Details

Time bar (total: 5.8s)

sample99.0ms

Algorithm
intervals
Results
20.0ms305×body80nan
12.0ms171×body80valid
10.0ms27×body640valid
9.0ms29×body1280valid
8.0ms24×body1280nan
6.0ms23×body640nan
3.0ms17×body320valid
2.0ms13×body320nan
2.0ms12×body160valid
1.0ms5×body160nan

simplify70.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (68.0ms)

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: 42.7b

Counts
2 → 2

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)
14.4b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
21.7b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite50.0ms

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))))
7.0ms
(* (sqrt 2.0) t)
13.0ms
(- (* (/ (+ 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)))

series345.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(/ (* (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)
58.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
191.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify33.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 0 (22.0ms)

IterNodesCost
051772025

prune211.0ms

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

7 alts after pruning (7 fresh and 0 done)

PrunedKeptTotal
New86692
Fresh011
Picked101
Done000
Total87794

Merged error: 2.8b

Counts
94 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) t)
0.6b
(+ (* t t) (/ l (/ x l)))
4.0b
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
26.7b
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite37.0ms

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:
5.0ms
(* (sqrt 2.0) t)
10.0ms
(+ (* t t) (/ l (/ x l)))
11.0ms
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
9.0ms
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

series52.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* (sqrt 2.0) t)
9.0ms
(+ (* t t) (/ l (/ x l)))
14.0ms
(+ (* 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))))))

simplify24.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (16.0ms)

IterNodesCost
050171361

prune185.0ms

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

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New69877
Fresh066
Picked101
Done000
Total701484

Merged error: 2.7b

Counts
84 → 14

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))))
0.6b
(+ (* t t) (/ l (/ x l)))
4.0b
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
26.7b
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite43.0ms

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:
12.0ms
(* (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))) (* t (cbrt (sqrt 2.0))))
11.0ms
(+ (* t t) (/ l (/ x l)))
9.0ms
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
9.0ms
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

series52.0ms

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))))))

simplify27.0ms

Algorithm
egg-herbie
Counts
77 → 77
Iterations

Useful iterations: 0 (18.0ms)

IterNodesCost
050231357

prune227.0ms

Filtered
55 candidates to 77 candidates (-40.0%)
Pruning

14 alts after pruning (14 fresh and 0 done)

PrunedKeptTotal
New73477
Fresh31013
Picked101
Done000
Total771491

Merged error: 2.6b

Counts
91 → 14

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
0.6b
(+ (* t t) (/ l (/ x l)))
4.0b
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
26.7b
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
12×sqrt-prod
10×pow1
9×add-exp-log add-sqr-sqrt associate-*l* add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity associate-*r/ add-log-exp
5×flip3-+ flip-+
4×sqrt-div frac-add
3×pow-prod-down prod-exp cbrt-unprod
2×+-commutative associate-+r+ sum-log
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 associate-*r* *-commutative
Counts
4 → 67
Calls
4 calls:
9.0ms
(* (sqrt (sqrt 2.0)) (* t (sqrt (sqrt 2.0))))
10.0ms
(+ (* t t) (/ l (/ x l)))
10.0ms
(+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l)))))
10.0ms
(sqrt (+ (* 4.0 (/ t (/ x t))) (* 2.0 (+ (* t t) (/ l (/ x l))))))

series55.0ms

Counts
4 → 12
Calls
4 calls:
6.0ms
(* (sqrt (sqrt 2.0)) (* t (sqrt (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))))))

simplify26.0ms

Algorithm
egg-herbie
Counts
79 → 79
Iterations

Useful iterations: 0 (18.0ms)

IterNodesCost
051551386

prune156.0ms

Filtered
60 candidates to 79 candidates (-31.7%)
Pruning

13 alts after pruning (12 fresh and 1 done)

PrunedKeptTotal
New76379
Fresh4913
Picked011
Done000
Total801393

Merged error: 2.6b

Counts
93 → 13

regimes679.0ms

Accuracy

76.4% (5.7b remaining)

Error of 9.3b against oracle of 3.7b and baseline of 27.8b

bsearch258.0ms

Steps
ItersRangePoint
9
3.718007497691488e+128
1.0155085577474121e+136
6.909272875938842e+132
9
-4.768171039488465e-229
-1.9045487533186338e-234
-1.1517568437915858e-229
5
-1.1874625757630797e-197
-5.359521600434338e-198
-1.0771499433412337e-197
10
-3.8097776440185395e+145
-7.864640314842827e+132
-1.5247085837859912e+136

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
066184
166184

end0.0ms

sample3.0s

Algorithm
intervals
Results
663.0ms10115×body80nan
496.0ms5080×body80valid
291.0ms878×body1280valid
271.0ms1028×body640valid
191.0ms607×body1280nan
152.0ms596×body640nan
123.0ms629×body320valid
66.0ms351×body320nan
50.0ms385×body160valid
22.0ms179×body160nan

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