Details

Time bar (total: 2.5s)

sample21.0ms

Algorithm
intervals
Results
6.0ms201×body80valid
2.0ms17×body640valid
2.0ms12×body1280valid
1.0ms15×body320valid
1.0ms11×body160valid

simplify237.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (235.0ms)

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: 12.7b

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)))
3.9b
(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

rewrite29.0ms

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
distribute-lft-out-- difference-of-squares
pow1 associate-/l* add-log-exp
associate-/r* associate-/r/
flip3-+ associate-*l* flip-+
cbrt-undiv div-exp prod-exp cbrt-unprod div-inv associate-/l/ unswap-sqr
+-commutative flip3-- frac-2neg div-sub associate-*r/ pow-prod-down clear-num sum-log *-commutative flip--
Counts
3 → 102
Calls
3 calls:
8.0ms
(/ (- x 1.0) (+ 1.0 y))
13.0ms
(* y (/ (- x 1.0) (+ 1.0 y)))
3.0ms
(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

series25.0ms

Counts
3 → 9
Calls
3 calls:
8.0ms
(/ (- x 1.0) (+ 1.0 y))
6.0ms
(* y (/ (- x 1.0) (+ 1.0 y)))
11.0ms
(+ 1.0 (* y (/ (- x 1.0) (+ 1.0 y))))

simplify60.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 0 (51.0ms)

IterNodesCost
061631269

prune177.0ms

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

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1029111
Fresh011
Picked101
Done000
Total10310113

Merged error: 5.4b

Counts
113 → 10

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y)
0.6b
(cbrt y)
0.6b
(cbrt y)
9.7b
(+ 1.0 (* (* (cbrt y) (cbrt y)) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
cbrt-prod
add-sqr-sqrt add-cube-cbrt *-un-lft-identity
add-log-exp
pow1 add-exp-log add-cbrt-cube
pow1/3
+-commutative flip3-+ sum-log flip-+
Counts
4 → 44
Calls
4 calls:
1.0ms
(cbrt y)
1.0ms
(cbrt y)
1.0ms
(cbrt y)
4.0ms
(+ 1.0 (* (* (cbrt y) (cbrt y)) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

series84.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(cbrt y)
22.0ms
(cbrt y)
24.0ms
(cbrt y)
15.0ms
(+ 1.0 (* (* (cbrt y) (cbrt y)) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

simplify54.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 0 (49.0ms)

IterNodesCost
04943365
14943365

prune87.0ms

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

11 alts after pruning (10 fresh and 1 done)

PrunedKeptTotal
New54256
Fresh189
Picked011
Done000
Total551166

Merged error: 5.4b

Counts
66 → 11

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)))
9.0b
(+ 1.0 (* y (* (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y)))) (cbrt (/ (- x 1.0) (+ 1.0 y))))))

rewrite31.0ms

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
associate-/r/ add-log-exp
pow1 add-exp-log flip3-+ add-cbrt-cube flip-+
cbrt-div pow1/3 div-inv
+-commutative sum-log
Counts
4 → 116
Calls
4 calls:
7.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
7.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
7.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
4.0ms
(+ 1.0 (* y (* (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y)))) (cbrt (/ (- x 1.0) (+ 1.0 y))))))

series62.0ms

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

simplify83.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (68.0ms)

IterNodesCost
049231974
149231974

prune307.0ms

Filtered
91 candidates to 128 candidates (-40.7%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1262128
Fresh369
Picked101
Done011
Total1309139

Merged error: 5.4b

Counts
139 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt (cbrt y))
0.6b
(cbrt (cbrt y))
0.6b
(cbrt (cbrt y))
10.7b
(+ 1.0 (* (* (cbrt y) (* (* (cbrt (cbrt y)) (cbrt (cbrt y))) (cbrt (cbrt y)))) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

rewrite11.0ms

Algorithm
rewrite-expression-head
Rules
27×cbrt-prod
10×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
add-log-exp
pow1 add-exp-log add-cbrt-cube
pow1/3
+-commutative flip3-+ sum-log flip-+
Counts
4 → 53
Calls
4 calls:
2.0ms
(cbrt (cbrt y))
2.0ms
(cbrt (cbrt y))
2.0ms
(cbrt (cbrt y))
5.0ms
(+ 1.0 (* (* (cbrt y) (* (* (cbrt (cbrt y)) (cbrt (cbrt y))) (cbrt (cbrt y)))) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

series109.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(cbrt (cbrt y))
30.0ms
(cbrt (cbrt y))
30.0ms
(cbrt (cbrt y))
17.0ms
(+ 1.0 (* (* (cbrt y) (* (* (cbrt (cbrt y)) (cbrt (cbrt y))) (cbrt (cbrt y)))) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

simplify55.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 0 (50.0ms)

IterNodesCost
04925500
14925500

prune80.0ms

Filtered
56 candidates to 65 candidates (-16.1%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New65065
Fresh077
Picked011
Done011
Total65974

Merged error: 5.4b

Counts
74 → 9

regimes330.0ms

Accuracy

96.9% (0.2b remaining)

Error of 7.7b against oracle of 7.4b and baseline of 14.7b

bsearch26.0ms

Steps
ItersRangePoint
9
50227932113049.875
1.601522318771203e+21
9873204879837964.0
5
-4.466342909995239e+27
-1.9759118902619576e+27
-2.1394493469517594e+27

simplify7.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (6.0ms)

IterNodesCost
033131
133131

end0.0ms

sample583.0ms

Algorithm
intervals
Results
182.0ms6131×body80valid
74.0ms663×body640valid
55.0ms386×body1280valid
47.0ms519×body320valid
17.0ms301×body160valid

Profiling

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