Details

Time bar (total: 2.0s)

analyze46.0ms

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

sample35.0ms

Algorithm
intervals
Results
18.0ms95×body1280valid
5.0ms40×body640valid
2.0ms84×body80valid
2.0ms23×body320valid
1.0ms14×body160valid
0.0ms5×body80invalid

simplify54.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (52.0ms)

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: 29.8b

Counts
2 → 2

localize5.0ms

Local error

Found 2 expressions with local error:

0.0b
(exp (* a x))
3.4b
(- (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 → 23
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)

simplify60.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 0 (57.0ms)

IterNodesCost
04915224
14915224

prune43.0ms

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

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New27229
Fresh101
Picked011
Done000
Total28331

Merged error: 4.3b

Counts
31 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

2.9b
(* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))))
4.6b
(* x (* 1/6 (pow a 3)))
7.6b
(* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))
10.9b
(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))

rewrite28.0ms

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)))))))
7.0ms
(* x (* 1/6 (pow a 3)))
8.0ms
(* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))
6.0ms
(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))

series62.0ms

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)))
22.0ms
(* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))
8.0ms
(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))

simplify29.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (19.0ms)

IterNodesCost
052811359

prune127.0ms

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

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New83386
Fresh101
Picked101
Done011
Total85489

Merged error: 0.3b

Counts
89 → 4

localize8.0ms

Local error

Found 3 expressions with local error:

3.1b
(* a (* (* a 1/2) (* x x)))
4.0b
(+ (* a x) (* a (* (* a 1/2) (* x x))))
9.4b
(* (* a 1/2) (* x x))

rewrite22.0ms

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:
9.0ms
(* a (* (* a 1/2) (* x x)))
4.0ms
(+ (* a x) (* a (* (* a 1/2) (* x x))))
6.0ms
(* (* a 1/2) (* x x))

series26.0ms

Counts
3 → 9
Calls
3 calls:
8.0ms
(* a (* (* a 1/2) (* x x)))
11.0ms
(+ (* a x) (* a (* (* a 1/2) (* x x))))
7.0ms
(* (* a 1/2) (* x x))

simplify44.0ms

Algorithm
egg-herbie
Counts
70 → 70
Iterations

Useful iterations: 0 (38.0ms)

IterNodesCost
04991683
14991683

prune66.0ms

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

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New68270
Fresh112
Picked101
Done011
Total70474

Merged error: 0.1b

Counts
74 → 4

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (* a (* 1/2 x)) x)
3.1b
(* a (* (* a (* 1/2 x)) x))
4.0b
(+ (* a x) (* a (* (* a (* 1/2 x)) x)))

rewrite21.0ms

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)
8.0ms
(* a (* (* a (* 1/2 x)) x))
5.0ms
(+ (* a x) (* a (* (* a (* 1/2 x)) x)))

series25.0ms

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

simplify31.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
04962651
14962651

prune56.0ms

Filtered
38 candidates to 66 candidates (-73.7%)
Pruning

4 alts after pruning (2 fresh and 2 done)

PrunedKeptTotal
New66066
Fresh022
Picked011
Done011
Total66470

Merged error: 0.1b

Counts
70 → 4

regimes246.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 21.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03125
13125

end0.0ms

sample939.0ms

Algorithm
intervals
Results
474.0ms2670×body1280valid
159.0ms1329×body640valid
72.0ms2797×body80valid
62.0ms792×body320valid
22.0ms412×body160valid
4.0ms135×body80invalid

Profiling

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