Details

Time bar (total: 9.9s)

sample2.4s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 43.75%

Guaranteed chance to sample good point: 31.901042%

Results
14.0ms31×body1280valid
11.0ms159×body80valid
8.0ms30×body640valid
7.0ms22×body1280nan
7.0ms28×body640nan
4.0ms60×body80nan
3.0ms17×body320valid
3.0ms19×body160valid
2.0ms12×body320nan
1.0ms7×body160nan

simplify81.0ms

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: 42.1b

Counts
2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (* (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)
13.5b
(- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l))
19.1b
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

rewrite49.0ms

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))))
5.0ms
(* (sqrt 2.0) t)
14.0ms
(- (* (/ (+ 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)))

series339.0ms

Counts
4 → 12
Calls
4 calls:
97.0ms
(/ (* (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))
181.0ms
(sqrt (- (* (/ (+ x 1.0) (- x 1.0)) (+ (* l l) (* 2.0 (* t t)))) (* l l)))

simplify58.0ms

Algorithm
egg-herbie
Counts
92 → 92
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
04171207
120511099
250021094

prune207.0ms

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: 5.9b

Counts
93 → 6

localize16.0ms

Local error

Found 4 expressions with local error:

2.4b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x))))
5.5b
(/ (pow l 2) x)
8.3b
(/ (pow t 2) x)
25.6b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (/ (pow l 2) x)))))

rewrite30.0ms

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))))
6.0ms
(/ (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)))))

series44.0ms

Counts
4 → 12
Calls
4 calls:
14.0ms
(+ (* 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)
24.0ms
(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

prune343.0ms

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

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New1384142
Fresh055
Picked101
Done000
Total1399148

Merged error: 3.8b

Counts
148 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.8b
(+ (pow t 2) (* l (/ l x)))
2.4b
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
8.3b
(/ (pow t 2) x)
25.6b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

rewrite28.0ms

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)))
8.0ms
(+ (* 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))))))

series51.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(+ (pow t 2) (* l (/ l x)))
14.0ms
(+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x)))))
3.0ms
(/ (pow t 2) x)
23.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (+ (pow t 2) (* l (/ l x))))))

simplify57.0ms

Algorithm
egg-herbie
Counts
104 → 104
Iterations

Useful iterations: 2 (47.0ms)

IterNodesCost
0456925
11936858
25003855

prune239.0ms

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

10 alts after pruning (9 fresh and 1 done)

PrunedKeptTotal
New1031104
Fresh088
Picked011
Done000
Total10310113

Merged error: 3.8b

Counts
113 → 10

localize19.0ms

Local error

Found 4 expressions with local error:

8.3b
(/ (pow t 2) x)
25.5b
(sqrt (+ (pow t 2) (* l (/ l x))))
25.5b
(sqrt (+ (pow t 2) (* l (/ l x))))
25.6b
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (* l (/ l x)))) (sqrt (+ (pow t 2) (* l (/ l x))))))))

rewrite27.0ms

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

series54.0ms

Counts
4 → 12
Calls
4 calls:
3.0ms
(/ (pow t 2) x)
13.0ms
(sqrt (+ (pow t 2) (* l (/ l x))))
13.0ms
(sqrt (+ (pow t 2) (* l (/ l x))))
25.0ms
(sqrt (+ (* 4.0 (/ (pow t 2) x)) (* 2.0 (* (sqrt (+ (pow t 2) (* l (/ l x)))) (sqrt (+ (pow t 2) (* l (/ l x))))))))

simplify58.0ms

Algorithm
egg-herbie
Counts
114 → 114
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
05071342
117571284
250031281

prune288.0ms

Filtered
83 candidates to 114 candidates (-37.3%)
Pruning

10 alts after pruning (8 fresh and 2 done)

PrunedKeptTotal
New1140114
Fresh088
Picked011
Done011
Total11410124

Merged error: 3.8b

Counts
124 → 10

regimes725.0ms

Accuracy

77% (5.5b remaining)

Error of 9.3b against oracle of 3.9b and baseline of 27.7b

bsearch304.0ms

Steps
ItersRangePoint
8
5.495247582719736e+83
6.645653152778353e+87
1.4150749603138452e+87
9
-1.2750377022894129e-281
-5.862104377187075e-289
-8.707374429043231e-283
6
-6.833051469828207e-256
-4.982621764803382e-257
-2.2052563172895628e-256
9
-1.4355602058628014e+85
-9.158662607019488e+79
-1.66616567371532e+82

simplify2.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
06692
16692

end0.0ms

sample4.4s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 43.75%

Guaranteed chance to sample good point: 31.901042%

Results
372.0ms5147×body80valid
299.0ms873×body1280valid
260.0ms979×body640valid
191.0ms569×body1280nan
160.0ms606×body640nan
133.0ms661×body320valid
99.0ms1416×body80nan
70.0ms352×body320nan
48.0ms340×body160valid
24.0ms182×body160nan

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