Details

Time bar (total: 2.1s)

analyze44.0ms

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
18.0ms96×body1280valid
5.0ms43×body640valid
2.0ms81×body80valid
2.0ms22×body320valid
1.0ms14×body160valid
0.0ms3×body80invalid

simplify65.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (63.0ms)

IterNodesCost
048076
148076

prune10.0ms

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: 31.6b

Counts
2 → 2

localize4.0ms

Local error

Found 1 expressions with local error:

3.9b
(- (exp (* a x)) 1.0)

rewrite4.0ms

Algorithm
rewrite-expression-head
Rules
3×add-sqr-sqrt *-un-lft-identity add-log-exp
1×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out-- difference-of-squares
Counts
1 → 13
Calls
1 calls:
4.0ms
(- (exp (* a x)) 1.0)

series7.0ms

Counts
1 → 3
Calls
1 calls:
7.0ms
(- (exp (* a x)) 1.0)

simplify40.0ms

Algorithm
egg-herbie
Counts
16 → 16
Iterations

Useful iterations: 0 (37.0ms)

IterNodesCost
05465161

prune31.0ms

Filtered
13 candidates to 16 candidates (-23.1%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New15116
Fresh011
Picked011
Done000
Total15318

Merged error: 3.3b

Counts
18 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

0.3b
(* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))))
4.5b
(* x (* 1/6 (pow a 3)))
7.5b
(* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))
8.2b
(+ (* 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
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)))
9.0ms
(* 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)))
23.0ms
(* 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 (22.0ms)

IterNodesCost
059151359

prune130.0ms

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: 0.2b

Counts
89 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b
(* x (+ a (+ (* a (* a (* 1/2 x))) (* x (* x (* 1/6 (pow a 3)))))))
4.5b
(* x (* 1/6 (pow a 3)))
5.4b
(* x (* x (* 1/6 (pow a 3))))
8.4b
(+ (* a (* a (* 1/2 x))) (* x (* x (* 1/6 (pow a 3)))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log
20×prod-exp add-cbrt-cube
13×pow1
10×add-sqr-sqrt *-un-lft-identity cbrt-unprod
9×associate-*l*
8×add-cube-cbrt
6×associate-*r* add-log-exp
5×pow-prod-down
3×*-commutative
2×pow-to-exp flip3-+ associate-*r/ pow-exp flip-+
1×+-commutative distribute-rgt-in distribute-lft-in sum-log distribute-lft-out unswap-sqr
Counts
4 → 75
Calls
4 calls:
10.0ms
(* x (+ a (+ (* a (* a (* 1/2 x))) (* x (* x (* 1/6 (pow a 3)))))))
6.0ms
(* x (* 1/6 (pow a 3)))
8.0ms
(* x (* x (* 1/6 (pow a 3))))
9.0ms
(+ (* a (* a (* 1/2 x))) (* x (* x (* 1/6 (pow a 3)))))

series57.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(* x (+ a (+ (* a (* a (* 1/2 x))) (* x (* x (* 1/6 (pow a 3)))))))
10.0ms
(* x (* 1/6 (pow a 3)))
12.0ms
(* x (* x (* 1/6 (pow a 3))))
14.0ms
(+ (* a (* a (* 1/2 x))) (* x (* x (* 1/6 (pow a 3)))))

simplify32.0ms

Algorithm
egg-herbie
Counts
87 → 87
Iterations

Useful iterations: 0 (24.0ms)

IterNodesCost
054581304

prune125.0ms

Filtered
52 candidates to 87 candidates (-67.3%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New85287
Fresh112
Picked011
Done011
Total86591

Merged error: 0.1b

Counts
91 → 5

localize8.0ms

Local error

Found 2 expressions with local error:

0.1b
(* a (* a (* 1/2 x)))
0.5b
(* x (+ a (* a (* a (* 1/2 x)))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
13×pow1 add-exp-log add-cbrt-cube
7×add-sqr-sqrt pow-prod-down prod-exp cbrt-unprod
6×associate-*l*
5×add-cube-cbrt *-un-lft-identity
4×associate-*r*
2×associate-*r/ *-commutative add-log-exp
1×distribute-rgt-in distribute-lft-in flip3-+ flip-+ unswap-sqr
Counts
2 → 43
Calls
2 calls:
6.0ms
(* a (* a (* 1/2 x)))
6.0ms
(* x (+ a (* a (* a (* 1/2 x)))))

series16.0ms

Counts
2 → 6
Calls
2 calls:
4.0ms
(* a (* a (* 1/2 x)))
12.0ms
(* x (+ a (* a (* a (* 1/2 x)))))

simplify56.0ms

Algorithm
egg-herbie
Counts
49 → 49
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
04950492
14950492

prune54.0ms

Filtered
33 candidates to 49 candidates (-48.5%)
Pruning

5 alts after pruning (2 fresh and 3 done)

PrunedKeptTotal
New49049
Fresh022
Picked011
Done022
Total49554

Merged error: 0.1b

Counts
54 → 5

regimes247.0ms

Accuracy

97.8% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 21.7b

bsearch0.0ms

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07223
17223

end0.0ms

sample949.0ms

Algorithm
intervals
Results
478.0ms2675×body1280valid
154.0ms1332×body640valid
74.0ms2807×body80valid
61.0ms782×body320valid
22.0ms404×body160valid
5.0ms172×body80invalid

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