Details

Time bar (total: 9.0s)

sample2.2s

Algorithm
intervals
sampling

Space saved by range analysis: 43.832357%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 0%

Results
14.0ms26×body1280valid
11.0ms159×body80valid
10.0ms40×body640valid
6.0ms19×body1280nan
4.0ms16×body640nan
4.0ms54×body80nan
3.0ms18×body320valid
2.0ms12×body320nan
2.0ms13×body160valid
1.0ms7×body160nan

simplify80.0ms

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: 43.4b

Counts
2 → 1

localize17.0ms

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)
14.8b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.9b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite53.0ms

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:
20.0ms
(/ (* (sqrt 2.0) t) (sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))))
5.0ms
(* (sqrt 2.0) t)
13.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
13.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

series353.0ms

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)
60.0ms
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
197.0ms
(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

prune203.0ms

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

4 alts after pruning (4 fresh and 0 done)

PrunedKeptTotal
New88492
Fresh000
Picked101
Done000
Total89493

Merged error: 7.0b

Counts
93 → 4

localize17.0ms

Local error

Found 4 expressions with local error:

3.4b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
8.1b
(/ (pow l 2) x)
10.1b
(/ (pow t 2) x)
26.3b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite32.0ms

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)))))

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))))
3.0ms
(/ (pow l 2) x)
3.0ms
(/ (pow t 2) x)
28.0ms
(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 (49.0ms)

IterNodesCost
05261067
12113984
25001978

prune356.0ms

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

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1366142
Fresh033
Picked101
Done000
Total1379146

Merged error: 3.1b

Counts
146 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (pow t 2) (/ l (/ x l)))
3.4b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
10.1b
(/ (pow t 2) x)
26.3b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

rewrite47.0ms

Algorithm
rewrite-expression-head
Rules
24×*-un-lft-identity times-frac
23×add-sqr-sqrt
22×add-cube-cbrt
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 distribute-lft-out
Counts
4 → 93
Calls
4 calls:
23.0ms
(+ (pow t 2) (/ l (/ x l)))
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))))))

series53.0ms

Counts
4 → 12
Calls
4 calls:
9.0ms
(+ (pow t 2) (/ l (/ x l)))
15.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l)))))
3.0ms
(/ (pow t 2) x)
26.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ l (/ x l))))))

simplify64.0ms

Algorithm
egg-herbie
Counts
105 → 105
Iterations

Useful iterations: 2 (51.0ms)

IterNodesCost
0453932
11835862
25001859

prune250.0ms

Filtered
76 candidates to 105 candidates (-38.2%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New1041105
Fresh178
Picked011
Done000
Total1059114

Merged error: 3.1b

Counts
114 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b
(+ (pow t 2) (* l (/ l x)))
3.4b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
10.1b
(/ (pow t 2) x)
26.3b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite29.0ms

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

series56.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(+ (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)
27.0ms
(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 (48.0ms)

IterNodesCost
0456925
11936858
25003855

prune204.0ms

Filtered
75 candidates to 104 candidates (-38.7%)
Pruning

9 alts after pruning (7 fresh and 2 done)

PrunedKeptTotal
New1040104
Fresh077
Picked011
Done011
Total1049113

Merged error: 3.1b

Counts
113 → 9

regimes551.0ms

Accuracy

75.9% (5.6b remaining)

Error of 9.4b against oracle of 3.8b and baseline of 27.0b

bsearch147.0ms

Steps
ItersRangePoint
9
3.7807284094656145e+25
9.508915051874514e+32
9.353561367842775e+32
9
-5.114666546453935e+160
-1.1097550231900001e+152
-1.1980124057781741e+152

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
05957
15957

end0.0ms

sample4.0s

Algorithm
intervals
sampling

Space saved by range analysis: 43.832357%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 0%

Results
370.0ms5098×body80valid
280.0ms1032×body640valid
277.0ms835×body1280valid
187.0ms562×body1280nan
148.0ms570×body640nan
127.0ms643×body320valid
101.0ms1474×body80nan
70.0ms346×body320nan
53.0ms392×body160valid
25.0ms195×body160nan

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