Details

Time bar (total: 2.1s)

analyze119.0ms

Algorithm
search
sampling

Space saved by range analysis: 0.097632%

Space saved by search: 30.341513%

Guaranteed chance to sample good point: 98.573179%

sample27.0ms

Algorithm
intervals
Results
11.0ms233×body80valid
4.0ms12×body640valid
3.0ms5×body1280valid
1.0ms4×body320valid
0.0ms2×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0125
1195
2195

prune3.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.8b

Counts
2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (log (+ 1.0 (exp x))) (* x y))
0.7b
(log (+ 1.0 (exp x)))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
8×log-prod *-un-lft-identity
4×add-sqr-sqrt add-cube-cbrt log-div associate--l+
3×pow1 add-exp-log add-log-exp
2×associate--l- flip3-+ add-cbrt-cube flip-+ distribute-lft-out
1×sub-neg flip3-- diff-log rem-log-exp log-pow flip--
Counts
2 → 33
Calls
2 calls:
8.0ms
(- (log (+ 1.0 (exp x))) (* x y))
3.0ms
(log (+ 1.0 (exp x)))

series22.0ms

Counts
2 → 6
Calls
2 calls:
10.0ms
(- (log (+ 1.0 (exp x))) (* x y))
13.0ms
(log (+ 1.0 (exp x)))

simplify43.0ms

Algorithm
egg-herbie
Counts
39 → 39
Iterations

Useful iterations: 3 (39.0ms)

IterNodesCost
0180262
1479246
21456243
35001242

prune64.0ms

Filtered
30 candidates to 39 candidates (-30.0%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New36339
Fresh000
Picked101
Done000
Total37340

Merged error: 0.7b

Counts
40 → 3

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (log (sqrt (+ 1.0 (exp x)))) (- (log (sqrt (+ 1.0 (exp x)))) (* x y)))
0.0b
(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
1.4b
(log (sqrt (+ 1.0 (exp x))))
1.4b
(log (sqrt (+ 1.0 (exp x))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
35×log-prod
27×*-un-lft-identity
20×sqrt-prod
14×add-sqr-sqrt add-cube-cbrt associate--l+
9×pow1 associate-+r+
8×log-div sqrt-div
7×associate-+l+ log-pow distribute-lft-out add-log-exp
6×add-exp-log
5×flip3-+ flip-+
4×add-cbrt-cube
2×associate--l- associate-+l- sub-neg sqrt-pow1 pow1/2 diff-log rem-log-exp sum-log
1×+-commutative associate-+r- flip3-- flip--
Counts
4 → 94
Calls
4 calls:
13.0ms
(+ (log (sqrt (+ 1.0 (exp x)))) (- (log (sqrt (+ 1.0 (exp x)))) (* x y)))
7.0ms
(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
4.0ms
(log (sqrt (+ 1.0 (exp x))))
4.0ms
(log (sqrt (+ 1.0 (exp x))))

series61.0ms

Counts
4 → 12
Calls
4 calls:
17.0ms
(+ (log (sqrt (+ 1.0 (exp x)))) (- (log (sqrt (+ 1.0 (exp x)))) (* x y)))
14.0ms
(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
14.0ms
(log (sqrt (+ 1.0 (exp x))))
17.0ms
(log (sqrt (+ 1.0 (exp x))))

simplify86.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 3 (76.0ms)

IterNodesCost
0309981
1933906
23159857
35001826

prune187.0ms

Filtered
75 candidates to 106 candidates (-41.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1060106
Fresh022
Picked011
Done000
Total1063109

Merged error: 0.7b

Counts
109 → 3

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))
0.0b
(+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))
0.0b
(- (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)) (* x y))

rewrite19.0ms

Algorithm
rewrite-expression-head
Rules
16×add-log-exp
7×sum-log
4×add-sqr-sqrt add-cube-cbrt associate-+l+ associate-+r+ *-un-lft-identity
3×pow1 add-exp-log sub-neg log-prod diff-log add-cbrt-cube
2×+-commutative distribute-rgt-in distribute-lft-in flip3-+ flip-+
1×flip3-- associate--l+ flip--
Counts
3 → 46
Calls
3 calls:
4.0ms
(+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))
6.0ms
(+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))
8.0ms
(- (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)) (* x y))

series44.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))
6.0ms
(+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))
11.0ms
(- (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)) (* x y))

simplify37.0ms

Algorithm
egg-herbie
Counts
55 → 55
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0271625
11051590
25002570

prune130.0ms

Filtered
41 candidates to 55 candidates (-34.1%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New52355
Fresh011
Picked101
Done011
Total53558

Merged error: 0.7b

Counts
58 → 5

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (exp (log (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))))) (* 0.5 x))
0.0b
(- (+ (exp (log (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))))) (* 0.5 x)) (* x y))
1.0b
(exp (log (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))))
7.1b
(log (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×pow1 log-prod
5×add-exp-log
4×log-div exp-prod add-cbrt-cube
3×flip3-+ exp-sum flip-+
2×exp-diff diff-log sum-log log-pow
1×+-commutative sub-neg flip3-- rem-log-exp associate--l+ flip-- rem-exp-log
Counts
4 → 56
Calls
4 calls:
7.0ms
(+ (exp (log (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))))) (* 0.5 x))
9.0ms
(- (+ (exp (log (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))))) (* 0.5 x)) (* x y))
4.0ms
(exp (log (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))))
3.0ms
(log (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))))

series60.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(+ (exp (log (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))))) (* 0.5 x))
11.0ms
(- (+ (exp (log (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))))) (* 0.5 x)) (* x y))
30.0ms
(exp (log (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))))
14.0ms
(log (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))))

simplify43.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
0346949
11258872
25001819

prune174.0ms

Filtered
51 candidates to 68 candidates (-33.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New67168
Fresh213
Picked101
Done011
Total70373

Merged error: 0.6b

Counts
73 → 3

regimes80.0ms

Accuracy

0% (0.8b remaining)

Error of 1.0b against oracle of 0.2b and baseline of 1.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01311
11311

end0.0ms

analyze114.0ms

Algorithm
search
sampling

Space saved by range analysis: 0.097632%

Space saved by search: 30.341513%

Guaranteed chance to sample good point: 98.573179%

sample681.0ms

Algorithm
intervals
Results
346.0ms7371×body80valid
81.0ms267×body640valid
64.0ms114×body1280valid
29.0ms155×body320valid
10.0ms93×body160valid
2.0ms28×body80invalid
0.0ms8×body80overflowed

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