Details

Time bar (total: 2.6s)

sample37.0ms

Algorithm
intervals
Results
13.0ms70×body1280valid
7.0ms60×body640valid
4.0ms174×body80valid
3.0ms32×body320valid
1.0ms11×body160valid

simplify62.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0113
1183
2263
3483
41103
53183
616233
750013

prune2.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 34.1b

Counts
2 → 1

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(exp (* a x))
3.0b
(- (exp (* a x)) 1.0)

rewrite6.0ms

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:
2.0ms
(exp (* a x))
4.0ms
(- (exp (* a x)) 1.0)

series50.0ms

Counts
2 → 6
Calls
2 calls:
12.0ms
(exp (* a x))
37.0ms
(- (exp (* a x)) 1.0)

simplify44.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 2 (11.0ms)

IterNodesCost
0115135
1333127
21116125
35001125

prune64.0ms

Filtered
30 candidates to 20 candidates (66.7%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New24630
Fresh000
Picked101
Done000
Total25631

Merged error: 10.3b

Counts
31 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(* x (+ a (* (* 1/2 (pow a 2)) x)))
8.1b
(* (* 1/2 (pow a 2)) x)
10.8b
(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
18.9b
(* (pow a 3) (pow x 3))

rewrite30.0ms

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)))
6.0ms
(* (* 1/2 (pow a 2)) x)
7.0ms
(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
9.0ms
(* (pow a 3) (pow x 3))

series238.0ms

Counts
4 → 12
Calls
4 calls:
59.0ms
(* x (+ a (* (* 1/2 (pow a 2)) x)))
20.0ms
(* (* 1/2 (pow a 2)) x)
95.0ms
(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
64.0ms
(* (pow a 3) (pow x 3))

simplify98.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 1 (15.0ms)

IterNodesCost
0471797
12758738
25001738

prune256.0ms

Filtered
125 candidates to 75 candidates (60.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1223125
Fresh055
Picked101
Done000
Total1238131

Merged error: 3.5b

Counts
131 → 8

localize8.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (pow a 2))
0.0b
(+ a (* (* 1/2 (pow a 2)) x))
1.0b
(* x (+ a (* (* 1/2 (pow a 2)) x)))
8.1b
(* (* 1/2 (pow a 2)) x)

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
21×add-exp-log
18×add-sqr-sqrt
14×associate-*r*
13×add-cbrt-cube
11×prod-exp
10×add-cube-cbrt *-un-lft-identity
8×pow1
7×associate-*l*
6×add-log-exp
5×cbrt-unprod unswap-sqr
4×unpow-prod-down
3×*-commutative
2×pow-to-exp flip3-+ associate-*r/ pow-prod-down pow-exp flip-+ unpow2 sqr-pow
1×+-commutative distribute-rgt-in distribute-lft-in sum-log
Counts
4 → 79
Calls
4 calls:
5.0ms
(* 1/2 (pow a 2))
3.0ms
(+ a (* (* 1/2 (pow a 2)) x))
5.0ms
(* x (+ a (* (* 1/2 (pow a 2)) x)))
6.0ms
(* (* 1/2 (pow a 2)) x)

series153.0ms

Counts
4 → 12
Calls
4 calls:
24.0ms
(* 1/2 (pow a 2))
46.0ms
(+ a (* (* 1/2 (pow a 2)) x))
56.0ms
(* x (+ a (* (* 1/2 (pow a 2)) x)))
26.0ms
(* (* 1/2 (pow a 2)) x)

simplify60.0ms

Algorithm
egg-herbie
Counts
91 → 91
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0317462
11753406
25002404

prune139.0ms

Filtered
91 candidates to 57 candidates (62.6%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New88391
Fresh347
Picked101
Done000
Total92799

Merged error: 0.3b

Counts
99 → 7

localize6.0ms

rewrite0.0ms

Algorithm
rewrite-expression-head
Rules
Counts
0 → 0

series0.0ms

Counts
0 → 0

simplify3.0ms

Algorithm
egg-herbie
Counts
0 → 0
Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
000

prune0.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

PrunedKeptTotal
New000
Fresh066
Picked011
Done000
Total077

Merged error: 0.3b

Counts
7 → 7

regimes237.0ms

Accuracy

97.1% (0.6b remaining)

Error of 0.8b against oracle of 0.2b and baseline of 21.5b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01613
11613

end0.0ms

sample1.1s

Algorithm
intervals
Results
487.0ms2707×body1280valid
158.0ms1296×body640valid
141.0ms5508×body80valid
61.0ms766×body320valid
22.0ms393×body160valid