Details

Time bar (total: 2.2s)

sample20.0ms

Algorithm
intervals
Results
6.0ms209×body80valid
2.0ms20×body640valid
1.0ms13×body320valid
1.0ms7×body1280valid
0.0ms7×body160valid

simplify135.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (133.0ms)

IterNodesCost
0508011

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: 11.3b

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)))
2.9b
(+ 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))))

series24.0ms

Counts
3 → 9
Calls
3 calls:
8.0ms
(/ (- 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))))

simplify54.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
053321270

prune178.0ms

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

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1029111
Fresh101
Picked101
Done000
Total1049113

Merged error: 5.8b

Counts
113 → 9

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))
7.2b
(+ 1.0 (* y (* (/ 1 (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (cbrt (+ 1.0 y))))))

rewrite12.0ms

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))))))

series30.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(cbrt (+ 1.0 y))
6.0ms
(cbrt (+ 1.0 y))
6.0ms
(cbrt (+ 1.0 y))
12.0ms
(+ 1.0 (* y (* (/ 1 (* (cbrt (+ 1.0 y)) (cbrt (+ 1.0 y)))) (/ (- x 1.0) (cbrt (+ 1.0 y))))))

simplify50.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 0 (43.0ms)

IterNodesCost
04919683
14919683

prune135.0ms

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

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New65065
Fresh088
Picked011
Done000
Total65974

Merged error: 5.8b

Counts
74 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y)
0.6b
(cbrt y)
0.6b
(cbrt y)
7.0b
(+ 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))))

series81.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(cbrt y)
21.0ms
(cbrt y)
22.0ms
(cbrt y)
15.0ms
(+ 1.0 (* (* (cbrt y) (cbrt y)) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

simplify50.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 0 (45.0ms)

IterNodesCost
04967371
14967371

prune75.0ms

Filtered
40 candidates to 56 candidates (-40.0%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New56056
Fresh077
Picked011
Done011
Total56965

Merged error: 5.8b

Counts
65 → 9

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b
(cbrt (/ (- x 1.0) (+ 1.0 y)))
0.5b
(cbrt (/ (- x 1.0) (+ 1.0 y)))
0.5b
(cbrt (/ (- x 1.0) (+ 1.0 y)))
7.0b
(+ 1.0 (* (* y (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y))))) (cbrt (/ (- x 1.0) (+ 1.0 y)))))

rewrite26.0ms

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)))))

series79.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
33.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
14.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
17.0ms
(+ 1.0 (* (* y (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y))))) (cbrt (/ (- x 1.0) (+ 1.0 y)))))

simplify41.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (27.0ms)

IterNodesCost
057702034

prune300.0ms

Filtered
94 candidates to 128 candidates (-36.2%)
Pruning

10 alts after pruning (7 fresh and 3 done)

PrunedKeptTotal
New1271128
Fresh066
Picked011
Done022
Total12710137

Merged error: 5.8b

Counts
137 → 10

regimes139.0ms

Accuracy

96.8% (0.2b remaining)

Error of 7.4b against oracle of 7.2b and baseline of 14.9b

bsearch42.0ms

Steps
ItersRangePoint
11
1253.8160530937032
3.5748133113367078e+34
10457115104856364.0
10
-57441177770159.1
-592.0680558286634
-56814521536770.695

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
03444
13444

end0.0ms

sample607.0ms

Algorithm
intervals
Results
186.0ms6088×body80valid
89.0ms732×body640valid
62.0ms390×body1280valid
46.0ms494×body320valid
17.0ms296×body160valid

Profiling

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