Details

Time bar (total: 7.5s)

analyze758.0ms

Algorithm
search

sample100.0ms

Algorithm
intervals
Results
24.0ms49×body1280invalid
20.0ms42×body1280valid
12.0ms158×body80valid
10.0ms33×body640valid
9.0ms30×body640invalid
4.0ms16×body320invalid
2.0ms10×body320valid
2.0ms13×body160valid
2.0ms19×body80invalid
0.0ms3×body160invalid

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

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 0.5b

Counts
2 → 2

localize10.0ms

Local error

Found 2 expressions with local error:

0.4b
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
38×times-frac
31×add-cube-cbrt *-un-lft-identity
22×associate-*l* sqrt-prod
9×add-exp-log add-cbrt-cube
6×associate-/r*
4×pow1
3×associate-*r* associate-/l* unswap-sqr
2×cbrt-undiv frac-times flip3-+ associate-*r/ div-exp prod-exp cbrt-unprod flip-+ div-inv add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down associate-*l/ clear-num *-commutative
Counts
2 → 87
Calls
2 calls:
10.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
5.0ms
(/ (cos th) (sqrt 2.0))

series45.0ms

Counts
2 → 6
Calls
2 calls:
36.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
10.0ms
(/ (cos th) (sqrt 2.0))

simplify54.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0479795
12384738
25003725

prune174.0ms

Filtered
63 candidates to 93 candidates (-47.6%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New85893
Fresh101
Picked101
Done000
Total87895

Merged error: 0b

Counts
95 → 8

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
10×add-sqr-sqrt
9×add-exp-log add-cbrt-cube
8×add-cube-cbrt *-un-lft-identity
6×times-frac associate-/r* sqrt-prod
4×pow1 associate-*r/
3×associate-*r* associate-*l*
2×cbrt-undiv flip3-+ div-exp prod-exp cbrt-unprod flip-+ associate-/l/ add-log-exp
1×distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num *-commutative div-inv associate-/l* unswap-sqr
Counts
2 → 51
Calls
2 calls:
6.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
10.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

series57.0ms

Counts
2 → 6
Calls
2 calls:
22.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
35.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

simplify43.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0300487
11619424
25001417

prune98.0ms

Filtered
39 candidates to 57 candidates (-46.2%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New54357
Fresh347
Picked011
Done000
Total57865

Merged error: 0b

Counts
65 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
0.7b
(/ (cos th) (sqrt 2.0))
7.1b
(sqrt (+ (* a1 a1) (* a2 a2)))
7.1b
(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
54×add-sqr-sqrt
40×times-frac
36×add-cube-cbrt *-un-lft-identity
35×sqrt-prod
22×associate-*l*
11×add-exp-log add-cbrt-cube
8×pow1 sqrt-div
6×associate-*r* associate-/r* unswap-sqr
4×flip3-+ flip-+ add-log-exp
3×associate-/l*
2×cbrt-undiv frac-times rem-sqrt-square sqrt-pow1 pow1/2 associate-*r/ div-exp prod-exp cbrt-unprod div-inv
1×frac-2neg pow-prod-down associate-*l/ clear-num *-commutative
Counts
4 → 121
Calls
4 calls:
12.0ms
(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
5.0ms
(/ (cos th) (sqrt 2.0))
3.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
3.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

series46.0ms

Counts
4 → 12
Calls
4 calls:
29.0ms
(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
5.0ms
(/ (cos th) (sqrt 2.0))
6.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
6.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

simplify44.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (32.0ms)

IterNodesCost
03521093
112561042
250011028

prune175.0ms

Filtered
96 candidates to 133 candidates (-38.5%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New1330133
Fresh066
Picked011
Done011
Total1338141

Merged error: 0b

Counts
141 → 8

localize12.0ms

Local error

Found 3 expressions with local error:

0.4b
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))
0.7b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

rewrite141.0ms

Algorithm
rewrite-expression-head
Rules
1137×sqrt-prod
1119×times-frac
624×add-sqr-sqrt
577×add-cube-cbrt *-un-lft-identity
283×associate-*l*
34×associate-/l*
22×div-inv
19×add-exp-log add-cbrt-cube
18×associate-/r*
13×unswap-sqr
7×cbrt-undiv div-exp
5×pow1
3×associate-*r* prod-exp cbrt-unprod add-log-exp
2×frac-times frac-2neg flip3-+ associate-*r/ clear-num flip-+
1×distribute-rgt-in distribute-lft-in pow-prod-down associate-*l/ *-commutative associate-/l/
Counts
3 → 706
Calls
3 calls:
55.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
5.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
18.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

series48.0ms

Counts
3 → 9
Calls
3 calls:
35.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
8.0ms
(/ (cos th) (sqrt (sqrt 2.0)))
6.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))

simplify124.0ms

Algorithm
egg-herbie
Counts
715 → 715
Iterations

Useful iterations: 1 (39.0ms)

IterNodesCost
0195010359
150019505

prune1.4s

Filtered
362 candidates to 715 candidates (-97.5%)
Pruning

8 alts after pruning (5 fresh and 3 done)

PrunedKeptTotal
New7150715
Fresh055
Picked011
Done022
Total7158723

Merged error: 0b

Counts
723 → 8

regimes500.0ms

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
0137
1137

end0.0ms

analyze749.0ms

Algorithm
search

sample2.9s

Algorithm
intervals
Results
635.0ms1401×body1280valid
536.0ms1164×body1280invalid
359.0ms4661×body80valid
356.0ms1127×body640valid
308.0ms960×body640invalid
125.0ms518×body320valid
116.0ms509×body320invalid
45.0ms293×body160valid
45.0ms556×body80invalid
36.0ms231×body160invalid

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