Details

Time bar (total: 2.1s)

analyze62.0ms (3%)

Algorithm
1×search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
25%74.9%0.1%5
43.7%43.7%12.6%6
53.1%31.2%15.7%7
59.3%18.7%22%8
62.4%14%23.5%9
64.8%8.6%26.6%10
66%6.6%27.4%11
66.9%4.1%29%12
67.4%3.2%29.4%13
67.9%2%30.1%14

sample26.0ms (1.3%)

Algorithm
1×intervals
Results
11.0ms234×body80valid
4.0ms7×body1280valid
3.0ms8×body640valid
1.0ms5×body320valid
0.0ms2×body160valid
0.0ms1×body80invalid

simplify78.0ms (3.7%)

Algorithm
1×egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (76.0ms)

IterNodesCost
059739

prune9.0ms (0.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.5b

Counts
2 → 1

localize7.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b
(+ 1.0 (exp x))
0.0b
(- (log (+ 1.0 (exp x))) (* x y))
0.5b
(log (+ 1.0 (exp x)))

rewrite12.0ms (0.6%)

Algorithm
1×rewrite-expression-head
Rules
11×*-un-lft-identity
8×log-prod
6×add-log-exp
5×add-sqr-sqrt add-cube-cbrt
4×pow1 add-exp-log log-div associate--l+
3×flip3-+ add-cbrt-cube flip-+ distribute-lft-out
2×associate--l-
1×+-commutative sub-neg flip3-- diff-log rem-log-exp sum-log log-pow flip--
Counts
3 → 44
Calls

3 calls:

5.0ms
(- (log (+ 1.0 (exp x))) (* x y))
3.0ms
(log (+ 1.0 (exp x)))
3.0ms
(+ 1.0 (exp x))

series21.0ms (1%)

Counts
3 → 9
Calls

3 calls:

10.0ms
(log (+ 1.0 (exp x)))
9.0ms
(- (log (+ 1.0 (exp x))) (* x y))
2.0ms
(+ 1.0 (exp x))

simplify71.0ms (3.4%)

Algorithm
1×egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 0 (66.0ms)

IterNodesCost
04843504
14843504

prune95.0ms (4.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New49453
Fresh000
Picked101
Done000
Total50454

Merged error: 0.4b

Counts
54 → 4

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.2b
(sqrt (+ 1.0 (exp x)))
0.2b
(sqrt (+ 1.0 (exp x)))
0.9b
(log (sqrt (+ 1.0 (exp x))))
0.9b
(log (sqrt (+ 1.0 (exp x))))

rewrite17.0ms (0.8%)

Algorithm
1×rewrite-expression-head
Rules
18×*-un-lft-identity
16×sqrt-prod
14×log-prod
12×add-sqr-sqrt
10×pow1 add-cube-cbrt
8×sqrt-div
6×add-exp-log log-pow
4×log-div sqrt-pow1 flip3-+ pow1/2 add-cbrt-cube flip-+ distribute-lft-out add-log-exp
2×rem-sqrt-square rem-log-exp
Counts
4 → 72
Calls

4 calls:

4.0ms
(log (sqrt (+ 1.0 (exp x))))
4.0ms
(log (sqrt (+ 1.0 (exp x))))
4.0ms
(sqrt (+ 1.0 (exp x)))
3.0ms
(sqrt (+ 1.0 (exp x)))

series36.0ms (1.8%)

Counts
4 → 12
Calls

4 calls:

13.0ms
(log (sqrt (+ 1.0 (exp x))))
13.0ms
(log (sqrt (+ 1.0 (exp x))))
6.0ms
(sqrt (+ 1.0 (exp x)))
4.0ms
(sqrt (+ 1.0 (exp x)))

simplify38.0ms (1.8%)

Algorithm
1×egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
05046760

prune196.0ms (9.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New84084
Fresh033
Picked011
Done000
Total84488

Merged error: 0.4b

Counts
88 → 4

localize10.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b
(* (* x x) 1/2)
0.0b
(- (log (+ (* (* x x) 1/2) (+ x 2.0))) (* x y))
0.0b
(+ (* (* x x) 1/2) (+ x 2.0))
5.6b
(log (+ (* (* x x) 1/2) (+ x 2.0)))

rewrite34.0ms (1.6%)

Algorithm
1×rewrite-expression-head
Rules
10×pow1 add-exp-log add-log-exp
9×add-cbrt-cube
8×add-sqr-sqrt
7×add-cube-cbrt *-un-lft-identity
6×log-prod
4×log-div
3×flip3-+ associate-*r* pow-prod-down prod-exp associate--l+ sum-log cbrt-unprod flip-+
2×associate--l-
1×+-commutative sub-neg associate-+r+ flip3-- diff-log rem-log-exp associate-*l* log-pow *-commutative flip-- unswap-sqr
Counts
4 → 62
Calls

4 calls:

12.0ms
(- (log (+ (* (* x x) 1/2) (+ x 2.0))) (* x y))
8.0ms
(+ (* (* x x) 1/2) (+ x 2.0))
7.0ms
(log (+ (* (* x x) 1/2) (+ x 2.0)))
5.0ms
(* (* x x) 1/2)

series20.0ms (1%)

Counts
4 → 12
Calls

4 calls:

10.0ms
(- (log (+ (* (* x x) 1/2) (+ x 2.0))) (* x y))
4.0ms
(log (+ (* (* x x) 1/2) (+ x 2.0)))
3.0ms
(* (* x x) 1/2)
3.0ms
(+ (* (* x x) 1/2) (+ x 2.0))

simplify48.0ms (2.3%)

Algorithm
1×egg-herbie
Counts
74 → 74
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
04927934
14927934

prune131.0ms (6.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New72274
Fresh112
Picked011
Done011
Total73578

Merged error: 0.4b

Counts
78 → 5

localize16.0ms (0.8%)

Local error

Found 4 expressions with local error:

1.2b
(cbrt (log (+ (* (* x x) 1/2) (+ x 2.0))))
5.6b
(log (+ (* (* x x) 1/2) (+ x 2.0)))
5.6b
(log (+ (* (* x x) 1/2) (+ x 2.0)))
5.6b
(log (+ (* (* x x) 1/2) (+ x 2.0)))

rewrite25.0ms (1.2%)

Algorithm
1×rewrite-expression-head
Rules
9×log-prod
8×pow1 add-sqr-sqrt add-cube-cbrt *-un-lft-identity
7×add-exp-log
6×log-div
4×cbrt-prod log-pow add-cbrt-cube add-log-exp
3×flip3-+ rem-log-exp flip-+
1×pow1/3
Counts
4 → 54
Calls

4 calls:

8.0ms
(log (+ (* (* x x) 1/2) (+ x 2.0)))
7.0ms
(log (+ (* (* x x) 1/2) (+ x 2.0)))
7.0ms
(log (+ (* (* x x) 1/2) (+ x 2.0)))
1.0ms
(cbrt (log (+ (* (* x x) 1/2) (+ x 2.0))))

series26.0ms (1.2%)

Counts
4 → 12
Calls

4 calls:

13.0ms
(cbrt (log (+ (* (* x x) 1/2) (+ x 2.0))))
4.0ms
(log (+ (* (* x x) 1/2) (+ x 2.0)))
4.0ms
(log (+ (* (* x x) 1/2) (+ x 2.0)))
4.0ms
(log (+ (* (* x x) 1/2) (+ x 2.0)))

simplify39.0ms (1.9%)

Algorithm
1×egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
050611144

prune218.0ms (10.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New65166
Fresh112
Picked101
Done022
Total67471

Merged error: 0.4b

Counts
71 → 4

regimes129.0ms (6.2%)

Accuracy

Total 0.7b remaining (76.3%)

Threshold costs 0.7b (76.3%)

bsearch0.0ms (0%)

simplify1.0ms (0.1%)

Algorithm
1×egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03917
13917

end0.0ms (0%)

sample697.0ms (33.7%)

Algorithm
1×intervals
Results
342.0ms7326×body80valid
79.0ms144×body1280valid
74.0ms234×body640valid
34.0ms181×body320valid
13.0ms115×body160valid
3.0ms52×body80invalid
0.0ms6×body80overflowed

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