Details

Time bar (total: 6.3s)

sample99.0ms

Algorithm
intervals
Results
22.0ms325×body80nan
12.0ms166×body80valid
10.0ms29×body1280valid
7.0ms28×body640valid
7.0ms20×body1280nan
4.0ms19×body320valid
3.0ms11×body640nan
2.0ms12×body320nan
2.0ms14×body160valid
1.0ms6×body160nan

simplify79.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03914
19314
219314
341414
471814
5119214
6281614
7500114

prune4.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 41.4b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
0.4b
(* (sqrt 2.0) t)
13.0b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.7b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
17×add-sqr-sqrt
13×sqrt-prod
12×add-cube-cbrt *-un-lft-identity
11×add-exp-log add-cbrt-cube
7×pow1
6×times-frac associate-*l* associate-/r* add-log-exp
4×sqrt-div
3×flip3-- associate-*r* flip--
2×cbrt-undiv div-exp prod-exp associate--l+ associate-/r/ cbrt-unprod unswap-sqr
1×distribute-rgt-in sub-neg rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 diff-log pow-prod-down clear-num *-commutative div-inv associate-/l*
Counts
4 → 80
Calls
4 calls:
18.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
4.0ms
(* (sqrt 2.0) t)
12.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
12.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series337.0ms

Counts
4 → 12
Calls
4 calls:
91.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
4.0ms
(* (sqrt 2.0) t)
55.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
186.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify57.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
04171207
120511099
250021094

prune209.0ms

Filtered
65 candidates to 92 candidates (-41.5%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New87592
Fresh000
Picked101
Done000
Total88593

Merged error: 5.3b

Counts
93 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

3.2b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.7b
(/ (pow l 2) x)
9.6b
(/ (pow t 2) x)
26.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
48×times-frac
40×add-sqr-sqrt
39×add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
16×associate-/l*
14×add-exp-log
8×associate-*r/ add-cbrt-cube unpow2 sqr-pow
6×div-exp associate-/r* add-log-exp
5×pow1
4×flip3-+ sqrt-div frac-add flip-+
3×sqrt-prod
2×cbrt-undiv pow-to-exp associate-+r+ frac-2neg pow-exp clear-num div-inv
1×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log
Counts
4 → 130
Calls
4 calls:
8.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.0ms
(/ (pow l 2) x)
5.0ms
(/ (pow t 2) x)
7.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series46.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
3.0ms
(/ (pow l 2) x)
3.0ms
(/ (pow t 2) x)
25.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

simplify62.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
05261067
12113984
25001978

prune358.0ms

Filtered
97 candidates to 142 candidates (-46.4%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1339142
Fresh134
Picked101
Done000
Total13512147

Merged error: 3.1b

Counts
147 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

1.0b
(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
3.2b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
9.6b
(/ (pow t 2) x)
26.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt
22×add-cube-cbrt *-un-lft-identity
12×unpow-prod-down
9×add-exp-log
8×associate-*r/ associate-/l* add-log-exp
6×add-cbrt-cube
5×pow1 flip3-+ flip-+
4×sqrt-div frac-add unpow2 sqr-pow
3×div-exp associate-/r* sqrt-prod
2×+-commutative associate-+r+ sum-log
1×cbrt-undiv distribute-rgt-in pow-to-exp rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-exp clear-num div-inv
Counts
4 → 92
Calls
4 calls:
4.0ms
(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
8.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
5.0ms
(/ (pow t 2) x)
7.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

series63.0ms

Counts
4 → 12
Calls
4 calls:
12.0ms
(+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))
20.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x))))))
3.0ms
(/ (pow t 2) x)
28.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ l (* (cbrt x) (cbrt x))) (/ l (cbrt x)))))))

simplify60.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
04631308
119651213
250011210

prune248.0ms

Filtered
74 candidates to 104 candidates (-40.5%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1040104
Fresh01111
Picked011
Done000
Total10412116

Merged error: 3.1b

Counts
116 → 12

localize29.0ms

Local error

Found 4 expressions with local error:

3.2b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1)) (/ (pow (cbrt l) 2) (cbrt x))))))
6.7b
(/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1))
9.6b
(/ (pow t 2) x)
26.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1)) (/ (pow (cbrt l) 2) (cbrt x)))))))

rewrite35.0ms

Algorithm
rewrite-expression-head
Rules
46×add-exp-log
34×times-frac
29×add-sqr-sqrt
28×add-cube-cbrt *-un-lft-identity
24×unpow-prod-down
18×div-exp prod-exp associate-/l*
13×add-cbrt-cube
8×associate-*r/
6×cbrt-prod pow-to-exp 1-exp pow-exp add-log-exp sqr-pow
5×pow1
4×cbrt-undiv flip3-+ sqrt-div frac-add associate-/r* flip-+ unpow2
3×sqrt-prod cbrt-unprod
2×associate-+r+ frac-2neg clear-num div-inv
1×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log
Counts
4 → 130
Calls
4 calls:
9.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1)) (/ (pow (cbrt l) 2) (cbrt x))))))
10.0ms
(/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1))
5.0ms
(/ (pow t 2) x)
7.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1)) (/ (pow (cbrt l) 2) (cbrt x)))))))

series76.0ms

Counts
4 → 12
Calls
4 calls:
18.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1)) (/ (pow (cbrt l) 2) (cbrt x))))))
23.0ms
(/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1))
6.0ms
(/ (pow t 2) x)
28.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* (/ (pow (cbrt l) 4) (* (* (cbrt x) (cbrt x)) 1)) (/ (pow (cbrt l) 2) (cbrt x)))))))

simplify89.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (72.0ms)

IterNodesCost
07511867
134231725
250021693

prune356.0ms

Filtered
94 candidates to 142 candidates (-51.1%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New1420142
Fresh01010
Picked011
Done011
Total14212154

Merged error: 3.1b

Counts
154 → 12

regimes695.0ms

Accuracy

71.6% (6.6b remaining)

Error of 10.4b against oracle of 3.8b and baseline of 27.1b

bsearch317.0ms

Steps
ItersRangePoint
8
4.4279417700265055e-10
1.5258029315016124e-07
1.5062960314922014e-07
6
1.558132196883256e-236
2.221277331961581e-235
1.2151341517012058e-235
10
-8.465270959295778e-305
7.458599208619438e-302
7.377813458799392e-302
8
-7.491844144661297e+152
-5.0884505127919416e+148
-1.286125254120137e+152

simplify5.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
07097
17597
27897
37897

end0.0ms

sample3.0s

Algorithm
intervals
Results
696.0ms10047×body80nan
371.0ms5020×body80valid
296.0ms869×body1280valid
286.0ms1046×body640valid
189.0ms570×body1280nan
150.0ms726×body320valid
148.0ms561×body640nan
68.0ms336×body320nan
47.0ms339×body160valid
27.0ms205×body160nan

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