Details

Time bar (total: 2.7s)

sample43.0ms

Algorithm
intervals
Results
20.0ms114×body1280valid
4.0ms177×body80valid
4.0ms33×body640valid
2.0ms19×body320valid
0.0ms8×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

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 29.3b

Counts
2 → 1

localize4.0ms

Local error

Found 2 expressions with local error:

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

series11.0ms

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

simplify40.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 2 (10.0ms)

IterNodesCost
0115135
1333127
21116125
35001125

prune62.0ms

Filtered
20 candidates to 30 candidates (-50.0%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New22830
Fresh000
Picked101
Done000
Total23831

Merged error: 7.6b

Counts
31 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.5b
(* x (+ a (* (* 1/2 (pow a 2)) x)))
5.0b
(* (* 1/2 (pow a 2)) x)
11.8b
(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (* (pow a 3) (pow x 3))))
12.9b
(* (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)
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))

series45.0ms

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))))
10.0ms
(* (pow a 3) (pow x 3))

simplify101.0ms

Algorithm
egg-herbie
Counts
125 → 125
Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
0471797
12758737
25001737

prune205.0ms

Filtered
75 candidates to 125 candidates (-66.7%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1232125
Fresh167
Picked101
Done000
Total1258133

Merged error: 2.8b

Counts
133 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (* a x) 3)
0.5b
(* x (+ a (* (* 1/2 (pow a 2)) x)))
5.0b
(* (* 1/2 (pow a 2)) x)
11.8b
(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

rewrite24.0ms

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:
5.0ms
(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)))

series42.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(pow (* a x) 3)
12.0ms
(* x (+ a (* (* 1/2 (pow a 2)) x)))
4.0ms
(* (* 1/2 (pow a 2)) x)
19.0ms
(+ (* x (+ a (* (* 1/2 (pow a 2)) x))) (* 1/6 (pow (* a x) 3)))

simplify77.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 1 (12.0ms)

IterNodesCost
0376525
12297477
25003477

prune141.0ms

Filtered
56 candidates to 88 candidates (-57.1%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New85388
Fresh347
Picked101
Done000
Total89796

Merged error: 0.1b

Counts
96 → 7

localize11.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (* a x) 3)
0.2b
(pow (* a x) 2)
4.4b
(+ (* a x) (* 1/2 (pow (* a x) 2)))
11.8b
(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

rewrite19.0ms

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:
4.0ms
(pow (* a x) 3)
4.0ms
(pow (* a x) 2)
3.0ms
(+ (* a x) (* 1/2 (pow (* a x) 2)))
7.0ms
(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

series40.0ms

Counts
4 → 12
Calls
4 calls:
7.0ms
(pow (* a x) 3)
4.0ms
(pow (* a x) 2)
11.0ms
(+ (* a x) (* 1/2 (pow (* a x) 2)))
18.0ms
(+ (+ (* a x) (* 1/2 (pow (* a x) 2))) (* 1/6 (pow (* a x) 3)))

simplify65.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0285425
11622391
25002391

prune96.0ms

Filtered
48 candidates to 76 candidates (-58.3%)
Pruning

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New74276
Fresh156
Picked101
Done000
Total76783

Merged error: 0.1b

Counts
83 → 7

regimes368.0ms

Accuracy

96.6% (0.7b remaining)

Error of 0.8b against oracle of 0.0b and baseline of 20.9b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02615
12615

end0.0ms

sample1.1s

Algorithm
intervals
Results
478.0ms2781×body1280valid
152.0ms1311×body640valid
128.0ms5321×body80valid
60.0ms767×body320valid
21.0ms390×body160valid

Profiling

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