Details

Time bar (total: 1.9s)

analyze43.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
50%50%0.1%3
50%50%0.1%4
62.4%37.5%0.1%5
62.4%31.2%6.3%6
68.7%21.9%9.5%7
68.7%17.2%14.1%8
71.8%11.7%16.5%9
71.8%9%19.2%10
73.4%6%20.6%11
73.4%4.6%22%12
74.1%3.1%22.8%13
74.1%2.3%23.5%14

sample39.0ms

Algorithm
intervals
Results
20.0ms88×body1280valid
5.0ms46×body640valid
3.0ms91×body80valid
2.0ms20×body320valid
1.0ms11×body160valid
0.0msbody80invalid

simplify55.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (53.0ms)

IterNodesCost
047786
147786

prune9.0ms

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: 29.4b

Counts
2 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(exp (* a x))
2.7b
(- (exp (* a x)) 1.0)

rewrite6.0ms

Algorithm
rewrite-expression-head
Rules
add-log-exp
add-sqr-sqrt *-un-lft-identity
pow1 add-exp-log add-cube-cbrt add-cbrt-cube
sub-neg exp-prod flip3-- exp-to-pow diff-log flip-- rem-exp-log distribute-lft-out-- difference-of-squares
Counts
2 → 23
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)

simplify61.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 0 (58.0ms)

IterNodesCost
04915224
14915224

prune39.0ms

Filtered
20 candidates to 29 candidates (-45.0%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New28129
Fresh011
Picked011
Done000
Total28331

Merged error: 2.6b

Counts
31 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

1.7b
(* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))))
3.8b
(* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))
5.7b
(* x (* 1/6 (pow a 3)))
11.3b
(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log
13×add-sqr-sqrt add-cbrt-cube
10×pow1
add-cube-cbrt *-un-lft-identity associate-*l* prod-exp
associate-*r*
add-log-exp
cbrt-unprod
associate-*r/
flip3-+ pow-prod-down *-commutative flip-+
distribute-rgt-in distribute-lft-in unswap-sqr
+-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)))))))
8.0ms
(* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))
6.0ms
(* x (* 1/6 (pow a 3)))
6.0ms
(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))

series65.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))))
24.0ms
(* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))
11.0ms
(* x (* 1/6 (pow a 3)))
9.0ms
(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))

simplify30.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (21.0ms)

IterNodesCost
052811359

prune116.0ms

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

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New85186
Fresh101
Picked011
Done011
Total86389

Merged error: 0.0b

Counts
89 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

2.0b
(* a (* (* a 1/2) (* x x)))
5.2b
(+ (* a x) (* a (* (* a 1/2) (* x x))))
6.6b
(* (* a 1/2) (* x x))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
33×pow1 add-exp-log add-cbrt-cube
21×pow-prod-down prod-exp cbrt-unprod
add-log-exp
add-sqr-sqrt add-cube-cbrt *-un-lft-identity associate-*l*
associate-*r* *-commutative
+-commutative flip3-+ sum-log flip-+ distribute-lft-out
Counts
3 → 61
Calls
3 calls:
9.0ms
(* a (* (* a 1/2) (* x x)))
5.0ms
(+ (* a x) (* a (* (* a 1/2) (* x x))))
7.0ms
(* (* a 1/2) (* x x))

series29.0ms

Counts
3 → 9
Calls
3 calls:
8.0ms
(* a (* (* a 1/2) (* x x)))
11.0ms
(+ (* a x) (* a (* (* a 1/2) (* x x))))
10.0ms
(* (* a 1/2) (* x x))

simplify47.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
04991683
14991683

prune55.0ms

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

3 alts after pruning (0 fresh and 3 done)

PrunedKeptTotal
New70070
Fresh000
Picked011
Done022
Total70373

Merged error: 0.0b

Counts
73 → 3

regimes201.0ms

Accuracy

87.5% (3.0b remaining)

Error of 3.2b against oracle of 0.2b and baseline of 24.1b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03025
13025

end0.0ms

sample993.0ms

Algorithm
intervals
Results
502.0ms2716×body1280valid
159.0ms1341×body640valid
74.0ms2778×body80valid
68.0ms782×body320valid
27.0ms383×body160valid
3.0ms122×body80invalid

Profiling

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