Details

Time bar (total: 2.9s)

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

sample45.0ms

Algorithm
intervals
Results
6.0ms189×body80valid
5.0ms13×body1280valid
4.0ms29×body640valid
1.0ms14×body320valid
1.0ms11×body160valid

simplify233.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (231.0ms)

IterNodesCost
0520611

prune9.0ms

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: 15.4b

Counts
2 → 2

localize8.0ms

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)))
15.4b
(+ 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))))

simplify59.0ms

Algorithm
egg-herbie
Counts
111 → 111
Iterations

Useful iterations: 0 (47.0ms)

IterNodesCost
061631269

prune203.0ms

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

11 alts after pruning (11 fresh and 0 done)

PrunedKeptTotal
New10011111
Fresh101
Picked101
Done000
Total10211113

Merged error: 8.3b

Counts
113 → 11

localize15.0ms

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))
15.4b
(+ 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:
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))))))

simplify79.0ms

Algorithm
egg-herbie
Counts
65 → 65
Iterations

Useful iterations: 0 (72.0ms)

IterNodesCost
04908683
14908683

prune159.0ms

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

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New63265
Fresh01010
Picked011
Done000
Total631376

Merged error: 8.2b

Counts
76 → 13

localize13.0ms

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)))
15.4b
(+ 1.0 (* y (* (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y)))) (cbrt (/ (- x 1.0) (+ 1.0 y))))))

rewrite27.0ms

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))))))

series58.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
14.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
16.0ms
(cbrt (/ (- x 1.0) (+ 1.0 y)))
14.0ms
(+ 1.0 (* y (* (* (cbrt (/ (- x 1.0) (+ 1.0 y))) (cbrt (/ (- x 1.0) (+ 1.0 y)))) (cbrt (/ (- x 1.0) (+ 1.0 y))))))

simplify79.0ms

Algorithm
egg-herbie
Counts
128 → 128
Iterations

Useful iterations: 0 (65.0ms)

IterNodesCost
049231974
149231974

prune310.0ms

Filtered
90 candidates to 128 candidates (-42.2%)
Pruning

14 alts after pruning (12 fresh and 2 done)

PrunedKeptTotal
New1271128
Fresh01111
Picked011
Done011
Total12714141

Merged error: 8.2b

Counts
141 → 14

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt y)
0.6b
(cbrt y)
0.6b
(cbrt y)
15.4b
(+ 1.0 (* (* (cbrt y) (cbrt y)) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

rewrite8.0ms

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)
4.0ms
(+ 1.0 (* (* (cbrt y) (cbrt y)) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

series77.0ms

Counts
4 → 12
Calls
4 calls:
22.0ms
(cbrt y)
20.0ms
(cbrt y)
21.0ms
(cbrt y)
14.0ms
(+ 1.0 (* (* (cbrt y) (cbrt y)) (* (/ (- x 1.0) (+ 1.0 y)) (cbrt y))))

simplify51.0ms

Algorithm
egg-herbie
Counts
56 → 56
Iterations

Useful iterations: 0 (46.0ms)

IterNodesCost
04943365
14943365

prune58.0ms

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

14 alts after pruning (11 fresh and 3 done)

PrunedKeptTotal
New56056
Fresh01111
Picked011
Done022
Total561470

Merged error: 8.2b

Counts
70 → 14

regimes195.0ms

Accuracy

96.6% (0.3b remaining)

Error of 7.4b against oracle of 7.1b and baseline of 14.6b

bsearch41.0ms

Steps
ItersRangePoint
9
1.2177692274389285e+27
1.1913414585670746e+33
1.8268171308460768e+31
8
-5.116884898180177e+22
-6.363704482110802e+19
-1.5091161540073787e+20

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
04544
14544

end0.0ms

sample965.0ms

Algorithm
intervals
Results
179.0ms6122×body80valid
86.0ms729×body640valid
56.0ms363×body1280valid
44.0ms509×body320valid
16.0ms277×body160valid

Profiling

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