Details

Time bar (total: 5.5s)

sample92.0ms

Algorithm
intervals
Results
26.0ms341×body80valid
26.0ms53×body1280valid
14.0ms45×body640valid
5.0ms75×body80overflowed
2.0ms11×body320valid
1.0ms8×body160valid

simplify39.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 4 (37.0ms)

IterNodesCost
04616
112216
234716
3129516
4500115

prune6.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New101
Fresh011
Picked000
Done000
Total112

Merged error: 27.2b

Counts
2 → 1

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 eps) x)
0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
1.2b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite63.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
80×exp-neg frac-times
60×neg-sub0 exp-diff
42×associate-*l/
40×associate-*r/
31×flip3-- flip3-+ flip-- flip-+
21×add-sqr-sqrt
20×un-div-inv
16×*-un-lft-identity
14×associate-*l*
10×pow1 add-cube-cbrt add-cbrt-cube
9×associate-*r*
8×add-exp-log
6×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×distribute-lft-out difference-of-squares
1×sub-neg times-frac diff-log distribute-lft-out--
Counts
4 → 172
Calls
4 calls:
6.0ms
(* (+ 1.0 eps) x)
12.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
14.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
21.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series310.0ms

Counts
4 → 12
Calls
4 calls:
28.0ms
(* (+ 1.0 eps) x)
45.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x))))
50.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
188.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify151.0ms

Algorithm
egg-herbie
Counts
184 → 184
Iterations

Useful iterations: 1 (25.0ms)

IterNodesCost
012574061
147723783
250013783

prune401.0ms

Filtered
184 candidates to 94 candidates (51.1%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New1822184
Fresh000
Picked101
Done000
Total1832185

Merged error: 0.2b

Counts
185 → 2

localize9.0ms

Local error

Found 2 expressions with local error:

0.0b
(* 0.6666666666666667 (pow x 3))
7.2b
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
12×associate-*r*
7×add-exp-log add-log-exp
6×add-cube-cbrt *-un-lft-identity
4×unpow-prod-down cube-prod add-cbrt-cube unswap-sqr
3×associate-*l* prod-exp
2×pow1 diff-log sqr-pow
1×cube-mult pow-to-exp sub-neg flip3-- unpow3 pow-exp associate--l+ sum-log *-commutative flip-- cbrt-unprod
Counts
2 → 45
Calls
2 calls:
6.0ms
(* 0.6666666666666667 (pow x 3))
7.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

series75.0ms

Counts
2 → 6
Calls
2 calls:
37.0ms
(* 0.6666666666666667 (pow x 3))
38.0ms
(- (+ (* 0.6666666666666667 (pow x 3)) 2.0) (* 1.0 (pow x 2)))

simplify34.0ms

Algorithm
egg-herbie
Counts
51 → 51
Iterations

Useful iterations: 2 (29.0ms)

IterNodesCost
0207270
1894242
25002238

prune88.0ms

Filtered
51 candidates to 31 candidates (60.8%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New49251
Fresh011
Picked011
Done000
Total49453

Merged error: 0.2b

Counts
53 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 0.6666666666666667 (pow x 3))
0.0b
(* 0.6666666666666667 (pow x 3))
10.2b
(+ (* (- (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)))
11.6b
(/ (+ (* (- (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0))) (+ (* (pow x 2) (+ (* 0.6666666666666667 x) 1.0)) 2.0))

rewrite37.0ms

Algorithm
rewrite-expression-head
Rules
34×add-sqr-sqrt
24×associate-*r*
20×add-cube-cbrt *-un-lft-identity
16×add-exp-log
10×add-cbrt-cube
9×times-frac
8×unpow-prod-down cube-prod unswap-sqr
6×associate-*l* prod-exp add-log-exp
4×pow1 sqr-pow
3×flip3-+ associate-/r* flip-+ associate-/l*
2×cube-mult pow-to-exp associate-+r+ unpow3 pow-exp associate-/r/ *-commutative cbrt-unprod associate-/l/
1×cbrt-undiv +-commutative distribute-rgt-in frac-2neg distribute-lft-in div-exp clear-num sum-log div-inv
Counts
4 → 106
Calls
4 calls:
6.0ms
(* 0.6666666666666667 (pow x 3))
6.0ms
(* 0.6666666666666667 (pow x 3))
5.0ms
(+ (* (- (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)))
16.0ms
(/ (+ (* (- (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0))) (+ (* (pow x 2) (+ (* 0.6666666666666667 x) 1.0)) 2.0))

series231.0ms

Counts
4 → 12
Calls
4 calls:
37.0ms
(* 0.6666666666666667 (pow x 3))
35.0ms
(* 0.6666666666666667 (pow x 3))
50.0ms
(+ (* (- (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0)))
110.0ms
(/ (+ (* (- (* 1.0 1.0)) (pow x 4)) (* (+ (* 0.6666666666666667 (pow x 3)) 2.0) (+ (* 0.6666666666666667 (pow x 3)) 2.0))) (+ (* (pow x 2) (+ (* 0.6666666666666667 x) 1.0)) 2.0))

simplify68.0ms

Algorithm
egg-herbie
Counts
118 → 118
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
04121392
119941252
250011242

prune339.0ms

Filtered
118 candidates to 81 candidates (68.6%)
Pruning

3 alts after pruning (2 fresh and 1 done)

PrunedKeptTotal
New1171118
Fresh112
Picked101
Done011
Total1193122

Merged error: 0.2b

Counts
122 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (pow x 2) (+ (* 0.6666666666666667 x) 1.0))
0.1b
(* 2.666666666666667 (pow x 3))
11.3b
(- (+ (* 2.666666666666667 (pow x 3)) 4.0) (* 1.0 (pow x 4)))
12.8b
(/ (- (+ (* 2.666666666666667 (pow x 3)) 4.0) (* 1.0 (pow x 4))) (+ (* (pow x 2) (+ (* 0.6666666666666667 x) 1.0)) 2.0))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
32×add-sqr-sqrt
19×add-cube-cbrt *-un-lft-identity
16×add-exp-log
15×associate-*r*
11×associate-*l*
10×add-cbrt-cube
9×times-frac add-log-exp
8×unpow-prod-down unswap-sqr
6×prod-exp
4×pow1 cube-prod sqr-pow
3×associate-/r* associate-/l*
2×pow-to-exp flip3-- flip3-+ diff-log associate-*r/ pow-exp associate-/r/ *-commutative flip-- cbrt-unprod flip-+ associate-/l/ unpow2
1×cbrt-undiv distribute-rgt-in cube-mult sub-neg frac-2neg distribute-lft-in unpow3 div-sub div-exp associate--l+ clear-num sum-log div-inv
Counts
4 → 108
Calls
4 calls:
8.0ms
(* (pow x 2) (+ (* 0.6666666666666667 x) 1.0))
6.0ms
(* 2.666666666666667 (pow x 3))
7.0ms
(- (+ (* 2.666666666666667 (pow x 3)) 4.0) (* 1.0 (pow x 4)))
18.0ms
(/ (- (+ (* 2.666666666666667 (pow x 3)) 4.0) (* 1.0 (pow x 4))) (+ (* (pow x 2) (+ (* 0.6666666666666667 x) 1.0)) 2.0))

series233.0ms

Counts
4 → 12
Calls
4 calls:
66.0ms
(* (pow x 2) (+ (* 0.6666666666666667 x) 1.0))
38.0ms
(* 2.666666666666667 (pow x 3))
51.0ms
(- (+ (* 2.666666666666667 (pow x 3)) 4.0) (* 1.0 (pow x 4)))
78.0ms
(/ (- (+ (* 2.666666666666667 (pow x 3)) 4.0) (* 1.0 (pow x 4))) (+ (* (pow x 2) (+ (* 0.6666666666666667 x) 1.0)) 2.0))

simplify83.0ms

Algorithm
egg-herbie
Counts
120 → 120
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
05661098
126151007
250031000

prune287.0ms

Filtered
120 candidates to 80 candidates (66.7%)
Pruning

4 alts after pruning (3 fresh and 1 done)

PrunedKeptTotal
New1182120
Fresh011
Picked101
Done011
Total1194123

Merged error: 0.2b

Counts
123 → 4

regimes73.0ms

Accuracy

96.7% (0.5b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 16.5b

bsearch144.0ms

Steps
ItersRangePoint
9
0.1542532533028917
36059.131207501
398.73590062221984

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05025
15825
25825

end0.0ms

sample2.6s

Algorithm
intervals
Results
879.0ms1729×body1280valid
710.0ms10160×body80valid
395.0ms1288×body640valid
135.0ms1986×body80overflowed
129.0ms618×body320valid
46.0ms336×body160valid

Profiling

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