Details

Time bar (total: 11.8s)

sample84.0ms

Algorithm
intervals
Results
25.0ms77×body1280valid
18.0ms84×body640valid
15.0ms245×body80valid
7.0ms40×body320valid
2.0ms22×body160valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1507
2777
3967
41127
51277
61417
71417

prune8.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.4b
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b
(/ (cos th) (sqrt 2.0))

rewrite28.0ms

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))
18.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
4.0ms
(/ (cos th) (sqrt 2.0))

series314.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* a1 a1) (* a2 a2))
224.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
63.0ms
(/ (cos th) (sqrt 2.0))

simplify56.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (46.0ms)

IterNodesCost
0490872
12426805
25003791

prune306.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 3 expressions with local error:

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

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt
10×add-exp-log add-cbrt-cube
9×add-cube-cbrt *-un-lft-identity
6×times-frac associate-/r* sqrt-prod
5×pow1 add-log-exp
4×associate-*r/
3×flip3-+ associate-*r* associate-*l* flip-+
2×cbrt-undiv div-exp prod-exp cbrt-unprod associate-/l/
1×+-commutative distribute-rgt-in frac-2neg distribute-lft-in pow-prod-down clear-num sum-log *-commutative div-inv associate-/l* unswap-sqr
Counts
3 → 62
Calls
3 calls:
3.0ms
(+ (* a1 a1) (* a2 a2))
9.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
7.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

series359.0ms

Counts
3 → 9
Calls
3 calls:
27.0ms
(+ (* a1 a1) (* a2 a2))
109.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
223.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (sqrt 2.0))

simplify45.0ms

Algorithm
egg-herbie
Counts
71 → 71
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0309564
11642490
25001481

prune193.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm
rewrite-expression-head
Rules
56×times-frac
36×add-exp-log cbrt-prod add-sqr-sqrt
34×add-cube-cbrt *-un-lft-identity
23×add-cbrt-cube
18×sqrt-prod
13×cbrt-undiv div-exp
12×div-inv
10×associate-/r*
9×prod-exp cbrt-unprod
6×pow1 associate-/l* add-log-exp
4×associate-*r/
3×flip3-+ associate-*r* associate-*l* flip-+ associate-/l/
2×frac-2neg clear-num
1×+-commutative distribute-rgt-in distribute-lft-in pow-prod-down sum-log *-commutative unswap-sqr
Counts
4 → 136
Calls
4 calls:
3.0ms
(+ (* a1 a1) (* a2 a2))
9.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
13.0ms
(/ (/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
14.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

series1.0s

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* a1 a1) (* a2 a2))
109.0ms
(* (cos th) (+ (* a1 a1) (* a2 a2)))
217.0ms
(/ (/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0)))) (cbrt (sqrt 2.0)))
670.0ms
(/ (* (cos th) (+ (* a1 a1) (* a2 a2))) (* (cbrt (sqrt 2.0)) (cbrt (sqrt 2.0))))

simplify86.0ms

Algorithm
egg-herbie
Counts
148 → 148
Iterations

Useful iterations: 2 (68.0ms)

IterNodesCost
05942437
131832092
250022064

prune436.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))
0.2b
(/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0)))
0.3b
(* (/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
0.7b
(/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

rewrite437.0ms

Algorithm
rewrite-expression-head
Rules
1848×times-frac
1647×cbrt-prod
1173×add-sqr-sqrt
812×add-cube-cbrt *-un-lft-identity
510×sqrt-prod
376×associate-*r*
92×add-exp-log
85×unswap-sqr
65×associate-/l*
49×add-cbrt-cube
43×cbrt-undiv div-exp
35×associate-*l*
33×div-inv
23×prod-exp cbrt-unprod
22×associate-/r*
6×pow1
4×associate-/l/ add-log-exp
3×frac-2neg clear-num
1×frac-times flip3-+ associate-*r/ pow-prod-down associate-*l/ *-commutative flip-+
Counts
4 → 1103
Calls
4 calls:
27.0ms
(/ (/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))
10.0ms
(/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0)))
275.0ms
(* (/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
15.0ms
(/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

series1.5s

Counts
4 → 12
Calls
4 calls:
418.0ms
(/ (/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))
491.0ms
(/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0)))
227.0ms
(* (/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0))))) (/ (/ (+ (* a1 a1) (* a2 a2)) (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))
355.0ms
(/ (/ (cos th) (cbrt (sqrt 2.0))) (* (cbrt (cbrt (sqrt 2.0))) (cbrt (cbrt (sqrt 2.0)))))

simplify268.0ms

Algorithm
egg-herbie
Counts
1115 → 1115
Iterations

Useful iterations: 1 (63.0ms)

IterNodesCost
0368528410
1500127811

prune4.0s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0b

regimes197.0ms

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
01923
11923

end0.0ms

sample2.3s

Algorithm
intervals
Results
827.0ms2502×body1280valid
481.0ms2132×body640valid
406.0ms8008×body80valid
172.0ms1094×body320valid
57.0ms504×body160valid