Details

Time bar (total: 2.2s)

analyze45.0ms

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
16.0ms87×body1280valid
6.0ms50×body640valid
2.0ms78×body80valid
2.0ms21×body320valid
1.0ms20×body160valid
0.0ms5×body80invalid

simplify50.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (48.0ms)

IterNodesCost
047936
147936

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: 32.3b

Counts
2 → 2

localize4.0ms

Local error

Found 1 expressions with local error:

4.9b
(- (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)

series8.0ms

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

simplify34.0ms

Algorithm
egg-herbie
Counts
16 → 16
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
04940161
14940161

prune204.0ms

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: 4.5b

Counts
18 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

1.2b
(* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))))
5.0b
(* x (* 1/6 (pow a 3)))
7.0b
(* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))
8.5b
(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))

rewrite25.0ms

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))))

series67.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))))
13.0ms
(* x (* 1/6 (pow a 3)))
22.0ms
(* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))
9.0ms
(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))

simplify41.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
050311233

prune105.0ms

Filtered
59 candidates to 86 candidates (-45.8%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New84286
Fresh101
Picked101
Done011
Total86389

Merged error: 0.2b

Counts
89 → 3

localize7.0ms

Local error

Found 2 expressions with local error:

1.7b
(* a (+ x (* (* a 1/2) (* x x))))
7.5b
(* (* a 1/2) (* x x))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
16×pow1 add-exp-log add-cbrt-cube
9×pow-prod-down prod-exp cbrt-unprod
6×add-sqr-sqrt
4×add-cube-cbrt *-un-lft-identity associate-*r* associate-*l*
2×associate-*r/ *-commutative add-log-exp
1×distribute-rgt-in distribute-lft-in flip3-+ flip-+ unswap-sqr
Counts
2 → 44
Calls
2 calls:
5.0ms
(* a (+ x (* (* a 1/2) (* x x))))
7.0ms
(* (* a 1/2) (* x x))

series20.0ms

Counts
2 → 6
Calls
2 calls:
12.0ms
(* a (+ x (* (* a 1/2) (* x x))))
7.0ms
(* (* a 1/2) (* x x))

simplify51.0ms

Algorithm
egg-herbie
Counts
50 → 50
Iterations

Useful iterations: 0 (44.0ms)

IterNodesCost
04950495
14950495

prune52.0ms

Filtered
30 candidates to 50 candidates (-66.7%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New48250
Fresh011
Picked101
Done011
Total49453

Merged error: 0.1b

Counts
53 → 4

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(* a (* 1/2 x))
0.1b
(* (* a (* 1/2 x)) x)
1.7b
(* a (+ x (* (* a (* 1/2 x)) x)))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
19×pow1 add-exp-log add-cbrt-cube
10×pow-prod-down prod-exp cbrt-unprod
9×add-sqr-sqrt associate-*r*
8×*-un-lft-identity
7×add-cube-cbrt associate-*l*
3×*-commutative add-log-exp
2×associate-*r/
1×distribute-rgt-in distribute-rgt-out distribute-lft-in flip3-+ distribute-rgt1-in flip-+ unswap-sqr
Counts
3 → 63
Calls
3 calls:
5.0ms
(* a (* 1/2 x))
6.0ms
(* (* a (* 1/2 x)) x)
5.0ms
(* a (+ x (* (* a (* 1/2 x)) x)))

series23.0ms

Counts
3 → 9
Calls
3 calls:
3.0ms
(* a (* 1/2 x))
7.0ms
(* (* a (* 1/2 x)) x)
12.0ms
(* a (+ x (* (* a (* 1/2 x)) x)))

simplify40.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
05083622

prune60.0ms

Filtered
47 candidates to 72 candidates (-53.2%)
Pruning

5 alts after pruning (3 fresh and 2 done)

PrunedKeptTotal
New71172
Fresh022
Picked011
Done011
Total71576

Merged error: 0.1b

Counts
76 → 5

regimes234.0ms

Accuracy

98.6% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 22.2b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02123
12123

end0.0ms

analyze40.0ms

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

sample954.0ms

Algorithm
intervals
Results
487.0ms2699×body1280valid
150.0ms1266×body640valid
74.0ms2861×body80valid
58.0ms745×body320valid
26.0ms429×body160valid
4.0ms151×body80invalid

Profiling

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