Details

Time bar (total: 4.5s)

sample49.0ms

Algorithm
intervals
Results
24.0ms62×body10240exit
9.0ms259×body80valid
3.0ms5×body1280valid
2.0ms9×body640valid
1.0ms6×body320valid
0.0ms4×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0125
1195
2195

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize7.0ms

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

Algorithm
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 → 45
Calls
3 calls:
3.0ms
(+ 1.0 (exp x))
5.0ms
(- (log (+ 1.0 (exp x))) (* x y))
3.0ms
(log (+ 1.0 (exp x)))

series136.0ms

Counts
3 → 9
Calls
3 calls:
8.0ms
(+ 1.0 (exp x))
62.0ms
(- (log (+ 1.0 (exp x))) (* x y))
66.0ms
(log (+ 1.0 (exp x)))

simplify49.0ms

Algorithm
egg-herbie
Counts
54 → 54
Iterations

Useful iterations: 3 (45.0ms)

IterNodesCost
0207322
1584301
21729298
35001297

prune125.0ms

Filtered
54 candidates to 40 candidates (74.1%)
Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.2b

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))
1.2b
(log (sqrt (+ 1.0 (exp x))))
1.2b
(log (sqrt (+ 1.0 (exp x))))

rewrite38.0ms

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:
18.0ms
(+ (log (sqrt (+ 1.0 (exp x)))) (- (log (sqrt (+ 1.0 (exp x)))) (* x y)))
10.0ms
(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
3.0ms
(log (sqrt (+ 1.0 (exp x))))
3.0ms
(log (sqrt (+ 1.0 (exp x))))

series494.0ms

Counts
4 → 12
Calls
4 calls:
151.0ms
(+ (log (sqrt (+ 1.0 (exp x)))) (- (log (sqrt (+ 1.0 (exp x)))) (* x y)))
131.0ms
(- (log (sqrt (+ 1.0 (exp x)))) (* x y))
105.0ms
(log (sqrt (+ 1.0 (exp x))))
106.0ms
(log (sqrt (+ 1.0 (exp x))))

simplify83.0ms

Algorithm
egg-herbie
Counts
106 → 106
Iterations

Useful iterations: 3 (74.0ms)

IterNodesCost
0309981
1933910
23159857
35001826

prune268.0ms

Filtered
106 candidates to 76 candidates (71.7%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* 1/2 (pow x 2)) (+ x 2.0))
0.0b
(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
8.5b
(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
9×add-log-exp
6×log-prod
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log log-div
3×flip3-+ associate--l+ sum-log add-cbrt-cube flip-+
2×associate--l-
1×+-commutative sub-neg associate-+r+ flip3-- diff-log rem-log-exp log-pow flip--
Counts
3 → 44
Calls
3 calls:
8.0ms
(+ (* 1/2 (pow x 2)) (+ x 2.0))
10.0ms
(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
8.0ms
(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

series151.0ms

Counts
3 → 9
Calls
3 calls:
17.0ms
(+ (* 1/2 (pow x 2)) (+ x 2.0))
78.0ms
(- (log (+ (* 1/2 (pow x 2)) (+ x 2.0))) (* x y))
56.0ms
(log (+ (* 1/2 (pow x 2)) (+ x 2.0)))

simplify143.0ms

Algorithm
egg-herbie
Counts
53 → 53
Iterations

Useful iterations: 2 (28.0ms)

IterNodesCost
0292480
11010443
24638436
35001436

prune156.0ms

Filtered
53 candidates to 43 candidates (81.1%)
Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

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))

rewrite136.0ms

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:
50.0ms
(* (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)))))
67.0ms
(- (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)) (* x y))
12.0ms
(+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x))

series543.0ms

Counts
4 → 12
Calls
4 calls:
82.0ms
(* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))
334.0ms
(+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))
72.0ms
(- (+ (+ (log 2.0) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* 0.5 x)) (* x y))
54.0ms
(+ (+ (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 (47.0ms)

IterNodesCost
0442901
11771849
25001840

prune264.0ms

Filtered
97 candidates to 68 candidates (70.1%)
Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.2b

regimes34.0ms

Accuracy

0% (0.8b remaining)

Error of 1.1b against oracle of 0.3b and baseline of 1.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01311
11311

end0.0ms

sample1.7s

Algorithm
intervals
Results
1.0s2449×body10240exit
314.0ms8350×body80valid
69.0ms259×body640valid
58.0ms113×body1280valid
33.0ms210×body320valid
9.0ms96×body160valid