Details

Time bar (total: 14.1s)

sample75.0ms

Algorithm
intervals
Results
32.0ms85×body1280valid
12.0ms138×body80valid
6.0ms19×body640valid
2.0msbody320valid
1.0msbody160valid

simplify1.4s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01113
12413
25813
320113
4121913
done500013

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.4b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b
(* 2.0 (pow a 2.0))
1.8b
(- 1.0 (exp (/ (- (pow x 2.0)) (* 2.0 (pow a 2.0)))))
15.5b
(/ (- (pow x 2.0)) (* 2.0 (pow a 2.0)))

rewrite118.0ms

Algorithm
rewrite-expression-head
Rules
23×add-sqr-sqrt
18×*-un-lft-identity times-frac add-exp-log associate-/l*
16×unpow-prod-down add-cube-cbrt
14×distribute-lft-neg-in distribute-rgt-neg-in
10×add-cbrt-cube
associate-*r*
prod-exp sqr-pow
add-log-exp
div-exp
pow1 associate-*l* unswap-sqr
pow-to-exp cbrt-undiv neg-mul-1 pow-exp cbrt-unprod
neg-sub0 clear-num associate-/r* sub-neg frac-2neg flip3-- diff-log div-sub distribute-frac-neg *-commutative div-inv flip-- distribute-lft-out-- difference-of-squares
Counts
3 → 94
Calls
3 calls:
23.0ms
(* 2.0 (pow a 2.0))
56.0ms
(- 1.0 (exp (/ (- (pow x 2.0)) (* 2.0 (pow a 2.0)))))
34.0ms
(/ (- (pow x 2.0)) (* 2.0 (pow a 2.0)))

series1.4s

Counts
3 → 9
Calls
3 calls:
818.0ms
(* 2.0 (pow a 2.0))
203.0ms
(- 1.0 (exp (/ (- (pow x 2.0)) (* 2.0 (pow a 2.0)))))
339.0ms
(/ (- (pow x 2.0)) (* 2.0 (pow a 2.0)))

simplify1.1s

Counts
103 → 103
Iterations

Useful iterations: 2 (359.0ms)

IterNodesCost
01831378
14141328
214141225
done50001225

prune591.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 9.8b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 2.0 (pow a 2.0))
1.8b
(- 1.0 (exp (/ (- (pow x (/ 2.0 2))) (/ (* 2.0 (pow a 2.0)) (pow x (/ 2.0 2))))))
3.9b
(/ (- (pow x (/ 2.0 2))) (/ (* 2.0 (pow a 2.0)) (pow x (/ 2.0 2))))
6.5b
(/ (* 2.0 (pow a 2.0)) (pow x (/ 2.0 2)))

rewrite240.0ms

Algorithm
rewrite-expression-head
Rules
338×times-frac
139×unpow-prod-down
135×add-sqr-sqrt
130×*-un-lft-identity
128×add-cube-cbrt
84×distribute-lft-neg-in distribute-rgt-neg-in
75×add-exp-log
47×sqr-pow
37×div-exp
21×prod-exp div-inv
20×add-cbrt-cube
19×associate-/l*
18×associate-/r*
15×pow-to-exp pow-exp
12×neg-mul-1
cbrt-undiv associate-*r*
add-log-exp
pow1
associate-*l* cbrt-unprod unswap-sqr
clear-num frac-2neg
neg-sub0 sub-neg flip3-- diff-log div-sub distribute-frac-neg associate-/r/ *-commutative flip-- distribute-lft-out-- difference-of-squares
Counts
4 → 334
Calls
4 calls:
27.0ms
(* 2.0 (pow a 2.0))
90.0ms
(- 1.0 (exp (/ (- (pow x (/ 2.0 2))) (/ (* 2.0 (pow a 2.0)) (pow x (/ 2.0 2))))))
59.0ms
(/ (- (pow x (/ 2.0 2))) (/ (* 2.0 (pow a 2.0)) (pow x (/ 2.0 2))))
27.0ms
(/ (* 2.0 (pow a 2.0)) (pow x (/ 2.0 2)))

series2.2s

Counts
4 → 12
Calls
4 calls:
822.0ms
(* 2.0 (pow a 2.0))
499.0ms
(- 1.0 (exp (/ (- (pow x (/ 2.0 2))) (/ (* 2.0 (pow a 2.0)) (pow x (/ 2.0 2))))))
450.0ms
(/ (- (pow x (/ 2.0 2))) (/ (* 2.0 (pow a 2.0)) (pow x (/ 2.0 2))))
436.0ms
(/ (* 2.0 (pow a 2.0)) (pow x (/ 2.0 2)))

simplify1.1s

Counts
346 → 346
Iterations

Useful iterations: done (1.1s)

IterNodesCost
05409614
116689012
done50008689

prune2.1s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 9.8b

regimes179.0ms

Accuracy

-12.9% (6.5b remaining)

Error of 16.0b against oracle of 9.5b and baseline of 15.2b

bsearch258.0ms

Steps
ItersRangePoint
7
-3.1647617934541664e-127
-1.3232791960630542e-128
-2.768001142293592e-128
8
-1.0308317897183547e-22
-1.2500612482012891e-26
-1.5032933475536696e-26

simplify26.0ms

Iterations

Useful iterations: 3 (16.0ms)

IterNodesCost
032115
14469
24869
35268
45468
done5468

end0.0ms

sample3.3s

Algorithm
intervals
Results
2.1s2879×body1280valid
505.0ms4129×body80valid
250.0ms564×body640valid
71.0ms278×body320valid
25.0ms150×body160valid