Details

Time bar (total: 4.4s)

analyze264.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%87.4%12.6%6
20.3%59.3%20.4%7
21.1%51.5%27.4%8
35.5%30.4%34%9
35.7%26.1%38.1%10
42.8%15.4%41.8%11
42.9%13.2%44%12
46.4%7.8%45.8%13
46.4%6.6%47%14

sample81.0ms

Algorithm
intervals
Results
37.0ms64×body1280valid
16.0ms48×body640valid
10.0ms117×body80valid
5.0ms19×body320valid
1.0ms8×body160valid
1.0ms13×body80invalid
1.0ms1×body1280invalid
0.0ms1×body640invalid
0.0ms2×body80overflowed

simplify35.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (33.0ms)

IterNodesCost
0498027
1498027

prune13.0ms

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: 32.8b

Counts
2 → 2

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
78×exp-neg
76×frac-times
59×neg-sub0 exp-diff
38×associate-*r/ associate-*l/
30×flip3-+ flip-+
28×flip3-- flip--
19×un-div-inv
12×exp-prod
10×add-sqr-sqrt *-un-lft-identity add-log-exp
8×add-cube-cbrt
6×pow1 add-cbrt-cube
5×add-exp-log
4×associate-*l* rem-exp-log
3×associate-*r*
2×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in neg-log
1×sub-neg diff-log pow-prod-down prod-exp *-commutative cbrt-unprod distribute-lft-out unswap-sqr
Counts
4 → 154
Calls
4 calls:
12.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
3.0ms
(exp (neg (* (+ 1.0 eps) x)))
4.0ms
(exp (neg (* (- 1.0 eps) x)))
17.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series70.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
6.0ms
(exp (neg (* (+ 1.0 eps) x)))
6.0ms
(exp (neg (* (- 1.0 eps) x)))
48.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

simplify94.0ms

Algorithm
egg-herbie
Counts
166 → 166
Iterations

Useful iterations: 0 (62.0ms)

IterNodesCost
049726292
149726292

prune341.0ms

Filtered
92 candidates to 166 candidates (-80.4%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1633166
Fresh101
Picked101
Done000
Total1653168

Merged error: 0.2b

Counts
168 → 3

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b
(* (* x x) (- (* x 0.6666666666666667) 1.0))

rewrite9.0ms

Algorithm
rewrite-expression-head
Rules
6×pow1 add-exp-log add-cbrt-cube
3×add-sqr-sqrt associate-*r* pow-prod-down prod-exp cbrt-unprod
2×add-cube-cbrt sub-neg *-un-lft-identity associate-*r/
1×distribute-rgt-in flip3-- distribute-lft-in associate-*l* *-commutative flip-- add-log-exp unswap-sqr
Counts
1 → 23
Calls
1 calls:
8.0ms
(* (* x x) (- (* x 0.6666666666666667) 1.0))

series9.0ms

Counts
1 → 3
Calls
1 calls:
9.0ms
(* (* x x) (- (* x 0.6666666666666667) 1.0))

simplify32.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 0 (28.0ms)

IterNodesCost
05430272

prune37.0ms

Filtered
16 candidates to 26 candidates (-62.5%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New25126
Fresh022
Picked101
Done000
Total26329

Merged error: 0.2b

Counts
29 → 3

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (* x (- (* x (* x (* 0.6666666666666667 0.6666666666666667))) (* 1.0 1.0))))
0.1b
(* x (* x (* 0.6666666666666667 0.6666666666666667)))
0.2b
(* x (* 0.6666666666666667 0.6666666666666667))
1.2b
(/ (* x (* x (- (* x (* x (* 0.6666666666666667 0.6666666666666667))) (* 1.0 1.0)))) (+ (* x 0.6666666666666667) 1.0))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
32×add-exp-log add-cbrt-cube
23×pow1
15×prod-exp cbrt-unprod
12×pow-prod-down
10×add-sqr-sqrt
9×add-cube-cbrt *-un-lft-identity associate-*l*
8×associate-*r/
4×distribute-rgt-in sub-neg distribute-lft-in add-log-exp
3×cbrt-undiv times-frac div-exp associate-*r* associate-/r* *-commutative
2×flip3-- associate-/r/ flip-- associate-/l/
1×frac-2neg flip3-+ clear-num flip-+ div-inv associate-/l* unswap-sqr
Counts
4 → 91
Calls
4 calls:
11.0ms
(* x (* x (- (* x (* x (* 0.6666666666666667 0.6666666666666667))) (* 1.0 1.0))))
7.0ms
(* x (* x (* 0.6666666666666667 0.6666666666666667)))
6.0ms
(* x (* 0.6666666666666667 0.6666666666666667))
17.0ms
(/ (* x (* x (- (* x (* x (* 0.6666666666666667 0.6666666666666667))) (* 1.0 1.0)))) (+ (* x 0.6666666666666667) 1.0))

series26.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(* x (* x (- (* x (* x (* 0.6666666666666667 0.6666666666666667))) (* 1.0 1.0))))
3.0ms
(* x (* x (* 0.6666666666666667 0.6666666666666667)))
2.0ms
(* x (* 0.6666666666666667 0.6666666666666667))
12.0ms
(/ (* x (* x (- (* x (* x (* 0.6666666666666667 0.6666666666666667))) (* 1.0 1.0)))) (+ (* x 0.6666666666666667) 1.0))

simplify40.0ms

Algorithm
egg-herbie
Counts
103 → 103
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
055331091

prune117.0ms

Filtered
59 candidates to 103 candidates (-74.6%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1021103
Fresh022
Picked101
Done000
Total1033106

Merged error: 0.2b

Counts
106 → 3

localize18.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
1.2b
(/ (* x (* x (- (* x (* (* (cbrt x) (cbrt x)) (* 0.6666666666666667 (* 0.6666666666666667 (cbrt x))))) (* 1.0 1.0)))) (+ (* x 0.6666666666666667) 1.0))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
13×add-exp-log add-cbrt-cube
9×cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 associate-*r/ add-log-exp
3×cbrt-undiv times-frac pow1/3 div-exp prod-exp associate-/r* cbrt-unprod
2×associate-/r/ associate-/l/
1×flip3-- frac-2neg flip3-+ clear-num flip-- flip-+ div-inv associate-/l*
Counts
4 → 60
Calls
4 calls:
1.0ms
(cbrt x)
1.0ms
(cbrt x)
1.0ms
(cbrt x)
22.0ms
(/ (* x (* x (- (* x (* (* (cbrt x) (cbrt x)) (* 0.6666666666666667 (* 0.6666666666666667 (cbrt x))))) (* 1.0 1.0)))) (+ (* x 0.6666666666666667) 1.0))

series105.0ms

Counts
4 → 12
Calls
4 calls:
39.0ms
(cbrt x)
25.0ms
(cbrt x)
24.0ms
(cbrt x)
18.0ms
(/ (* x (* x (- (* x (* (* (cbrt x) (cbrt x)) (* 0.6666666666666667 (* 0.6666666666666667 (cbrt x))))) (* 1.0 1.0)))) (+ (* x 0.6666666666666667) 1.0))

simplify47.0ms

Algorithm
egg-herbie
Counts
72 → 72
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
04971818
14971818

prune90.0ms

Filtered
52 candidates to 72 candidates (-38.5%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New71172
Fresh022
Picked101
Done000
Total72375

Merged error: 0.2b

Counts
75 → 3

regimes121.0ms

Accuracy

96.8% (0.5b remaining)

Error of 1.0b against oracle of 0.5b and baseline of 16.8b

bsearch146.0ms

Steps
ItersRangePoint
9
5.621192387683475
1005278.0331657071
246.92990390970124

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07892
17892

end0.0ms

analyze241.0ms

Algorithm
search
Search
TrueOtherFalseIter
0%99.9%0.1%0
0%99.9%0.1%1
0%99.9%0.1%2
0%99.9%0.1%3
0%99.9%0.1%4
0%99.9%0.1%5
0%87.4%12.6%6
20.3%59.3%20.4%7
21.1%51.5%27.4%8
35.5%30.4%34%9
35.7%26.1%38.1%10
42.8%15.4%41.8%11
42.9%13.2%44%12
46.4%7.8%45.8%13
46.4%6.6%47%14

sample2.3s

Algorithm
intervals
Results
1.0s1737×body1280valid
482.0ms1264×body640valid
355.0ms4054×body80valid
172.0ms666×body320valid
47.0ms279×body160valid
22.0ms239×body80invalid
18.0ms193×body80overflowed
9.0ms21×body640invalid
6.0ms9×body1280invalid
2.0ms4×body160invalid
1.0ms5×body320invalid

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