Details

Time bar (total: 6.1s)

sample285.0ms

Algorithm
intervals
Results
199.0ms36×body1280valid
21.0ms304×body80nan
11.0ms156×body80valid
8.0ms31×body640valid
6.0ms18×body1280nan
4.0ms16×body640nan
4.0ms20×body320valid
2.0ms13×body160valid
1.0ms7×body320nan
1.0ms4×body160nan

simplify85.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03914
19314
219314
341414
471814
5119214
6281614
7500114

prune5.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 43.7b

Counts
2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 2.0 (* t t))
0.4b
(* (sqrt 2.0) t)
12.8b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
20.1b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
15×add-sqr-sqrt
12×pow1
11×add-exp-log add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity associate-*l*
7×sqrt-prod
6×add-log-exp
4×associate-*r* pow-prod-down prod-exp cbrt-unprod
3×unswap-sqr
2×flip3-- sqrt-div associate--l+ *-commutative flip--
1×distribute-rgt-in sub-neg rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 diff-log
Counts
4 → 70
Calls
4 calls:
5.0ms
(* 2.0 (* t t))
5.0ms
(* (sqrt 2.0) t)
12.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
16.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series274.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(* 2.0 (* t t))
4.0ms
(* (sqrt 2.0) t)
59.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
207.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify51.0ms

Algorithm
egg-herbie
Counts
82 → 82
Iterations

Useful iterations: 2 (42.0ms)

IterNodesCost
0397712
11849656
25001637

prune179.0ms

Filtered
82 candidates to 59 candidates (28.0%)
Pruning

3 alts after pruning (3 fresh and 0 done)

PrunedKeptTotal
New79382
Fresh000
Picked101
Done000
Total80383

Merged error: 7.4b

Counts
83 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

3.8b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
6.2b
(/ (pow l 2) x)
8.2b
(/ (pow t 2) x)
26.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite31.0ms

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:
9.0ms
(+ (* 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)
8.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series50.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
6.0ms
(/ (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)))))

simplify63.0ms

Algorithm
egg-herbie
Counts
142 → 142
Iterations

Useful iterations: 2 (50.0ms)

IterNodesCost
05261067
12113984
25001978

prune352.0ms

Filtered
142 candidates to 97 candidates (31.7%)
Pruning

10 alts after pruning (10 fresh and 0 done)

PrunedKeptTotal
New1348142
Fresh022
Picked101
Done000
Total13510145

Merged error: 3.5b

Counts
145 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (pow t 2) (* l (/ l x)))
3.8b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
8.2b
(/ (pow t 2) x)
26.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite30.0ms

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:
5.0ms
(+ (pow t 2) (* l (/ l x)))
9.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
6.0ms
(/ (pow t 2) x)
7.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

series52.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(+ (pow t 2) (* l (/ l x)))
15.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
3.0ms
(/ (pow t 2) x)
25.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify59.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0456938
12000858
25001855

prune258.0ms

Filtered
104 candidates to 75 candidates (27.9%)
Pruning

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1004104
Fresh189
Picked101
Done000
Total10212114

Merged error: 3.5b

Counts
114 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

8.2b
(/ (pow t 2) x)
26.2b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (* l (/ l x)))) (sqrt (+ (pow t 2) (* l (/ l x))))))))
26.2b
(sqrt (+ (pow t 2) (* l (/ l x))))
26.2b
(sqrt (+ (pow t 2) (* l (/ l x))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
27×add-sqr-sqrt
26×sqrt-div
24×add-cube-cbrt *-un-lft-identity times-frac
18×associate-*r/
12×unpow-prod-down
9×add-exp-log flip3-+ sqrt-prod flip-+
8×frac-add associate-/l*
7×pow1
6×add-cbrt-cube
4×frac-times unpow2 add-log-exp sqr-pow
3×rem-sqrt-square sqrt-pow1 pow1/2 div-exp associate-/r*
2×associate-*l/
1×cbrt-undiv pow-to-exp frac-2neg pow-exp clear-num div-inv
Counts
4 → 102
Calls
4 calls:
7.0ms
(/ (pow t 2) x)
10.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (* l (/ l x)))) (sqrt (+ (pow t 2) (* l (/ l x))))))))
4.0ms
(sqrt (+ (pow t 2) (* l (/ l x))))
4.0ms
(sqrt (+ (pow t 2) (* l (/ l x))))

series57.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(/ (pow t 2) x)
26.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (* l (/ l x)))) (sqrt (+ (pow t 2) (* l (/ l x))))))))
14.0ms
(sqrt (+ (pow t 2) (* l (/ l x))))
14.0ms
(sqrt (+ (pow t 2) (* l (/ l x))))

simplify58.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05071355
118061284
250021281

prune299.0ms

Filtered
114 candidates to 83 candidates (27.2%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New1122114
Fresh11011
Picked011
Done000
Total11313126

Merged error: 3.5b

Counts
126 → 13

regimes434.0ms

Accuracy

75.9% (5.7b remaining)

Error of 9.7b against oracle of 4.0b and baseline of 27.6b

bsearch296.0ms

Steps
ItersRangePoint
7
1.849374285703014e+25
3.25330858629139e+26
3.203271237216745e+26
8
-1.8002600144550513e-278
-1.9536415029185778e-281
-1.2736627265375275e-279
9
-4.6789416617014705e-206
-2.4002776511307787e-212
-2.155267655794612e-209
7
-6.512962292552405e+125
-8.310516236779094e+123
-9.89774605087061e+124

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
072100
172100

end0.0ms

sample3.0s

Algorithm
intervals
Results
695.0ms9976×body80nan
359.0ms5108×body80valid
308.0ms878×body1280valid
283.0ms1034×body640valid
223.0ms625×body1280nan
167.0ms609×body640nan
128.0ms615×body320valid
72.0ms355×body320nan
51.0ms365×body160valid
28.0ms208×body160nan

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