Details

Time bar (total: 2.2s)

sample38.0ms

Algorithm
intervals
Results
11.0ms265×body80valid
7.0ms12×body1280valid
3.0ms84×body80overflowed
2.0ms8×body640valid
1.0ms6×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

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (log (+ 1.0 (exp x))) (* x y))
0.8b
(log (+ 1.0 (exp x)))

rewrite9.0ms

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

series19.0ms

Counts
2 → 6
Calls
2 calls:
9.0ms
(- (log (+ 1.0 (exp x))) (* x y))
10.0ms
(log (+ 1.0 (exp x)))

simplify41.0ms

Algorithm
egg-herbie
Counts
39 → 39
Iterations

Useful iterations: 3 (37.0ms)

IterNodesCost
0180262
1479246
21456243
35001242

prune58.0ms

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

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New37239
Fresh000
Picked011
Done000
Total37340

Merged error: 0.4b

Counts
40 → 3

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(sqrt (+ 1.0 (exp x)))
0.0b
(sqrt (+ 1.0 (exp x)))
1.5b
(log (sqrt (+ 1.0 (exp x))))
1.5b
(log (sqrt (+ 1.0 (exp x))))

rewrite15.0ms

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

series35.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(sqrt (+ 1.0 (exp x)))
4.0ms
(sqrt (+ 1.0 (exp x)))
15.0ms
(log (sqrt (+ 1.0 (exp x))))
13.0ms
(log (sqrt (+ 1.0 (exp x))))

simplify50.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 3 (43.0ms)

IterNodesCost
0162564
1453526
21549508
35001496

prune136.0ms

Filtered
60 candidates to 84 candidates (-40.0%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New84084
Fresh011
Picked011
Done011
Total84387

Merged error: 0.4b

Counts
87 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
17×add-log-exp
10×*-un-lft-identity
9×add-exp-log associate-*r*
8×add-cube-cbrt associate-*l*
7×sum-log
6×add-cbrt-cube
5×sub-neg unpow-prod-down difference-of-squares
4×pow1 distribute-rgt-in associate-+l+ associate-+r+ distribute-lft-in times-frac unswap-sqr
3×log-prod diff-log prod-exp unpow2 sqr-pow
2×+-commutative flip3-- flip3-+ associate-*r/ flip-- flip-+
1×pow-to-exp pow-exp associate--l+ *-commutative cbrt-unprod distribute-lft-out--
Counts
4 → 85
Calls
4 calls:
14.0ms
(* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))
4.0ms
(+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))
7.0ms
(- (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)) (* x y))
7.0ms
(+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))

series50.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))
25.0ms
(+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))
10.0ms
(- (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)) (* x y))
6.0ms
(+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))

simplify57.0ms

Algorithm
egg-herbie
Counts
97 → 97
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0442901
11771845
25001836

prune193.0ms

Filtered
68 candidates to 97 candidates (-42.6%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New95297
Fresh000
Picked101
Done022
Total964100

Merged error: 0.4b

Counts
100 → 4

localize21.0ms

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)))) (* x y))
0.0b
(+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))
1.1b
(exp (log (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))))
5.6b
(log (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
10×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 sum-log flip-+
2×exp-diff log-pow
1×+-commutative sub-neg associate-+l+ flip3-- diff-log rem-log-exp flip-- rem-exp-log
Counts
4 → 56
Calls
4 calls:
8.0ms
(- (exp (log (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)))) (* x y))
5.0ms
(+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))
5.0ms
(exp (log (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))))
4.0ms
(log (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)))

series30.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(- (exp (log (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)))) (* x y))
6.0ms
(+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))
6.0ms
(exp (log (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))))
8.0ms
(log (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)))

simplify38.0ms

Algorithm
egg-herbie
Counts
68 → 68
Iterations

Useful iterations: 2 (27.0ms)

IterNodesCost
03281033
11169952
25002897

prune166.0ms

Filtered
52 candidates to 68 candidates (-30.8%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New66268
Fresh101
Picked011
Done022
Total67572

Merged error: 0.4b

Counts
72 → 5

regimes138.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.3b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
0105
1105

end0.0ms

sample956.0ms

Algorithm
intervals
Results
373.0ms8364×body80valid
96.0ms2407×body80overflowed
76.0ms261×body640valid
76.0ms141×body1280valid
33.0ms180×body320valid
12.0ms115×body160valid

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