Details

Time bar (total: 2.2s)

sample40.0ms

Algorithm
intervals
Results
15.0ms80×body1280valid
5.0ms186×body80valid
4.0ms36×body640valid
2.0ms27×body320valid
1.0ms15×body160valid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
047966
147966

prune13.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 28.8b

Counts
2 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(exp (* a x))
4.0b
(- (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:
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))
8.0ms
(- (exp (* a x)) 1.0)

simplify68.0ms

Algorithm
egg-herbie
Counts
30 → 30
Iterations

Useful iterations: 0 (64.0ms)

IterNodesCost
04947226
14947226

prune35.0ms

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

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New29130
Fresh011
Picked011
Done000
Total29332

Merged error: 5.0b

Counts
32 → 3

localize15.0ms

Local error

Found 4 expressions with local error:

1.2b
(* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))))
5.5b
(* x (* 1/6 (pow a 3)))
9.1b
(* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))
13.5b
(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
13×add-sqr-sqrt add-cbrt-cube
10×pow1
9×add-cube-cbrt *-un-lft-identity associate-*l* prod-exp
7×associate-*r*
6×add-log-exp
5×cbrt-unprod
4×associate-*r/
3×flip3-+ pow-prod-down *-commutative flip-+
2×distribute-rgt-in distribute-lft-in unswap-sqr
1×+-commutative pow-to-exp pow-exp sum-log
Counts
4 → 74
Calls
4 calls:
5.0ms
(* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))))
6.0ms
(* x (* 1/6 (pow a 3)))
7.0ms
(* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))
5.0ms
(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))

series60.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))))
10.0ms
(* x (* 1/6 (pow a 3)))
21.0ms
(* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))
8.0ms
(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))

simplify31.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
051991359

prune115.0ms

Filtered
54 candidates to 86 candidates (-59.3%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New84286
Fresh101
Picked101
Done011
Total86389

Merged error: 0.3b

Counts
89 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

4.0b
(+ (* a x) (* a (* (* a 1/2) (* x x))))
4.4b
(* a (* (* a 1/2) (* x x)))
8.2b
(* (* a 1/2) (* x x))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
33×pow1 add-exp-log add-cbrt-cube
21×pow-prod-down prod-exp cbrt-unprod
5×add-log-exp
4×add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*l*
2×associate-*r* *-commutative
1×+-commutative flip3-+ sum-log flip-+ distribute-lft-out
Counts
3 → 61
Calls
3 calls:
4.0ms
(+ (* a x) (* a (* (* a 1/2) (* x x))))
9.0ms
(* a (* (* a 1/2) (* x x)))
7.0ms
(* (* a 1/2) (* x x))

series25.0ms

Counts
3 → 9
Calls
3 calls:
11.0ms
(+ (* a x) (* a (* (* a 1/2) (* x x))))
7.0ms
(* a (* (* a 1/2) (* x x)))
7.0ms
(* (* a 1/2) (* x x))

simplify32.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (23.0ms)

IterNodesCost
05314677

prune58.0ms

Filtered
36 candidates to 70 candidates (-94.4%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New69170
Fresh011
Picked101
Done011
Total70373

Merged error: 0.2b

Counts
73 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (* a (* 1/2 x)) x)
4.0b
(+ (* a x) (* a (* (* a (* 1/2 x)) x)))
4.4b
(* a (* (* a (* 1/2 x)) x))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
26×pow1 add-exp-log add-cbrt-cube
16×pow-prod-down prod-exp cbrt-unprod
5×add-sqr-sqrt add-cube-cbrt *-un-lft-identity add-log-exp
4×associate-*r* associate-*l*
2×*-commutative
1×+-commutative flip3-+ sum-log flip-+ distribute-lft-out
Counts
3 → 57
Calls
3 calls:
6.0ms
(* (* a (* 1/2 x)) x)
4.0ms
(+ (* a x) (* a (* (* a (* 1/2 x)) x)))
8.0ms
(* a (* (* a (* 1/2 x)) x))

series25.0ms

Counts
3 → 9
Calls
3 calls:
7.0ms
(* (* a (* 1/2 x)) x)
10.0ms
(+ (* a x) (* a (* (* a (* 1/2 x)) x)))
7.0ms
(* a (* (* a (* 1/2 x)) x))

simplify46.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
04987649
14987649

prune52.0ms

Filtered
37 candidates to 66 candidates (-78.4%)
Pruning

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New66066
Fresh011
Picked011
Done011
Total66369

Merged error: 0.2b

Counts
69 → 3

regimes230.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.7b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02125
12125

end0.0ms

sample1.2s

Algorithm
intervals
Results
491.0ms2676×body1280valid
171.0ms1380×body640valid
134.0ms5472×body80valid
62.0ms761×body320valid
22.0ms386×body160valid

Profiling

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