Details

Time bar (total: 10.8s)

sample188.0ms

Algorithm
intervals
Results
79.0ms77×body2560valid
67.0ms116×body1280valid
9.0ms29×body640valid
7.0ms320×pre80true
4.0ms64×body80overflowed
3.0ms15×body320valid
1.0ms16×body80valid
0.0ms3×body160valid

simplify101.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04013
110113
224513
369713
4346313
5500113

prune4.0ms

Filtered
1 candidates to 0 candidates (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 59.8b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
2.1b
(- (exp (* a eps)) 1.0)
3.2b
(- (exp (* b eps)) 1.0)
4.3b
(- (exp (* (+ a b) eps)) 1.0)

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
16×*-un-lft-identity
10×add-log-exp
9×flip3-- flip--
6×pow1 add-exp-log add-cube-cbrt add-cbrt-cube
5×sub-neg associate-*r* associate-*l* distribute-lft-out-- difference-of-squares
4×frac-times
3×diff-log
2×distribute-rgt-in distribute-lft-in associate-*r/ associate-*l/
1×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
Counts
4 → 76
Calls
4 calls:
10.0ms
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
4.0ms
(- (exp (* a eps)) 1.0)
4.0ms
(- (exp (* b eps)) 1.0)
5.0ms
(- (exp (* (+ a b) eps)) 1.0)

series165.0ms

Counts
4 → 12
Calls
4 calls:
47.0ms
(* (- (exp (* a eps)) 1.0) (- (exp (* b eps)) 1.0))
36.0ms
(- (exp (* a eps)) 1.0)
31.0ms
(- (exp (* b eps)) 1.0)
50.0ms
(- (exp (* (+ a b) eps)) 1.0)

simplify62.0ms

Algorithm
egg-herbie
Counts
88 → 88
Iterations

Useful iterations: 1 (9.0ms)

IterNodesCost
0346733
11449673
25001673

prune330.0ms

Filtered
88 candidates to 66 candidates (75.0%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New82688
Fresh000
Picked101
Done000
Total83689

Merged error: 49.0b

Counts
89 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

3.0b
(+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))
4.3b
(- (exp (* (+ a b) eps)) 1.0)
13.8b
(* (pow eps 2) (pow b 2))
15.6b
(* (pow eps 3) (pow b 3))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
56×add-sqr-sqrt
32×unswap-sqr
28×add-exp-log unpow-prod-down
20×associate-*r* associate-*l* sqr-pow
18×prod-exp
16×*-un-lft-identity
14×add-cube-cbrt cube-prod
12×pow-to-exp pow-exp
11×add-log-exp
10×unpow2
8×add-cbrt-cube
4×pow1
3×sum-log
2×cube-mult unpow3 pow-prod-down *-commutative cbrt-unprod
1×+-commutative sub-neg associate-+r+ flip3-- flip3-+ diff-log flip-- flip-+ distribute-lft-out-- difference-of-squares
Counts
4 → 137
Calls
4 calls:
12.0ms
(+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))
4.0ms
(- (exp (* (+ a b) eps)) 1.0)
7.0ms
(* (pow eps 2) (pow b 2))
12.0ms
(* (pow eps 3) (pow b 3))

series251.0ms

Counts
4 → 12
Calls
4 calls:
108.0ms
(+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))
45.0ms
(- (exp (* (+ a b) eps)) 1.0)
31.0ms
(* (pow eps 2) (pow b 2))
66.0ms
(* (pow eps 3) (pow b 3))

simplify104.0ms

Algorithm
egg-herbie
Counts
149 → 149
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
0510927
12493815
25002772

prune517.0ms

Filtered
149 candidates to 78 candidates (52.3%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New1454149
Fresh145
Picked101
Done000
Total1478155

Merged error: 48.7b

Counts
155 → 8

localize30.0ms

Local error

Found 4 expressions with local error:

3.0b
(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
3.0b
(+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))
4.3b
(- (exp (* (+ a b) eps)) 1.0)
13.8b
(* (pow eps 2) (pow b 2))

rewrite39.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
18×add-exp-log
17×unswap-sqr
14×unpow-prod-down *-un-lft-identity
13×associate-*l*
11×associate-*r* add-log-exp
10×add-cube-cbrt prod-exp unpow2 sqr-pow
8×add-cbrt-cube
6×pow1 pow-to-exp pow-exp
4×frac-times flip3-- flip3-+ flip-- flip-+
3×sum-log
2×associate-*r/ pow-prod-down associate-*l/ *-commutative cbrt-unprod distribute-lft-out-- difference-of-squares
1×+-commutative distribute-rgt-in sub-neg associate-+r+ distribute-lft-in diff-log
Counts
4 → 108
Calls
4 calls:
14.0ms
(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
9.0ms
(+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))
4.0ms
(- (exp (* (+ a b) eps)) 1.0)
8.0ms
(* (pow eps 2) (pow b 2))

series395.0ms

Counts
4 → 12
Calls
4 calls:
214.0ms
(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b))))
98.0ms
(+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))
51.0ms
(- (exp (* (+ a b) eps)) 1.0)
32.0ms
(* (pow eps 2) (pow b 2))

simplify110.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (91.0ms)

IterNodesCost
06191334
132131186
250011182

prune500.0ms

Filtered
120 candidates to 75 candidates (62.5%)
Pruning

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New1137120
Fresh347
Picked101
Done000
Total11711128

Merged error: 48.2b

Counts
128 → 11

localize22.0ms

Local error

Found 4 expressions with local error:

2.7b
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (pow (* b eps) 2)) (* eps b)))))
3.0b
(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (pow (* b eps) 2)) (* eps b))))
3.0b
(+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (pow (* b eps) 2)) (* eps b)))
4.3b
(- (exp (* (+ a b) eps)) 1.0)

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
18×add-exp-log add-cbrt-cube
12×add-sqr-sqrt
11×add-log-exp
10×*-un-lft-identity
8×frac-times flip3-- associate-/r/ flip--
7×flip3-+ flip-+
6×pow1 add-cube-cbrt associate-*r/
5×associate-*l* prod-exp cbrt-unprod
4×cbrt-undiv div-exp associate-*l/
3×associate-*r* sum-log
2×associate-/l/ distribute-lft-out-- difference-of-squares
1×+-commutative distribute-rgt-in sub-neg associate-+r+ frac-2neg distribute-lft-in times-frac diff-log pow-prod-down clear-num associate-/r* *-commutative div-inv associate-/l* unswap-sqr
Counts
4 → 88
Calls
4 calls:
17.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (pow (* b eps) 2)) (* eps b)))))
16.0ms
(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (pow (* b eps) 2)) (* eps b))))
7.0ms
(+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (pow (* b eps) 2)) (* eps b)))
4.0ms
(- (exp (* (+ a b) eps)) 1.0)

series1.7s

Counts
4 → 12
Calls
4 calls:
1.3s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (pow (* b eps) 2)) (* eps b)))))
215.0ms
(* (- (exp (* a eps)) 1.0) (+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (pow (* b eps) 2)) (* eps b))))
97.0ms
(+ (* 1/6 (pow (* b eps) 3)) (+ (* 1/2 (pow (* b eps) 2)) (* eps b)))
46.0ms
(- (exp (* (+ a b) eps)) 1.0)

simplify130.0ms

Algorithm
egg-herbie
Counts
100 → 100
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
07652060
144961765
250031765

prune417.0ms

Filtered
100 candidates to 73 candidates (73.0%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New973100
Fresh9110
Picked101
Done000
Total1074111

Merged error: 0.0b

Counts
111 → 4

regimes79.0ms

Accuracy

0% (3.3b remaining)

Error of 3.4b against oracle of 0.1b and baseline of 3.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
093
193

end0.0ms

sample5.6s

Algorithm
intervals
Results
2.7s2626×body2560valid
1.8s3426×body1280valid
325.0ms1049×body640valid
205.0ms10004×pre80true
127.0ms2001×body80overflowed
75.0ms331×body320valid
29.0ms451×body80valid
17.0ms120×body160valid

Profiling

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