Details

Time bar (total: 1.9s)

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

sample34.0ms

Algorithm
intervals
Results
16.0ms91×body1280valid
5.0ms40×body640valid
2.0ms31×body320valid
2.0ms83×body80valid
1.0ms11×body160valid
0.0ms9×body80invalid

simplify49.0ms

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: 31.9b

Counts
2 → 2

localize4.0ms

Local error

Found 1 expressions with local error:

4.0b
(- (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:
3.0ms
(- (exp (* a x)) 1.0)

series10.0ms

Counts
1 → 3
Calls
1 calls:
10.0ms
(- (exp (* a x)) 1.0)

simplify36.0ms

Algorithm
egg-herbie
Counts
16 → 16
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
04940161
14940161

prune29.0ms

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

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New14216
Fresh101
Picked011
Done000
Total15318

Merged error: 4.4b

Counts
18 → 3

localize12.0ms

Local error

Found 4 expressions with local error:

0.9b
(* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))))
4.0b
(* x (* 1/6 (pow a 3)))
6.9b
(* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))
8.7b
(+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3))))

rewrite26.0ms

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))))

series61.0ms

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))))

simplify41.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
050311233

prune104.0ms

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: 0.3b

Counts
89 → 3

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (* (* a 1/2) (* x x)))
1.4b
(* a (+ x (* (* a 1/2) (* x x))))
7.9b
(* (* a 1/2) (* x x))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1 add-exp-log add-cbrt-cube
9×pow-prod-down prod-exp cbrt-unprod
7×add-sqr-sqrt
5×add-cube-cbrt *-un-lft-identity add-log-exp
4×associate-*r* associate-*l*
2×flip3-+ associate-*r/ *-commutative flip-+
1×+-commutative distribute-rgt-in distribute-lft-in sum-log unswap-sqr
Counts
3 → 55
Calls
3 calls:
3.0ms
(+ x (* (* a 1/2) (* x x)))
5.0ms
(* a (+ x (* (* a 1/2) (* x x))))
7.0ms
(* (* a 1/2) (* x x))

series25.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(+ x (* (* a 1/2) (* x x)))
12.0ms
(* a (+ x (* (* a 1/2) (* x x))))
7.0ms
(* (* a 1/2) (* x x))

simplify39.0ms

Algorithm
egg-herbie
Counts
64 → 64
Iterations

Useful iterations: 0 (34.0ms)

IterNodesCost
05134665

prune63.0ms

Filtered
40 candidates to 64 candidates (-60.0%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New62264
Fresh011
Picked101
Done011
Total63467

Merged error: 0.0b

Counts
67 → 4

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ x (* (* a (* 1/2 x)) x))
0.1b
(* (* a (* 1/2 x)) x)
1.4b
(* a (+ x (* (* a (* 1/2 x)) x)))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
14×pow1 add-exp-log add-cbrt-cube
8×add-sqr-sqrt *-un-lft-identity associate-*r*
7×pow-prod-down prod-exp cbrt-unprod
6×add-cube-cbrt
5×add-log-exp
4×associate-*l*
2×distribute-rgt-out flip3-+ associate-*r/ distribute-rgt1-in *-commutative flip-+
1×+-commutative distribute-rgt-in distribute-lft-in sum-log unswap-sqr
Counts
3 → 58
Calls
3 calls:
3.0ms
(+ x (* (* a (* 1/2 x)) x))
6.0ms
(* (* a (* 1/2 x)) x)
5.0ms
(* a (+ x (* (* a (* 1/2 x)) x)))

series26.0ms

Counts
3 → 9
Calls
3 calls:
6.0ms
(+ x (* (* a (* 1/2 x)) x))
7.0ms
(* (* a (* 1/2 x)) x)
12.0ms
(* a (+ x (* (* a (* 1/2 x)) x)))

simplify41.0ms

Algorithm
egg-herbie
Counts
67 → 67
Iterations

Useful iterations: 0 (35.0ms)

IterNodesCost
05012686

prune61.0ms

Filtered
46 candidates to 67 candidates (-45.7%)
Pruning

2 alts after pruning (1 fresh and 1 done)

PrunedKeptTotal
New66167
Fresh202
Picked101
Done011
Total69271

Merged error: 0.0b

Counts
71 → 2

regimes203.0ms

Accuracy

98.3% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 21.6b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02123
12123

end0.0ms

analyze41.0ms

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

sample934.0ms

Algorithm
intervals
Results
474.0ms2681×body1280valid
158.0ms1344×body640valid
75.0ms2794×body80valid
57.0ms734×body320valid
24.0ms447×body160valid
4.0ms136×body80invalid

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