Details

Time bar (total: 4.4s)

analyze235.0ms

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

sample73.0ms

Algorithm
intervals
Results
28.0ms50×body1280valid
13.0ms135×body80valid
13.0ms35×body640valid
5.0ms19×body320valid
3.0ms17×body160valid
2.0ms3×body1280invalid
1.0ms11×body80invalid
0.0ms1×body80overflowed

simplify33.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (32.0ms)

IterNodesCost
0498027
1498027

prune11.0ms

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: 27.7b

Counts
2 → 2

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
0.0b
(* (- 1.0 eps) x)
0.0b
(* (+ 1.0 eps) x)
3.1b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

rewrite51.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
76×exp-neg frac-times
57×neg-sub0 exp-diff
42×associate-*l/
38×associate-*r/
31×flip3-+ flip-+
29×flip3-- flip--
19×un-div-inv
18×add-sqr-sqrt
16×*-un-lft-identity
13×associate-*l*
10×pow1 add-cube-cbrt add-cbrt-cube
9×add-exp-log associate-*r*
6×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod unswap-sqr
2×distribute-lft-out
1×sub-neg diff-log distribute-lft-out-- difference-of-squares
Counts
4 → 163
Calls
4 calls:
11.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
6.0ms
(* (- 1.0 eps) x)
6.0ms
(* (+ 1.0 eps) x)
18.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (neg (* (+ 1.0 eps) x)))))

series66.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(* (+ 1.0 (/ 1.0 eps)) (exp (neg (* (- 1.0 eps) x))))
4.0ms
(* (- 1.0 eps) x)
4.0ms
(* (+ 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)))))

simplify113.0ms

Algorithm
egg-herbie
Counts
175 → 175
Iterations

Useful iterations: 0 (83.0ms)

IterNodesCost
049696327
149696327

prune346.0ms

Filtered
92 candidates to 175 candidates (-90.2%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New1723175
Fresh101
Picked101
Done000
Total1743177

Merged error: 0.5b

Counts
177 → 3

localize8.0ms

Local error

Found 1 expressions with local error:

0.1b
(* (* 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))

series7.0ms

Counts
1 → 3
Calls
1 calls:
7.0ms
(* (* x x) (- (* x 0.6666666666666667) 1.0))

simplify33.0ms

Algorithm
egg-herbie
Counts
26 → 26
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
05430272

prune41.0ms

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: 0.5b

Counts
29 → 3

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3))
0.1b
(pow (- (* x 0.6666666666666667) 1.0) 3)
16.8b
(cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3)))

rewrite23.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
16×add-exp-log unpow-prod-down
12×associate-*r* unswap-sqr
11×add-cube-cbrt *-un-lft-identity
10×sqr-pow
9×cube-prod prod-exp
7×pow-to-exp associate-*l* pow-exp
6×cube-div add-cbrt-cube
4×pow1 associate-*r/
3×pow-unpow flip3-- flip-- add-log-exp
2×cube-mult cbrt-div unpow3
1×cbrt-prod pow-pow pow1/3 *-commutative cbrt-unprod rem-cube-cbrt
Counts
3 → 87
Calls
3 calls:
10.0ms
(* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3))
5.0ms
(pow (- (* x 0.6666666666666667) 1.0) 3)
6.0ms
(cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3)))

series20.0ms

Counts
3 → 9
Calls
3 calls:
7.0ms
(* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3))
3.0ms
(pow (- (* x 0.6666666666666667) 1.0) 3)
10.0ms
(cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3)))

simplify39.0ms

Algorithm
egg-herbie
Counts
96 → 96
Iterations

Useful iterations: 0 (29.0ms)

IterNodesCost
053121231

prune159.0ms

Filtered
57 candidates to 96 candidates (-68.4%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New94296
Fresh022
Picked101
Done000
Total95499

Merged error: 0.5b

Counts
99 → 4

localize18.0ms

Local error

Found 4 expressions with local error:

16.8b
(cbrt (* (* (cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3))) (cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3)))) (cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3)))))
16.8b
(cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3)))
16.8b
(cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3)))
16.8b
(cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
86×cbrt-div
68×associate-*r/
60×cube-div
30×flip3-- flip--
28×frac-times
14×associate-*l/
4×pow1 add-exp-log cbrt-prod add-sqr-sqrt add-cube-cbrt *-un-lft-identity pow1/3 add-cbrt-cube add-log-exp
1×pow3 rem-cbrt-cube
Counts
4 → 69
Calls
4 calls:
13.0ms
(cbrt (* (* (cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3))) (cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3)))) (cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3)))))
7.0ms
(cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3)))
7.0ms
(cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3)))
7.0ms
(cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3)))

series47.0ms

Counts
4 → 12
Calls
4 calls:
13.0ms
(cbrt (* (* (cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3))) (cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3)))) (cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3)))))
9.0ms
(cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3)))
10.0ms
(cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3)))
14.0ms
(cbrt (* (pow x 6) (pow (- (* x 0.6666666666666667) 1.0) 3)))

simplify65.0ms

Algorithm
egg-herbie
Counts
81 → 81
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049762459
149762459

prune258.0ms

Filtered
56 candidates to 81 candidates (-44.6%)
Pruning

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New80181
Fresh033
Picked101
Done000
Total81485

Merged error: 0.5b

Counts
85 → 4

regimes113.0ms

Accuracy

96.9% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 16.7b

bsearch128.0ms

Steps
ItersRangePoint
7
0.06474422705516336
8.038335740008245
7.910279052275709

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
076123
176123

end0.0ms

analyze236.0ms

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

sample2.1s

Algorithm
intervals
Results
941.0ms1688×body1280valid
442.0ms1259×body640valid
331.0ms4064×body80valid
167.0ms674×body320valid
50.0ms315×body160valid
19.0ms222×body80invalid
14.0ms174×body80overflowed
8.0ms15×body1280invalid
4.0ms9×body640invalid
1.0ms5×body320invalid
0.0ms1×body160invalid

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