Details

Time bar (total: 2.6s)

sample45.0ms

Algorithm
intervals
Results
17.0ms97×body1280valid
8.0ms43×body640valid
4.0ms163×body80valid
2.0ms25×body320valid
0.0ms9×body160valid

simplify57.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0113
1183
2263
3483
41103
53183
616233
750013

prune3.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 30.2b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(exp (* a x))
2.5b
(- (exp (* a x)) 1.0)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
6×add-log-exp
4×add-sqr-sqrt *-un-lft-identity
2×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
1×sub-neg exp-prod flip3-- exp-to-pow diff-log flip-- rem-exp-log distribute-lft-out-- difference-of-squares
Counts
2 → 24
Calls
2 calls:
1.0ms
(exp (* a x))
4.0ms
(- (exp (* a x)) 1.0)

series11.0ms

Counts
2 → 6
Calls
2 calls:
4.0ms
(exp (* a x))
7.0ms
(- (exp (* a x)) 1.0)

simplify39.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
0115135
1333127
21116125
35001125

prune57.0ms

Filtered
30 candidates to 20 candidates (33.3%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New25530
Fresh000
Picked101
Done000
Total26531

Merged error: 8.6b

Counts
31 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

1.2b
(* x (+ a (* (* 1/2 (pow a 2)) x)))
8.7b
(* (* 1/2 (pow a 2)) x)
11.8b
(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
15.8b
(* (pow a 3) (pow x 3))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
28×add-exp-log
18×associate-*r*
17×prod-exp unswap-sqr
16×associate-*l*
14×unpow-prod-down cube-prod
13×add-cube-cbrt *-un-lft-identity add-cbrt-cube
10×sqr-pow
8×pow1
7×pow-to-exp pow-exp
6×add-log-exp
5×cbrt-unprod
3×pow-prod-down *-commutative
2×distribute-rgt-in cube-mult associate-+l+ distribute-lft-in flip3-+ unpow3 associate-*r/ flip-+
1×+-commutative sum-log
Counts
4 → 113
Calls
4 calls:
5.0ms
(* x (+ a (* (* 1/2 (pow a 2)) x)))
5.0ms
(* (* 1/2 (pow a 2)) x)
6.0ms
(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
9.0ms
(* (pow a 3) (pow x 3))

series46.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(* x (+ a (* (* 1/2 (pow a 2)) x)))
4.0ms
(* (* 1/2 (pow a 2)) x)
18.0ms
(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
12.0ms
(* (pow a 3) (pow x 3))

simplify98.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0471797
12758737
25001737

prune213.0ms

Filtered
125 candidates to 75 candidates (40.0%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1223125
Fresh134
Picked101
Done000
Total1246130

Merged error: 2.2b

Counts
130 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (* a x) 3)
1.2b
(* x (+ a (* (* 1/2 (pow a 2)) x)))
8.7b
(* (* 1/2 (pow a 2)) x)
11.8b
(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

rewrite22.0ms

Algorithm
rewrite-expression-head
Rules
19×add-exp-log
14×add-cbrt-cube
11×pow1
10×add-sqr-sqrt
9×prod-exp
8×add-cube-cbrt *-un-lft-identity
6×associate-*r* add-log-exp
5×cbrt-unprod
4×associate-*l*
3×pow-unpow pow-prod-down pow-exp
2×distribute-rgt-in pow-to-exp associate-+l+ pow-pow distribute-lft-in flip3-+ associate-*r/ *-commutative flip-+ rem-cube-cbrt
1×+-commutative cube-mult unpow-prod-down unpow3 cube-prod sum-log unswap-sqr sqr-pow
Counts
4 → 76
Calls
4 calls:
3.0ms
(pow (* a x) 3)
5.0ms
(* x (+ a (* (* 1/2 (pow a 2)) x)))
6.0ms
(* (* 1/2 (pow a 2)) x)
6.0ms
(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

series43.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(pow (* a x) 3)
14.0ms
(* x (+ a (* (* 1/2 (pow a 2)) x)))
4.0ms
(* (* 1/2 (pow a 2)) x)
18.0ms
(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

simplify75.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0376525
12297477
25003477

prune137.0ms

Filtered
88 candidates to 56 candidates (36.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New86288
Fresh325
Picked101
Done000
Total90494

Merged error: 0.0b

Counts
94 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (* a x) 3)
0.2b
(pow (* a x) 2)
5.0b
(+ (* a x) (* 1/2 (pow (* a x) 2)))
11.8b
(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
11×add-log-exp
10×pow1 add-exp-log
7×add-cbrt-cube
6×add-sqr-sqrt add-cube-cbrt pow-unpow *-un-lft-identity
4×pow-pow pow-exp sum-log
2×+-commutative pow-to-exp unpow-prod-down flip3-+ pow-prod-down prod-exp flip-+ rem-cube-cbrt sqr-pow
1×cube-mult associate-+l+ unpow3 cube-prod cbrt-unprod unpow2
Counts
4 → 64
Calls
4 calls:
3.0ms
(pow (* a x) 3)
3.0ms
(pow (* a x) 2)
4.0ms
(+ (* a x) (* 1/2 (pow (* a x) 2)))
7.0ms
(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

series42.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(pow (* a x) 3)
4.0ms
(pow (* a x) 2)
10.0ms
(+ (* a x) (* 1/2 (pow (* a x) 2)))
20.0ms
(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

simplify63.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0285425
11622391
25002391

prune101.0ms

Filtered
76 candidates to 48 candidates (36.8%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New76076
Fresh033
Picked011
Done000
Total76480

Merged error: 0.0b

Counts
80 → 4

regimes309.0ms

Accuracy

98.9% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03424
13424

end0.0ms

sample1.2s

Algorithm
intervals
Results
487.0ms2682×body1280valid
160.0ms1312×body640valid
136.0ms5490×body80valid
60.0ms739×body320valid
26.0ms424×body160valid

Profiling

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