Details

Time bar (total: 11.3s)

sample2.3s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 21.264648%

Guaranteed chance to sample good point: 60.031008%

Results
16.0ms37×body1280invalid
15.0ms35×body1280valid
12.0ms40×body640valid
12.0ms40×body640invalid
11.0ms150×body80valid
5.0ms21×body320invalid
5.0ms21×body320valid
2.0ms10×body160valid
1.0ms6×body160invalid
1.0ms11×body80invalid

simplify14.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1507
2777
3967
41127
51277
61417
71417

prune11.0ms

Filtered
1 candidates to 1 candidates (0.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 0.5b

Counts
2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.3b
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
40×add-sqr-sqrt
38×times-frac
32×add-cube-cbrt *-un-lft-identity
22×associate-*l* sqrt-prod
10×add-exp-log add-cbrt-cube
6×associate-/r*
5×pow1 add-log-exp
3×flip3-+ associate-*r* flip-+ associate-/l* unswap-sqr
2×cbrt-undiv frac-times associate-*r/ div-exp prod-exp cbrt-unprod div-inv
1×+-commutative distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down associate-*l/ clear-num sum-log *-commutative
Counts
3 → 98
Calls
3 calls:
3.0ms
(+ (* a1 a1) (* a2 a2))
10.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
4.0ms
(/ (cos th) (sqrt 2.0))

series47.0ms

Counts
3 → 9
Calls
3 calls:
7.0ms
(+ (* a1 a1) (* a2 a2))
34.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
5.0ms
(/ (cos th) (sqrt 2.0))

simplify52.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (43.0ms)

IterNodesCost
0490872
12426805
25001791

prune188.0ms

Filtered
75 candidates to 107 candidates (-42.7%)
Pruning

9 alts after pruning (9 fresh and 0 done)

PrunedKeptTotal
New989107
Fresh000
Picked101
Done000
Total999108

Merged error: 0b

Counts
108 → 9

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow a2 2) (pow a1 2))
0.1b
(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
0.4b
(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
96×*-un-lft-identity
62×times-frac
48×add-sqr-sqrt
40×add-cube-cbrt
34×associate-*r* sqrt-prod
28×unpow-prod-down distribute-lft-out
10×add-exp-log add-cbrt-cube
6×associate-/r*
5×pow1 associate-/l* add-log-exp
3×associate-*l* unswap-sqr
2×cbrt-undiv flip3-+ div-exp prod-exp cbrt-unprod flip-+ div-inv associate-/l/
1×+-commutative frac-2neg associate-*r/ pow-prod-down clear-num sum-log *-commutative
Counts
3 → 122
Calls
3 calls:
7.0ms
(+ (pow a2 2) (pow a1 2))
17.0ms
(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
12.0ms
(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

series53.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ (pow a2 2) (pow a1 2))
37.0ms
(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
11.0ms
(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

simplify48.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
03441118
115571023
250011018

prune210.0ms

Filtered
70 candidates to 131 candidates (-87.1%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1292131
Fresh538
Picked011
Done000
Total1346140

Merged error: 0b

Counts
140 → 6

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (pow a2 2) (pow a1 2))
0.1b
(* (cos th) (/ (/ (+ (pow a2 2) (pow a1 2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))
0.3b
(/ (/ (+ (pow a2 2) (pow a1 2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
0.3b
(/ (+ (pow a2 2) (pow a1 2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

rewrite85.0ms

Algorithm
rewrite-expression-head
Rules
271×times-frac
191×*-un-lft-identity
123×add-sqr-sqrt
118×cbrt-prod
103×add-cube-cbrt
85×associate-*r*
59×sqrt-prod
44×unpow-prod-down distribute-lft-out
32×add-exp-log
22×div-inv
20×add-cbrt-cube
14×associate-/l*
12×cbrt-undiv div-exp
10×associate-/r*
7×prod-exp cbrt-unprod unswap-sqr
6×pow1 add-log-exp
3×associate-*l* associate-/l/
2×frac-2neg flip3-+ clear-num flip-+
1×+-commutative associate-*r/ pow-prod-down sum-log *-commutative
Counts
4 → 269
Calls
4 calls:
7.0ms
(+ (pow a2 2) (pow a1 2))
34.0ms
(* (cos th) (/ (/ (+ (pow a2 2) (pow a1 2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))
17.0ms
(/ (/ (+ (pow a2 2) (pow a1 2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
13.0ms
(/ (+ (pow a2 2) (pow a1 2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

series90.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(+ (pow a2 2) (pow a1 2))
34.0ms
(* (cos th) (/ (/ (+ (pow a2 2) (pow a1 2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0))))
14.0ms
(/ (/ (+ (pow a2 2) (pow a1 2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
35.0ms
(/ (+ (pow a2 2) (pow a1 2)) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

simplify105.0ms

Algorithm
egg-herbie
Counts
281 → 281
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
07874456
137724048
250013913

prune743.0ms

Filtered
159 candidates to 281 candidates (-76.7%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New2810281
Fresh044
Picked011
Done011
Total2816287

Merged error: 0b

Counts
287 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.3b
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite131.0ms

Algorithm
rewrite-expression-head
Rules
1137×sqrt-prod
1119×times-frac
625×add-sqr-sqrt
578×add-cube-cbrt *-un-lft-identity
283×associate-*l*
34×associate-/l*
22×div-inv
20×add-exp-log add-cbrt-cube
18×associate-/r*
13×unswap-sqr
7×cbrt-undiv div-exp
6×pow1 add-log-exp
3×flip3-+ associate-*r* prod-exp cbrt-unprod flip-+
2×frac-times frac-2neg associate-*r/ clear-num
1×+-commutative distribute-rgt-in distribute-lft-in pow-prod-down associate-*l/ sum-log *-commutative associate-/l/
Counts
4 → 717
Calls
4 calls:
4.0ms
(+ (* a1 a1) (* a2 a2))
50.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
5.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
15.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series58.0ms

Counts
4 → 12
Calls
4 calls:
5.0ms
(+ (* a1 a1) (* a2 a2))
40.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
8.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
5.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify122.0ms

Algorithm
egg-herbie
Counts
729 → 729
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0196110436
150019573

prune1.4s

Filtered
374 candidates to 729 candidates (-94.9%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New7290729
Fresh033
Picked011
Done022
Total7296735

Merged error: 0b

Counts
735 → 6

regimes516.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01714
11714

end0.0ms

sample5.1s

Algorithm
intervals
sampling

Space saved by range analysis: 0%

Space saved by search: 21.264648%

Guaranteed chance to sample good point: 60.031008%

Results
616.0ms1384×body1280valid
498.0ms1110×body1280invalid
347.0ms1112×body640valid
346.0ms4604×body80valid
309.0ms999×body640invalid
137.0ms597×body320valid
108.0ms489×body320invalid
46.0ms303×body160valid
40.0ms262×body160invalid
31.0ms376×body80invalid

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