Details

Time bar (total: 6.4s)

sample94.0ms

Algorithm
intervals
Results
37.0ms86×body1280valid
16.0ms63×body640valid
15.0ms255×body80valid
6.0ms30×body320valid
3.0ms24×body160valid

simplify17.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1507
2777
3967
41127
51277
61417
71417

prune7.0ms

Filtered
1 candidates to 1 candidates (100.0%)
Pruning

1 alts after pruning (1 fresh and 0 done)

PrunedKeptTotal
New011
Fresh101
Picked000
Done000
Total112

Merged error: 0.5b

Counts
2 → 1

localize11.0ms

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))

series277.0ms

Counts
2 → 6
Calls
2 calls:
213.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
64.0ms
(/ (cos th) (sqrt 2.0))

simplify58.0ms

Algorithm
egg-herbie
Counts
93 → 93
Iterations

Useful iterations: 2 (48.0ms)

IterNodesCost
0479795
12384738
25003725

prune249.0ms

Filtered
93 candidates to 64 candidates (68.8%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New85893
Fresh000
Picked101
Done000
Total86894

Merged error: 0.0b

Counts
94 → 8

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b
(* (cos th) (+ (* a1 a1) (* a2 a2)))
0.4b
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

rewrite16.0ms

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)))
8.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

series326.0ms

Counts
2 → 6
Calls
2 calls:
107.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
219.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

simplify45.0ms

Algorithm
egg-herbie
Counts
57 → 57
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0300487
11619424
25001417

prune141.0ms

Filtered
57 candidates to 39 candidates (68.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New54357
Fresh257
Picked101
Done000
Total57865

Merged error: 0b

Counts
65 → 8

localize15.0ms

Local error

Found 3 expressions with local error:

0.2b
(* (cos th) (+ (* a1 a1) (* a2 a2)))
0.2b
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
0.2b
(/ (/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

rewrite40.0ms

Algorithm
rewrite-expression-head
Rules
56×times-frac
36×cbrt-prod
35×add-exp-log add-sqr-sqrt
33×add-cube-cbrt *-un-lft-identity
22×add-cbrt-cube
18×sqrt-prod
13×cbrt-undiv div-exp
12×div-inv
10×associate-/r*
9×prod-exp cbrt-unprod
6×associate-/l*
5×pow1
4×associate-*r/
3×associate-*r* associate-*l* associate-/l/ add-log-exp
2×frac-2neg flip3-+ clear-num flip-+
1×distribute-rgt-in distribute-lft-in pow-prod-down *-commutative unswap-sqr
Counts
3 → 125
Calls
3 calls:
6.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
11.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
18.0ms
(/ (/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

series1.2s

Counts
3 → 9
Calls
3 calls:
104.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
863.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))
233.0ms
(/ (/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))

simplify88.0ms

Algorithm
egg-herbie
Counts
134 → 134
Iterations

Useful iterations: 2 (69.0ms)

IterNodesCost
05852360
131602026
250011998

prune330.0ms

Filtered
134 candidates to 91 candidates (67.9%)
Pruning

8 alts after pruning (7 fresh and 1 done)

PrunedKeptTotal
New1340134
Fresh077
Picked011
Done000
Total1348142

Merged error: 0b

Counts
142 → 8

localize11.0ms

Local error

Found 2 expressions with local error:

0.2b
(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
0.4b
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

rewrite25.0ms

Algorithm
rewrite-expression-head
Rules
39×add-sqr-sqrt
38×times-frac
31×add-cube-cbrt *-un-lft-identity
22×associate-*r* sqrt-prod
9×add-exp-log add-cbrt-cube
6×associate-/r*
4×pow1
3×associate-*l* associate-/l* unswap-sqr
2×cbrt-undiv div-exp prod-exp cbrt-unprod div-inv associate-/l/ add-log-exp
1×frac-2neg flip3-+ associate-*r/ pow-prod-down clear-num *-commutative flip-+
Counts
2 → 83
Calls
2 calls:
15.0ms
(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
7.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

series308.0ms

Counts
2 → 6
Calls
2 calls:
212.0ms
(* (cos th) (/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0)))
95.0ms
(/ (+ (* a1 a1) (* a2 a2)) (sqrt 2.0))

simplify48.0ms

Algorithm
egg-herbie
Counts
89 → 89
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0314880
11523816
25001800

prune172.0ms

Filtered
89 candidates to 58 candidates (65.2%)
Pruning

8 alts after pruning (6 fresh and 2 done)

PrunedKeptTotal
New89089
Fresh066
Picked011
Done011
Total89897

Merged error: 0b

Counts
97 → 8

regimes206.0ms

Accuracy

0% (0.4b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
01614
11614

end0.0ms

sample2.7s

Algorithm
intervals
Results
970.0ms2509×body1280valid
555.0ms2055×body640valid
516.0ms8158×body80valid
213.0ms1095×body320valid
68.0ms529×body160valid

Profiling

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