Details

Time bar (total: 1.6s)

analyze2.0ms

Algorithm
search

sample12.0ms

Algorithm
intervals
Results
7.0ms256×body80valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
084
184

prune2.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.2b

Counts
2 → 1

localize5.0ms

Local error

Found 3 expressions with local error:

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

rewrite16.0ms

Algorithm
rewrite-expression-head
Rules
25×*-un-lft-identity
14×add-sqr-sqrt
13×add-cube-cbrt
12×times-frac
6×distribute-lft-out
5×add-exp-log add-cbrt-cube add-log-exp
4×pow1 associate-/r* sqrt-prod
3×flip3-+ flip-+ associate-/l*
2×sqrt-div associate-/r/
1×cbrt-undiv +-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 div-exp clear-num sum-log div-inv
Counts
3 → 61
Calls
3 calls:
5.0ms
(+ 1.0 (sqrt (+ x 1.0)))
3.0ms
(sqrt (+ x 1.0))
7.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

series27.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ 1.0 (sqrt (+ x 1.0)))
3.0ms
(sqrt (+ x 1.0))
19.0ms
(/ x (+ 1.0 (sqrt (+ x 1.0))))

simplify47.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0460585
11938554
25002551

prune123.0ms

Filtered
55 candidates to 70 candidates (-27.3%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New67370
Fresh000
Picked101
Done000
Total68371

Merged error: 0b

Counts
71 → 3

localize6.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ x 1.0))
0.0b
(+ 1.0 (sqrt (+ x 1.0)))
0.1b
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
0.1b
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
42×*-un-lft-identity
31×add-sqr-sqrt
26×times-frac
23×add-cube-cbrt
18×associate-*r*
17×add-exp-log
11×add-cbrt-cube
9×distribute-lft-out
8×pow1
6×add-log-exp
4×flip3-+ div-exp prod-exp associate-/r* sqrt-prod associate-/r/ flip-+
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv rec-exp sqrt-div 1-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square pow-flip frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log un-div-inv *-commutative inv-pow
Counts
4 → 106
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
7.0ms
(+ 1.0 (sqrt (+ x 1.0)))
7.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
11.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

series35.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
4.0ms
(+ 1.0 (sqrt (+ x 1.0)))
11.0ms
(/ 1 (+ 1.0 (sqrt (+ x 1.0))))
16.0ms
(* x (/ 1 (+ 1.0 (sqrt (+ x 1.0)))))

simplify76.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (64.0ms)

IterNodesCost
06811007
13263915
25002876

prune168.0ms

Filtered
76 candidates to 118 candidates (-55.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1180118
Fresh022
Picked011
Done000
Total1183121

Merged error: 0b

Counts
121 → 3

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ 1.0 (exp (log (sqrt (+ x 1.0)))))
0.2b
(/ x (+ 1.0 (exp (log (sqrt (+ x 1.0))))))
1.8b
(exp (log (sqrt (+ x 1.0))))
2.4b
(log (sqrt (+ x 1.0)))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
32×*-un-lft-identity
18×add-sqr-sqrt add-cube-cbrt
14×log-prod
12×times-frac
8×pow1 sqrt-prod
7×add-exp-log exp-sum distribute-lft-out
6×exp-prod log-pow add-cbrt-cube add-log-exp
4×log-div flip3-+ sqrt-div associate-/r* flip-+
3×associate-/l*
2×sqrt-pow1 pow1/2 exp-diff associate-/r/
1×cbrt-undiv +-commutative frac-2neg div-exp rem-log-exp clear-num sum-log div-inv rem-exp-log
Counts
4 → 88
Calls
4 calls:
6.0ms
(+ 1.0 (exp (log (sqrt (+ x 1.0)))))
10.0ms
(/ x (+ 1.0 (exp (log (sqrt (+ x 1.0))))))
5.0ms
(exp (log (sqrt (+ x 1.0))))
4.0ms
(log (sqrt (+ x 1.0)))

series29.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(+ 1.0 (exp (log (sqrt (+ x 1.0)))))
15.0ms
(/ x (+ 1.0 (exp (log (sqrt (+ x 1.0))))))
4.0ms
(exp (log (sqrt (+ x 1.0))))
6.0ms
(log (sqrt (+ x 1.0)))

simplify56.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0588922
12331842
25002828

prune179.0ms

Filtered
77 candidates to 100 candidates (-29.9%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New1000100
Fresh011
Picked011
Done011
Total1003103

Merged error: 0b

Counts
103 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

Algorithm
rewrite-expression-head
Rules
69×*-un-lft-identity
56×add-sqr-sqrt
52×times-frac
39×add-cube-cbrt sqrt-prod
30×associate-*r*
15×distribute-lft-out
11×add-exp-log add-cbrt-cube
7×pow1
6×associate-*l* associate-/l* add-log-exp unswap-sqr
4×flip3-+ associate-/r* associate-/r/ flip-+
2×cbrt-undiv sqrt-div div-exp prod-exp cbrt-unprod div-inv
1×+-commutative rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
4 → 132
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
5.0ms
(+ 1.0 (sqrt (+ x 1.0)))
8.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
16.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

series52.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(sqrt (+ x 1.0))
4.0ms
(+ 1.0 (sqrt (+ x 1.0)))
29.0ms
(/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0))))
15.0ms
(* (sqrt x) (/ (sqrt x) (+ 1.0 (sqrt (+ x 1.0)))))

simplify96.0ms

Algorithm
egg-herbie
Counts
144 → 144
Iterations

Useful iterations: 2 (81.0ms)

IterNodesCost
08561494
141691377
250021353

prune200.0ms

Filtered
94 candidates to 144 candidates (-53.2%)
Pruning

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New1440144
Fresh000
Picked011
Done022
Total1443147

Merged error: 0b

Counts
147 → 3

regimes28.0ms

Accuracy

0% (0.2b 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
0135
1135

end0.0ms

analyze2.0ms

Algorithm
search

sample314.0ms

Algorithm
intervals
Results
222.0ms7996×body80valid
1.0ms4×body1280valid

Profiling

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