Details

Time bar (total: 2.8s)

analyze75.0ms

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

sample19.0ms

Algorithm
intervals
Results
6.0ms192×body80valid
3.0ms31×body640valid
2.0ms13×body1280valid
1.0ms11×body320valid
1.0ms9×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: 15.2b

Counts
2 → 2

localize7.0ms

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)))
4.0b
(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

rewrite28.0ms

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))
14.0ms
(* 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))))

simplify58.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
053191270

prune194.0ms

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

13 alts after pruning (13 fresh and 0 done)

PrunedKeptTotal
New9813111
Fresh101
Picked101
Done000
Total10013113

Merged error: 8.8b

Counts
113 → 13

localize12.0ms

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))
11.7b
(+ 1.0 (* y (* (/ 1 (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (cbrt (+ 1.0 y))))))

rewrite13.0ms

Algorithm
rewrite-expression-head
Rules
13×*-un-lft-identity
12×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt
6×cbrt-div add-log-exp
4×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
3×pow1/3 distribute-lft-out
1×+-commutative sum-log
Counts
4 → 53
Calls
4 calls:
3.0ms
(cbrt (+ 1.0 y))
3.0ms
(cbrt (+ 1.0 y))
3.0ms
(cbrt (+ 1.0 y))
3.0ms
(+ 1.0 (* y (* (/ 1 (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (cbrt (+ 1.0 y))))))

series29.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(cbrt (+ 1.0 y))
6.0ms
(cbrt (+ 1.0 y))
6.0ms
(cbrt (+ 1.0 y))
10.0ms
(+ 1.0 (* y (* (/ 1 (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (cbrt (+ 1.0 y))))))

simplify32.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 0 (25.0ms)

IterNodesCost
05056686

prune147.0ms

Filtered
49 candidates to 65 candidates (-32.7%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New65065
Fresh01212
Picked011
Done000
Total651378

Merged error: 8.8b

Counts
78 → 13

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (/ (- x 1.0) (+ 1.0 y)))
0.4b
(cbrt (/ (- x 1.0) (+ 1.0 y)))
0.4b
(cbrt (/ (- x 1.0) (+ 1.0 y)))
11.3b
(+ 1.0 (* (* y (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y))))) (cbrt (/ (- x 1.0) (+ 1.0 y)))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
88×*-un-lft-identity
78×cbrt-prod
60×times-frac
58×add-sqr-sqrt
34×add-cube-cbrt
15×distribute-lft-out
12×distribute-lft-out-- difference-of-squares
6×associate-/r/ add-log-exp
4×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
3×cbrt-div pow1/3 div-inv
1×+-commutative sum-log
Counts
4 → 116
Calls
4 calls:
6.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
6.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
6.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
3.0ms
(+ 1.0 (* (* y (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y))))) (cbrt (/ (- x 1.0) (+ 1.0 y)))))

series59.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
15.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
15.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
15.0ms
(+ 1.0 (* (* y (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y))))) (cbrt (/ (- x 1.0) (+ 1.0 y)))))

simplify65.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
049472025
149472025

prune302.0ms

Filtered
89 candidates to 128 candidates (-43.8%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1262128
Fresh01111
Picked011
Done011
Total12615141

Merged error: 8.8b

Counts
141 → 15

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(cbrt (/ (- x 1.0) (cbrt (+ 1.0 y))))
0.4b
(cbrt (/ (- x 1.0) (+ 1.0 y)))
0.4b
(cbrt (/ (- x 1.0) (+ 1.0 y)))
11.0b
(+ 1.0 (* (* y (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y))))) (* (cbrt (/ 1 (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y))))) (cbrt (/ (- x 1.0) (cbrt (+ 1.0 y)))))))

rewrite29.0ms

Algorithm
rewrite-expression-head
Rules
113×cbrt-prod
102×*-un-lft-identity
75×times-frac
72×add-sqr-sqrt
42×add-cube-cbrt
15×distribute-lft-out distribute-lft-out-- difference-of-squares
6×associate-/r/ add-log-exp
5×cbrt-div
4×pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
3×pow1/3 div-inv
1×+-commutative sum-log
Counts
4 → 131
Calls
4 calls:
7.0ms
(cbrt (/ (- x 1.0) (cbrt (+ 1.0 y))))
6.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
6.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
3.0ms
(+ 1.0 (* (* y (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y))))) (* (cbrt (/ 1 (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y))))) (cbrt (/ (- x 1.0) (cbrt (+ 1.0 y)))))))

series68.0ms

Counts
4 → 12
Calls
4 calls:
21.0ms
(cbrt (/ (- x 1.0) (cbrt (+ 1.0 y))))
14.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
14.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
18.0ms
(+ 1.0 (* (* y (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y))))) (* (cbrt (/ 1 (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y))))) (cbrt (/ (- x 1.0) (cbrt (+ 1.0 y)))))))

simplify96.0ms

Algorithm
egg-herbie
Counts
143 → 143
Iterations

Useful iterations: 0 (71.0ms)

IterNodesCost
049342867
149342867

prune530.0ms

Filtered
100 candidates to 143 candidates (-43.0%)
Pruning

16 alts after pruning (13 fresh and 3 done)

PrunedKeptTotal
New1403143
Fresh21012
Picked011
Done022
Total14216158

Merged error: 8.8b

Counts
158 → 16

regimes232.0ms

Accuracy

97.2% (0.2b remaining)

Error of 7.3b against oracle of 7.1b and baseline of 14.7b

bsearch76.0ms

Steps
ItersRangePoint
10
453366487548460.1
1.35119330956444e+26
5.5750201166678655e+20
8
-2.4163831104577378e+33
-7.73111052844845e+30
-8.804440934020806e+30

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03139
13139

end0.0ms

analyze80.0ms

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

sample519.0ms

Algorithm
intervals
Results
187.0ms6100×body80valid
82.0ms712×body640valid
50.0ms535×body320valid
49.0ms350×body1280valid
17.0ms303×body160valid

Profiling

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