Details

Time bar (total: 2.5s)

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

sample55.0ms

Algorithm
intervals
Results
13.0ms77×body1280valid
6.0ms53×body640valid
2.0ms103×body80valid
1.0ms17×body320valid
0.0ms6×body160valid

simplify53.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
047786
147786

prune12.0ms

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: 25.8b

Counts
2 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b
(exp (* a x))
25.9b
(- (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:
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)

simplify59.0ms

Algorithm
egg-herbie
Counts
29 → 29
Iterations

Useful iterations: 0 (56.0ms)

IterNodesCost
04915224
14915224

prune35.0ms

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: 3.1b

Counts
31 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.7b
(* x (+ a (* x (+ (* a (* a 1/2)) (* x (* 1/6 (pow a 3)))))))
3.0b
(* x (* 1/6 (pow a 3)))
5.7b
(* x (+ (* a (* a 1/2)) (* 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
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)))
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))))

series65.0ms

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

simplify28.0ms

Algorithm
egg-herbie
Counts
86 → 86
Iterations

Useful iterations: 0 (19.0ms)

IterNodesCost
052811359

prune119.0ms

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

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New84286
Fresh101
Picked101
Done011
Total86389

Merged error: 0.1b

Counts
89 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

3.8b
(* a (* (* a 1/2) (* x x)))
6.2b
(+ (* 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
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)))
5.0ms
(+ (* a x) (* a (* (* a 1/2) (* x x))))
7.0ms
(* (* a 1/2) (* x x))

series28.0ms

Counts
3 → 9
Calls
3 calls:
7.0ms
(* a (* (* a 1/2) (* x x)))
13.0ms
(+ (* 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

prune59.0ms

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

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New69170
Fresh011
Picked101
Done011
Total70373

Merged error: 0.0b

Counts
73 → 3

localize8.0ms

Local error

Found 3 expressions with local error:

0.1b
(* (* a (* 1/2 x)) x)
3.8b
(* a (* (* a (* 1/2 x)) x))
6.2b
(+ (* 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)
9.0ms
(* a (* (* a (* 1/2 x)) x))
5.0ms
(+ (* a x) (* a (* (* a (* 1/2 x)) x)))

series26.0ms

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)))

simplify33.0ms

Algorithm
egg-herbie
Counts
66 → 66
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
04962651
14962651

prune52.0ms

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

3 alts after pruning (1 fresh and 2 done)

PrunedKeptTotal
New66066
Fresh011
Picked011
Done011
Total66369

Merged error: 0.0b

Counts
69 → 3

regimes212.0ms

Accuracy

98.7% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 22.0b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03125
13125

end0.0ms

sample1.5s

Algorithm
intervals
Results
447.0ms2699×body1280valid
144.0ms1368×body640valid
58.0ms2846×body80valid
48.0ms694×body320valid
19.0ms393×body160valid

Profiling

Loading profile data...