Details

Time bar (total: 36.9s)

sample698.0ms

Algorithm
intervals
Results
461.0ms103×body1280valid
110.0ms78×body2560valid
69.0ms56×body10240exit
18.0ms39×body640valid
7.0ms312×pre80true
4.0ms12×body320valid
2.0ms20×body80valid
1.0ms4×body160valid

simplify2.8s

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
01724
14024
210124
325824
476524
5400824
done500024

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 58.8b

localize46.0ms

Local error

Found 4 expressions with local error:

0.5b
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
3.4b
(- (exp (* a eps)) 1.0)
4.2b
(- (exp (* b eps)) 1.0)
6.4b
(- (exp (* (+ a b) eps)) 1.0)

rewrite213.0ms

Algorithm
rewrite-expression-head
Rules
51×add-sqr-sqrt
49×*-un-lft-identity
45×prod-diff
39×add-cube-cbrt
11×distribute-rgt-in distribute-lft-in
10×add-log-exp
9×flip3-- fma-neg flip--
6×pow1 add-exp-log add-cbrt-cube
5×sub-neg associate-*r* associate-*l* distribute-lft-out-- difference-of-squares
4×expm1-log1p-u frac-times log1p-expm1-u
3×diff-log
2×associate-*r/ associate-*l/
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 138
Calls
4 calls:
106.0ms
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
40.0ms
(- (exp (* a eps)) 1.0)
29.0ms
(- (exp (* b eps)) 1.0)
32.0ms
(- (exp (* (+ a b) eps)) 1.0)

series236.0ms

Counts
4 → 12
Calls
4 calls:
70.0ms
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
49.0ms
(- (exp (* a eps)) 1.0)
45.0ms
(- (exp (* b eps)) 1.0)
71.0ms
(- (exp (* (+ a b) eps)) 1.0)

simplify1.9s

Counts
150 → 150
Iterations

Useful iterations: done (1.9s)

IterNodesCost
02213064
15392630
225962203
done50002041

prune776.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 48.2b

localize84.0ms

Local error

Found 4 expressions with local error:

4.2b
(- (exp (* b eps)) 1.0)
6.4b
(- (exp (* (+ a b) eps)) 1.0)
11.2b
(* (pow a 2) (pow eps 2))
16.2b
(* (pow a 3) (pow eps 3))

rewrite111.0ms

Algorithm
rewrite-expression-head
Rules
72×add-sqr-sqrt
32×*-un-lft-identity unswap-sqr
28×add-exp-log add-cube-cbrt unpow-prod-down
20×associate-*r* associate-*l* sqr-pow
18×prod-diff prod-exp
14×cube-prod
12×pow-to-exp pow-exp
10×unpow2
8×add-cbrt-cube add-log-exp
6×fma-neg
4×pow1 expm1-log1p-u log1p-expm1-u
2×cube-mult sub-neg flip3-- diff-log unpow3 pow-prod-down *-commutative flip-- cbrt-unprod distribute-lft-out-- difference-of-squares
Counts
4 → 170
Calls
4 calls:
18.0ms
(- (exp (* b eps)) 1.0)
17.0ms
(- (exp (* (+ a b) eps)) 1.0)
26.0ms
(* (pow a 2) (pow eps 2))
43.0ms
(* (pow a 3) (pow eps 3))

series241.0ms

Counts
4 → 12
Calls
4 calls:
40.0ms
(- (exp (* b eps)) 1.0)
72.0ms
(- (exp (* (+ a b) eps)) 1.0)
38.0ms
(* (pow a 2) (pow eps 2))
91.0ms
(* (pow a 3) (pow eps 3))

simplify3.0s

Counts
182 → 182
Iterations

Useful iterations: 2 (1.0s)

IterNodesCost
02542347
16112012
235181686
done50011686

prune1.2s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 47.2b

localize58.0ms

Local error

Found 4 expressions with local error:

3.5b
(fma 1/6 (pow (* a eps) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps)))
4.2b
(- (exp (* b eps)) 1.0)
6.4b
(- (exp (* (+ a b) eps)) 1.0)
11.2b
(* (pow a 2) (pow eps 2))

rewrite55.0ms

Algorithm
rewrite-expression-head
Rules
42×add-sqr-sqrt
26×*-un-lft-identity
22×add-cube-cbrt
18×prod-diff
16×add-exp-log unswap-sqr
14×unpow-prod-down
10×unpow2 sqr-pow
9×prod-exp
8×associate-*r* associate-*l* add-log-exp
6×pow-to-exp fma-neg pow-exp add-cbrt-cube
4×pow1 expm1-log1p-u log1p-expm1-u
2×sub-neg flip3-- diff-log flip-- distribute-lft-out-- difference-of-squares
1×pow-prod-down *-commutative cbrt-unprod fma-udef
Counts
4 → 119
Calls
4 calls:
0.0ms
(fma 1/6 (pow (* a eps) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps)))
15.0ms
(- (exp (* b eps)) 1.0)
16.0ms
(- (exp (* (+ a b) eps)) 1.0)
19.0ms
(* (pow a 2) (pow eps 2))

series300.0ms

Counts
4 → 12
Calls
4 calls:
128.0ms
(fma 1/6 (pow (* a eps) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps)))
46.0ms
(- (exp (* b eps)) 1.0)
65.0ms
(- (exp (* (+ a b) eps)) 1.0)
61.0ms
(* (pow a 2) (pow eps 2))

simplify2.1s

Counts
131 → 131
Iterations

Useful iterations: done (2.1s)

IterNodesCost
02091936
14801684
223561343
done50021261

prune771.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 47.2b

localize36.0ms

Local error

Found 4 expressions with local error:

3.7b
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* a eps) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (+ (- (pow (exp b) eps) 1.0) (fma 1.0 -1 1.0))))
5.7b
(* (fma 1/6 (pow (* a eps) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (+ (- (pow (exp b) eps) 1.0) (fma 1.0 -1 1.0)))
6.4b
(- (exp (* (+ a b) eps)) 1.0)
11.2b
(* (pow a 2) (pow eps 2))

rewrite488.0ms

Algorithm
rewrite-expression-head
Rules
37×add-sqr-sqrt
30×add-exp-log
24×*-un-lft-identity
20×add-cbrt-cube
17×add-cube-cbrt unswap-sqr
14×unpow-prod-down prod-exp
13×associate-*r*
11×associate-*l*
10×unpow2 sqr-pow
9×prod-diff
6×pow1 pow-to-exp associate-*r/ pow-exp cbrt-unprod add-log-exp
4×cbrt-undiv expm1-log1p-u div-exp log1p-expm1-u
3×fma-neg
2×flip3-- flip3-+ pow-prod-down associate-/r/ *-commutative flip-- flip-+ associate-/l/ distribute-lft-out distribute-lft-out--
1×distribute-rgt-in sub-neg frac-2neg distribute-lft-in times-frac diff-log clear-num associate-/r* div-inv associate-/l* difference-of-squares
Counts
4 → 134
Calls
4 calls:
144.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* a eps) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (+ (- (pow (exp b) eps) 1.0) (fma 1.0 -1 1.0))))
285.0ms
(* (fma 1/6 (pow (* a eps) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (+ (- (pow (exp b) eps) 1.0) (fma 1.0 -1 1.0)))
25.0ms
(- (exp (* (+ a b) eps)) 1.0)
26.0ms
(* (pow a 2) (pow eps 2))

series1.7s

Counts
4 → 12
Calls
4 calls:
1.4s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (pow (* a eps) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (+ (- (pow (exp b) eps) 1.0) (fma 1.0 -1 1.0))))
257.0ms
(* (fma 1/6 (pow (* a eps) 3) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (+ (- (pow (exp b) eps) 1.0) (fma 1.0 -1 1.0)))
73.0ms
(- (exp (* (+ a b) eps)) 1.0)
43.0ms
(* (pow a 2) (pow eps 2))

simplify3.3s

Counts
146 → 146
Iterations

Useful iterations: 2 (969.0ms)

IterNodesCost
02814229
17874027
248933249
done50003249

prune1.0s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

regimes68.0ms

Accuracy

0% (3.2b remaining)

Error of 3.3b against oracle of 0.1b and baseline of 3.3b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
067
197
done97

end0.0ms

sample15.5s

Algorithm
intervals
Results
5.0s2632×body2560valid
4.2s3364×body1280valid
3.5s2022×body10240exit
1.1s1091×body640valid
524.0ms344×body320valid
372.0ms10023×pre80true
46.0ms443×body80valid
28.0ms127×body160valid