0% (0.2b 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

sample881.0ms

Algorithm
intervals
Results
215.0ms1714×body1280valid
209.0ms8174×body80nan
124.0ms1298×body640valid
106.0ms4004×body80valid
46.0ms646×body320valid
16.0ms338×body160valid

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