Details

Time bar (total: 20.8s)

sample7.6s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 43.75%

Guaranteed chance to sample good point: 36.458333%

Results
11.0ms156×body80valid
10.0ms30×body1280valid
9.0ms33×body640valid
7.0ms20×body1280nan
5.0ms21×body640nan
5.0ms27×body320valid
3.0ms16×body320nan
3.0ms39×body80nan
1.0ms10×body160valid
1.0ms8×body160nan

simplify79.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03914
19314
219314
341414
471814
5119214
6281614
7500114

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 41.7b

Counts
2 → 1

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)
12.0b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
17.3b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite46.0ms

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)))

series335.0ms

Counts
4 → 12
Calls
4 calls:
89.0ms
(/ (* (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))
187.0ms
(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 (46.0ms)

IterNodesCost
04171207
120511099
250021094

prune208.0ms

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

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New86692
Fresh000
Picked101
Done000
Total87693

Merged error: 6.7b

Counts
93 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

1.6b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
4.8b
(/ (pow l 2) x)
8.4b
(/ (pow t 2) x)
25.3b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite29.0ms

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)
7.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

series48.0ms

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)
24.0ms
(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

prune363.0ms

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

12 alts after pruning (12 fresh and 0 done)

PrunedKeptTotal
New1357142
Fresh055
Picked101
Done000
Total13612148

Merged error: 4.6b

Counts
148 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt 2.0) t)
1.6b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
8.4b
(/ (pow t 2) x)
25.3b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
30×add-sqr-sqrt
25×add-cube-cbrt *-un-lft-identity
24×times-frac
12×unpow-prod-down
11×add-exp-log
8×associate-*r/ add-cbrt-cube associate-/l*
7×pow1 sqrt-prod
6×associate-*l* add-log-exp
4×flip3-+ sqrt-div frac-add flip-+ unpow2 sqr-pow
3×div-exp associate-*r* associate-/r*
2×associate-+r+ unswap-sqr
1×cbrt-undiv +-commutative distribute-rgt-in pow-to-exp rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down pow-exp prod-exp clear-num sum-log *-commutative cbrt-unprod div-inv
Counts
4 → 103
Calls
4 calls:
4.0ms
(* (sqrt 2.0) t)
9.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
5.0ms
(/ (pow t 2) x)
7.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

series46.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* (sqrt 2.0) t)
14.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
3.0ms
(/ (pow t 2) x)
24.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify65.0ms

Algorithm
egg-herbie
Counts
115 → 115
Iterations

Useful iterations: 2 (53.0ms)

IterNodesCost
0477917
12140851
25001848

prune267.0ms

Filtered
80 candidates to 115 candidates (-43.8%)
Pruning

12 alts after pruning (11 fresh and 1 done)

PrunedKeptTotal
New1114115
Fresh4711
Picked011
Done000
Total11512127

Merged error: 4.6b

Counts
127 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
1.6b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
8.4b
(/ (pow t 2) x)
25.3b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite32.0ms

Algorithm
rewrite-expression-head
Rules
26×add-sqr-sqrt
25×add-cube-cbrt *-un-lft-identity
24×times-frac
14×add-exp-log
12×unpow-prod-down sqrt-prod
11×add-cbrt-cube
10×pow1
9×associate-*l*
8×associate-*r/ associate-/l*
6×add-log-exp
4×flip3-+ sqrt-div frac-add flip-+ unpow2 sqr-pow
3×div-exp pow-prod-down prod-exp associate-/r* cbrt-unprod
2×associate-+r+
1×cbrt-undiv +-commutative distribute-rgt-in pow-to-exp rem-sqrt-square frac-2neg distribute-lft-in sqrt-pow1 pow1/2 associate-*r* pow-exp clear-num sum-log *-commutative div-inv
Counts
4 → 105
Calls
4 calls:
9.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
9.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
5.0ms
(/ (pow t 2) x)
7.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

series46.0ms

Counts
4 → 12
Calls
4 calls:
4.0ms
(* (sqrt (sqrt 2.0)) (* (sqrt (sqrt 2.0)) t))
14.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
3.0ms
(/ (pow t 2) x)
24.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify66.0ms

Algorithm
egg-herbie
Counts
117 → 117
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0517989
12133891
25001884

prune277.0ms

Filtered
81 candidates to 117 candidates (-44.4%)
Pruning

15 alts after pruning (13 fresh and 2 done)

PrunedKeptTotal
New1143117
Fresh01010
Picked011
Done011
Total11415129

Merged error: 4.6b

Counts
129 → 15

regimes816.0ms

Accuracy

77.7% (5.3b remaining)

Error of 9.1b against oracle of 3.8b and baseline of 27.5b

bsearch565.0ms

Steps
ItersRangePoint
7
1.983937874757735e+112
1.490223521311024e+114
1.390575972256714e+113
8
1.8807502569169677e-170
7.666174251209348e-168
7.797270078669955e-169
10
1.212697867684574e-234
2.4033626182788557e-219
5.616949938075709e-223
9
-1.6980936369892595e-223
-4.3490291362448604e-232
-1.28741882781246e-223
9
-5.4681405945839273e-160
-1.0422276859398919e-166
-3.0875211751855904e-164
5
-1.4538681223011594e+112
-4.570326418853631e+111
-5.904714761107109e+111

simplify3.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
089131
189131

end0.0ms

sample9.6s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 43.75%

Guaranteed chance to sample good point: 36.458333%

Results
373.0ms5107×body80valid
290.0ms865×body1280valid
277.0ms1035×body640valid
198.0ms579×body1280nan
151.0ms573×body640nan
132.0ms637×body320valid
96.0ms1417×body80nan
72.0ms354×body320nan
48.0ms356×body160valid
27.0ms197×body160nan

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