Details

Time bar (total: 9.8s)

sample59.0ms

Algorithm
intervals
Results
27.0ms68×body10240exit
12.0ms279×body80valid
6.0ms5×body1280valid
2.0ms9×body640valid
1.0ms6×body320valid
0.0ms2×body160valid

simplify6.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
089
1129
2199
done199

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize8.0ms

Local error

Found 3 expressions with local error:

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

series133.0ms

Counts
3 → 9
Calls
3 calls:
8.0ms
(+ 1.0 (exp x))
61.0ms
(- (log (+ 1.0 (exp x))) (* x y))
65.0ms
(log (+ 1.0 (exp x)))

simplify2.5s

Counts
54 → 54
Iterations

Useful iterations: 4 (1.3s)

IterNodesCost
092575
1207544
2503522
31378508
44235506
done5001506

prune143.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 3 expressions with local error:

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

rewrite89.0ms

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 flip3-+ associate-*r/ frac-add flip-+
3×pow1 add-exp-log sub-neg log-prod flip3-- diff-log add-cbrt-cube flip--
2×+-commutative distribute-rgt-in distribute-lft-in
1×associate--l+
Counts
3 → 50
Calls
3 calls:
14.0ms
(+ (+ (log 2.0) (* 0.5 x)) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))
3.0ms
(+ (log 2.0) (* 0.5 x))
71.0ms
(- (+ (+ (log 2.0) (* 0.5 x)) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* x y))

series300.0ms

Counts
3 → 9
Calls
3 calls:
53.0ms
(+ (+ (log 2.0) (* 0.5 x)) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))))
175.0ms
(+ (log 2.0) (* 0.5 x))
72.0ms
(- (+ (+ (log 2.0) (* 0.5 x)) (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2))))) (* x y))

simplify657.0ms

Counts
59 → 59
Iterations

Useful iterations: done (655.0ms)

IterNodesCost
01231503
14041391
215851330
done50001306

prune190.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y)))
0.0b
(+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0))
1.5b
(exp (log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0))))
7.3b
(log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0)))

rewrite235.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
13×log-prod
9×pow1 add-log-exp
8×add-sqr-sqrt add-cube-cbrt associate-*r/
7×associate-+r+
6×distribute-lft-out
5×add-exp-log associate-+l+ exp-sum log-pow
4×distribute-rgt-in sub-neg log-div exp-prod flip3-- distribute-lft-in flip3-+ frac-add sum-log add-cbrt-cube flip-- flip-+
2×+-commutative exp-diff
1×rem-log-exp rem-exp-log
Counts
4 → 76
Calls
4 calls:
16.0ms
(+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y)))
95.0ms
(+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0))
60.0ms
(exp (log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0))))
61.0ms
(log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0)))

series395.0ms

Counts
4 → 12
Calls
4 calls:
56.0ms
(+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y)))
74.0ms
(+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0))
73.0ms
(exp (log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0))))
192.0ms
(log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0)))

simplify657.0ms

Counts
88 → 88
Iterations

Useful iterations: done (653.0ms)

IterNodesCost
01862683
15292536
218412301
done50012300

prune303.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize29.0ms

Local error

Found 4 expressions with local error:

1.5b
(exp (* (* (cbrt (log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0)))) (cbrt (log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0))))) (cbrt (log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0))))))
7.3b
(log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0)))
7.3b
(log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0)))
7.3b
(log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0)))

rewrite183.0ms

Algorithm
rewrite-expression-head
Rules
16×*-un-lft-identity
15×log-prod
10×pow1
7×add-exp-log add-sqr-sqrt add-cube-cbrt
6×log-div log-pow distribute-lft-out add-log-exp
4×add-cbrt-cube
3×flip3-+ rem-log-exp flip-+
1×exp-prod exp-to-pow rem-exp-log
Counts
4 → 58
Calls
4 calls:
3.0ms
(exp (* (* (cbrt (log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0)))) (cbrt (log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0))))) (cbrt (log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0))))))
60.0ms
(log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0)))
60.0ms
(log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0)))
58.0ms
(log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0)))

series680.0ms

Counts
4 → 12
Calls
4 calls:
86.0ms
(exp (* (* (cbrt (log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0)))) (cbrt (log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0))))) (cbrt (log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0))))))
195.0ms
(log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0)))
200.0ms
(log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0)))
198.0ms
(log (+ (+ (* (pow x 2) (- 0.25 (/ 1/2 (pow 2.0 2)))) (* x (- 0.5 y))) (log 2.0)))

simplify974.0ms

Counts
70 → 70
Iterations

Useful iterations: 3 (299.0ms)

IterNodesCost
0972779
12172746
25882043
321071766
done50011766

prune368.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes74.0ms

Accuracy

98.8% (0.2b remaining)

Error of 0.4b against oracle of 0.2b and baseline of 14.7b

bsearch42.0ms

Steps
ItersRangePoint
8
-1.046355961971052
-1.6471395275746527e-05
-0.0015597679374155452

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03245
13745
done3745

end0.0ms

sample1.7s

Algorithm
intervals
Results
991.0ms2448×body10240exit
311.0ms8398×body80valid
74.0ms256×body640valid
61.0ms122×body1280valid
27.0ms170×body320valid
11.0ms114×body160valid