Details

Time bar (total: 5.6s)

sample93.0ms

Algorithm
intervals
Results
20.0ms302×body80nan
11.0ms157×body80valid
10.0ms30×body1280valid
9.0ms37×body640valid
5.0ms15×body1280nan
4.0ms18×body640nan
4.0ms22×body320valid
1.0ms10×body160valid
1.0ms7×body320nan
0.0ms4×body160nan

simplify68.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (67.0ms)

IterNodesCost
0500027

prune11.0ms

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: 44.0b

Counts
2 → 2

localize15.0ms

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)
13.6b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.5b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite48.0ms

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:
16.0ms
(/ (* (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)))

series349.0ms

Counts
4 → 12
Calls
4 calls:
95.0ms
(/ (* (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)
57.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
193.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify31.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 0 (18.0ms)

IterNodesCost
051772025

prune198.0ms

Filtered
67 candidates to 92 candidates (-37.3%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New87592
Fresh101
Picked101
Done000
Total89594

Merged error: 4.2b

Counts
94 → 5

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) t)
1.2b
(+ (* t t) (/ l (/ x l)))
4.4b
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
27.9b
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
13×add-sqr-sqrt
8×add-cube-cbrt *-un-lft-identity associate-*r/ add-log-exp
7×pow1 sqrt-prod
6×add-exp-log associate-*l* add-cbrt-cube
5×flip3-+ flip-+
4×sqrt-div frac-add
3×associate-*r*
2×+-commutative associate-+r+ sum-log unswap-sqr
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down prod-exp *-commutative cbrt-unprod
Counts
4 → 65
Calls
4 calls:
4.0ms
(* (sqrt 2.0) t)
10.0ms
(+ (* t t) (/ l (/ x l)))
9.0ms
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
8.0ms
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

series54.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* (sqrt 2.0) t)
9.0ms
(+ (* t t) (/ l (/ x l)))
15.0ms
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
27.0ms
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

simplify24.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (16.0ms)

IterNodesCost
050171361

prune161.0ms

Filtered
61 candidates to 77 candidates (-26.2%)
Pruning

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New71677
Fresh134
Picked011
Done000
Total721082

Merged error: 4.2b

Counts
82 → 10

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* t (cbrt (sqrt 2.0))))
1.2b
(+ (* t t) (/ l (/ x l)))
4.4b
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
27.9b
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
17×pow1
16×add-exp-log
10×add-cbrt-cube
8×associate-*r/ pow-prod-down prod-exp cbrt-unprod add-log-exp
6×add-sqr-sqrt
5×add-cube-cbrt *-un-lft-identity flip3-+ flip-+
4×sqrt-div frac-add
3×sqrt-prod
2×+-commutative associate-+r+ sum-log
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 associate-*r* associate-*l* *-commutative
Counts
4 → 65
Calls
4 calls:
10.0ms
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* t (cbrt (sqrt 2.0))))
12.0ms
(+ (* t t) (/ l (/ x l)))
9.0ms
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
8.0ms
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

series53.0ms

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

simplify25.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (17.0ms)

IterNodesCost
050231357

prune203.0ms

Filtered
56 candidates to 77 candidates (-37.5%)
Pruning

12 alts after pruning (10 fresh and 2 done)

PrunedKeptTotal
New75277
Fresh088
Picked011
Done011
Total751287

Merged error: 4.2b

Counts
87 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

4.4b
(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
4.4b
(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
27.9b
(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))
27.9b
(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

rewrite34.0ms

Algorithm
rewrite-expression-head
Rules
24×associate-*r/
8×add-sqr-sqrt flip3-+ sqrt-div frac-add flip-+ add-log-exp
6×pow1 add-cube-cbrt *-un-lft-identity sqrt-prod
4×add-exp-log associate-+r+ add-cbrt-cube
2×+-commutative distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 sum-log
Counts
4 → 64
Calls
4 calls:
8.0ms
(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
8.0ms
(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
7.0ms
(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))
9.0ms
(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

series81.0ms

Counts
4 → 12
Calls
4 calls:
16.0ms
(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
15.0ms
(+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x)))))
25.0ms
(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))
25.0ms
(sqrt (+ (* 4.0 (* t (/ t x))) (* 2.0 (+ (* t t) (* l (/ l x))))))

simplify27.0ms

Algorithm
egg-herbie
Counts
76 → 76
Iterations

Useful iterations: 0 (16.0ms)

IterNodesCost
052142076

prune175.0ms

Filtered
62 candidates to 76 candidates (-22.6%)
Pruning

12 alts after pruning (9 fresh and 3 done)

PrunedKeptTotal
New76076
Fresh099
Picked011
Done022
Total761288

Merged error: 4.2b

Counts
88 → 12

regimes589.0ms

Accuracy

77.6% (5.3b remaining)

Error of 9.2b against oracle of 3.8b and baseline of 27.6b

bsearch459.0ms

Steps
ItersRangePoint
7
3.2587736523592727e+77
1.5435460934798866e+79
1.510925923911934e+79
9
2.183530191549861e-163
4.819130854012089e-158
1.4760270171526467e-162
9
3.885092605063696e-291
3.3461677562655154e-285
3.313694702039962e-285
8
-6.968307208939926e-223
-2.387333216621575e-226
-9.346838011251571e-226
8
-3.661686466709731e-152
-1.141822718111867e-156
-1.1588459180228711e-156
10
-1.2275057452980505e+162
-1.6966324530734372e+148
-1.5002431537572544e+152

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
077226
177226

end0.0ms

sample2.8s

Algorithm
intervals
Results
654.0ms10034×body80nan
351.0ms5133×body80valid
286.0ms870×body1280valid
256.0ms1017×body640valid
179.0ms565×body1280nan
141.0ms570×body640nan
116.0ms605×body320valid
59.0ms309×body320nan
49.0ms375×body160valid
25.0ms202×body160nan

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