Details

Time bar (total: 2.8s)

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
6.0ms188×body80valid
3.0ms24×body640valid
2.0ms12×body1280valid
2.0ms19×body320valid
1.0ms13×body160valid

simplify255.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (253.0ms)

IterNodesCost
0520611

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: 15.7b

Counts
2 → 2

localize10.0ms

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)))
6.4b
(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

rewrite26.0ms

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))
11.0ms
(* y (/ (- x 1.0) (+ 1.0 y)))
3.0ms
(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

series21.0ms

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 (48.0ms)

IterNodesCost
061631269

prune186.0ms

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

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New10011111
Fresh101
Picked011
Done000
Total10112113

Merged error: 7.6b

Counts
113 → 12

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))
12.7b
(+ 1.0 (* y (* (/ 1 (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (cbrt (+ 1.0 y))))))

rewrite14.0ms

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))
5.0ms
(+ 1.0 (* y (* (/ 1 (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (cbrt (+ 1.0 y))))))

series30.0ms

Counts
4 → 12
Calls
4 calls:
8.0ms
(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))))))

simplify81.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 0 (74.0ms)

IterNodesCost
04908683
14908683

prune140.0ms

Filtered
48 candidates to 65 candidates (-35.4%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New63265
Fresh4610
Picked011
Done011
Total671077

Merged error: 7.6b

Counts
77 → 10

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))) (cbrt (/ (- x 1.0) (+ 1.0 y))))
12.2b
(+ 1.0 (* (* y (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y))))) (cbrt (/ (- x 1.0) (+ 1.0 y)))))

rewrite61.0ms

Algorithm
rewrite-expression-head
Rules
278×*-un-lft-identity
212×cbrt-prod
170×times-frac
156×add-sqr-sqrt
76×add-cube-cbrt
51×swap-sqr
48×distribute-lft-out
40×distribute-lft-out--
29×associate-*r* associate-*l*
28×difference-of-squares
12×associate-/r/
11×pow1
9×unswap-sqr
8×pow1/3
7×flip3-+ flip-+
6×add-exp-log cbrt-div div-inv add-log-exp
4×add-cbrt-cube
2×pow-prod-down pow-sqr pow-prod-up
1×+-commutative pow2 frac-times pow-plus associate-*r/ associate-*l/ prod-exp sum-log *-commutative cbrt-unprod
Counts
4 → 220
Calls
4 calls:
7.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
6.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
30.0ms
(* (cbrt (/ (- x 1.0) (+ 1.0 y))) (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)))))

series70.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
14.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
26.0ms
(* (cbrt (/ (- x 1.0) (+ 1.0 y))) (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)))))

simplify66.0ms

Algorithm
egg-herbie
Counts
232 → 232
Iterations

Useful iterations: 0 (40.0ms)

IterNodesCost
057294530

prune514.0ms

Filtered
143 candidates to 232 candidates (-62.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New2293232
Fresh167
Picked101
Done112
Total23210242

Merged error: 7.6b

Counts
242 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ 1.0 y))
0.4b
(cbrt (/ (- x 1.0) (+ 1.0 y)))
0.4b
(cbrt (/ (- x 1.0) (+ 1.0 y)))
11.7b
(+ 1.0 (* (* y (/ (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (- x 1.0))) (cbrt (+ 1.0 y)))) (cbrt (/ (- x 1.0) (+ 1.0 y)))))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
63×*-un-lft-identity
56×cbrt-prod
41×add-sqr-sqrt
40×times-frac
25×add-cube-cbrt
11×distribute-lft-out
8×distribute-lft-out-- difference-of-squares
6×add-log-exp
4×pow1 add-exp-log cbrt-div flip3-+ associate-/r/ add-cbrt-cube flip-+
3×pow1/3
2×div-inv
1×+-commutative sum-log
Counts
4 → 95
Calls
4 calls:
3.0ms
(cbrt (+ 1.0 y))
6.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
6.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
4.0ms
(+ 1.0 (* (* y (/ (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (- x 1.0))) (cbrt (+ 1.0 y)))) (cbrt (/ (- x 1.0) (+ 1.0 y)))))

series49.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(cbrt (+ 1.0 y))
14.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
14.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
15.0ms
(+ 1.0 (* (* y (/ (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (- x 1.0))) (cbrt (+ 1.0 y)))) (cbrt (/ (- x 1.0) (+ 1.0 y)))))

simplify62.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
049331850
149331850

prune263.0ms

Filtered
81 candidates to 107 candidates (-32.1%)
Pruning

11 alts after pruning (9 fresh and 2 done)

PrunedKeptTotal
New1052107
Fresh178
Picked011
Done011
Total10611117

Merged error: 7.6b

Counts
117 → 11

regimes177.0ms

Accuracy

95.3% (0.4b remaining)

Error of 8.0b against oracle of 7.6b and baseline of 15.3b

bsearch34.0ms

Steps
ItersRangePoint
9
4.8525951731860633e+33
6.095386722550116e+41
4.920744420668106e+33
9
-12414662.649268348
-0.014752780820992958
-12172248.367177077

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
07053
17053

end0.0ms

sample537.0ms

Algorithm
intervals
Results
188.0ms6025×body80valid
94.0ms790×body640valid
52.0ms373×body1280valid
46.0ms512×body320valid
18.0ms300×body160valid

Profiling

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