Details

Time bar (total: 2.2s)

analyze77.0ms

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
12.5%87.4%0.1%4
25%74.9%0.1%5
31.2%68.7%0.1%6
67.1%32.8%0.1%7
71%28.9%0.1%8
82.3%17.6%0.1%9
84.9%15%0.1%10
90.8%9.1%0.1%11
92.2%7.7%0.1%12
95.3%4.6%0.1%13
96%3.9%0.1%14

sample21.0ms

Algorithm
intervals
Results
5.0ms184×body80valid
4.0ms34×body640valid
3.0ms19×body1280valid
1.0ms14×body320valid
0.0ms5×body160valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (3.0ms)

IterNodesCost
06811
16811

prune8.0ms

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: 16.6b

Counts
2 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (- x 1.0) (+ 1.0 y))
0.1b
(* y (/ (- x 1.0) (+ 1.0 y)))
5.0b
(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
65×*-un-lft-identity
48×add-sqr-sqrt
41×times-frac
26×associate-*r*
25×add-cube-cbrt
11×distribute-lft-out
10×add-exp-log add-cbrt-cube
9×distribute-lft-out-- difference-of-squares
5×pow1 associate-/l* add-log-exp
4×associate-/r* associate-/r/
3×flip3-+ associate-*l* flip-+
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
1×+-commutative flip3-- frac-2neg div-sub associate-*r/ pow-prod-down clear-num sum-log *-commutative flip--
Counts
3 → 102
Calls
3 calls:
7.0ms
(/ (- x 1.0) (+ 1.0 y))
12.0ms
(* y (/ (- x 1.0) (+ 1.0 y)))
3.0ms
(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

series20.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(/ (- x 1.0) (+ 1.0 y))
5.0ms
(* y (/ (- x 1.0) (+ 1.0 y)))
10.0ms
(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

simplify50.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 0 (41.0ms)

IterNodesCost
053191270

prune184.0ms

Filtered
76 candidates to 111 candidates (-46.1%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New9912111
Fresh101
Picked101
Done000
Total10112113

Merged error: 9.3b

Counts
113 → 12

localize10.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ 1.0 y))
0.3b
(cbrt (+ 1.0 y))
0.3b
(* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))
10.8b
(+ 1.0 (* (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (cbrt (+ 1.0 y)))))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
32×cbrt-prod *-un-lft-identity
22×add-sqr-sqrt
16×cbrt-div
14×add-cube-cbrt
11×pow1
9×flip3-+ swap-sqr flip-+
8×pow1/3 distribute-lft-out
7×associate-*r* associate-*l*
6×add-exp-log add-log-exp
4×frac-times add-cbrt-cube unswap-sqr
2×associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×+-commutative pow2 pow-plus prod-exp sum-log *-commutative cbrt-unprod
Counts
4 → 92
Calls
4 calls:
3.0ms
(cbrt (+ 1.0 y))
3.0ms
(cbrt (+ 1.0 y))
9.0ms
(* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))
3.0ms
(+ 1.0 (* (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (cbrt (+ 1.0 y)))))

series28.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(cbrt (+ 1.0 y))
6.0ms
(cbrt (+ 1.0 y))
7.0ms
(* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))
10.0ms
(+ 1.0 (* (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (cbrt (+ 1.0 y)))))

simplify58.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
050061145

prune226.0ms

Filtered
74 candidates to 104 candidates (-40.5%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1004104
Fresh3811
Picked011
Done000
Total10313116

Merged error: 9.3b

Counts
116 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y)
0.6b
(cbrt y)
0.6b
(cbrt y)
12.0b
(+ 1.0 (* (* (cbrt y) (cbrt y)) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

rewrite7.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
6×add-log-exp
4×pow1 add-exp-log add-cbrt-cube
3×pow1/3
1×+-commutative flip3-+ sum-log flip-+
Counts
4 → 44
Calls
4 calls:
1.0ms
(cbrt y)
1.0ms
(cbrt y)
1.0ms
(cbrt y)
3.0ms
(+ 1.0 (* (* (cbrt y) (cbrt y)) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

series80.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(cbrt y)
23.0ms
(cbrt y)
21.0ms
(cbrt y)
15.0ms
(+ 1.0 (* (* (cbrt y) (cbrt y)) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

simplify35.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 0 (31.0ms)

IterNodesCost
05051365

prune88.0ms

Filtered
39 candidates to 56 candidates (-43.6%)
Pruning

13 alts after pruning (11 fresh and 2 done)

PrunedKeptTotal
New56056
Fresh01111
Picked011
Done011
Total561369

Merged error: 9.3b

Counts
69 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ 1.0 y))
0.3b
(* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))
0.3b
(pow (cbrt (cbrt (+ 1.0 y))) 2)
13.0b
(+ 1.0 (* (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (* (pow (cbrt (cbrt (+ 1.0 y))) 2) (cbrt (cbrt (+ 1.0 y)))))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
35×*-un-lft-identity
25×add-sqr-sqrt
17×add-cube-cbrt
14×cbrt-div
12×pow1
10×unpow-prod-down
9×swap-sqr
8×flip3-+ pow1/3 flip-+ distribute-lft-out
7×add-exp-log associate-*r* associate-*l*
6×add-log-exp
4×frac-times add-cbrt-cube unswap-sqr
3×pow-unpow
2×pow-pow associate-*r/ pow-prod-down associate-*l/ pow-sqr pow-prod-up
1×+-commutative pow2 pow-to-exp pow-plus pow-exp prod-exp sum-log *-commutative cbrt-unprod unpow2 sqr-pow
Counts
4 → 104
Calls
4 calls:
3.0ms
(cbrt (+ 1.0 y))
9.0ms
(* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))
5.0ms
(pow (cbrt (cbrt (+ 1.0 y))) 2)
3.0ms
(+ 1.0 (* (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (* (pow (cbrt (cbrt (+ 1.0 y))) 2) (cbrt (cbrt (+ 1.0 y)))))))

series32.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(cbrt (+ 1.0 y))
7.0ms
(* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))
9.0ms
(pow (cbrt (cbrt (+ 1.0 y))) 2)
10.0ms
(+ 1.0 (* (/ y (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (* (pow (cbrt (cbrt (+ 1.0 y))) 2) (cbrt (cbrt (+ 1.0 y)))))))

simplify51.0ms

Algorithm
egg-herbie
Counts
116 → 116
Iterations

Useful iterations: 0 (39.0ms)

IterNodesCost
049871459
149871459

prune279.0ms

Filtered
75 candidates to 116 candidates (-54.7%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1151116
Fresh1910
Picked011
Done112
Total11712129

Merged error: 9.3b

Counts
129 → 12

regimes181.0ms

Accuracy

97.2% (0.2b remaining)

Error of 7.7b against oracle of 7.5b and baseline of 15.4b

bsearch85.0ms

Steps
ItersRangePoint
10
1.175706627256631e+38
2.1619678863399553e+48
1.1898700674408897e+38
7
-9.113258409761583e+18
-1.5226453746207744e+17
-1.555969621816956e+17

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03947
13947

end0.0ms

analyze76.0ms

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
12.5%87.4%0.1%4
25%74.9%0.1%5
31.2%68.7%0.1%6
67.1%32.8%0.1%7
71%28.9%0.1%8
82.3%17.6%0.1%9
84.9%15%0.1%10
90.8%9.1%0.1%11
92.2%7.7%0.1%12
95.3%4.6%0.1%13
96%3.9%0.1%14

sample525.0ms

Algorithm
intervals
Results
188.0ms6046×body80valid
89.0ms785×body640valid
61.0ms392×body1280valid
44.0ms512×body320valid
15.0ms265×body160valid

Profiling

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