Details

Time bar (total: 17.0s)

sample79.0ms

Algorithm
intervals
Results
28.0ms81×body1280valid
16.0ms71×body640valid
12.0ms256×body80valid
4.0ms30×body320valid
1.0ms14×body160valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1507
2777
3967
41127
51277
61417
71417

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.5b

localize10.0ms

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))

rewrite23.0ms

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:
4.0ms
(+ (* a1 a1) (* a2 a2))
11.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
5.0ms
(/ (cos th) (sqrt 2.0))

series312.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(+ (* a1 a1) (* a2 a2))
216.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
63.0ms
(/ (cos th) (sqrt 2.0))

simplify53.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (44.0ms)

IterNodesCost
0490872
12426805
25003791

prune293.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.4b
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.6b
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))

rewrite154.0ms

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))
58.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
17.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

series426.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* a1 a1) (* a2 a2))
221.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
68.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
104.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

simplify119.0ms

Algorithm
egg-herbie
Counts
729 → 729
Iterations

Useful iterations: 1 (37.0ms)

IterNodesCost
0196110436
150019573

prune1.7s

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.3b
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))
0.3b
(* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))

rewrite189.0ms

Algorithm
rewrite-expression-head
Rules
1434×sqrt-prod
969×times-frac
518×add-sqr-sqrt
515×associate-*l*
507×add-cube-cbrt *-un-lft-identity
71×add-exp-log
47×add-cbrt-cube
27×prod-exp
25×div-exp
17×cbrt-unprod
15×div-inv
14×cbrt-undiv
11×pow1 frac-times associate-*r/
9×associate-/r*
7×flip3-+ flip-+
6×add-log-exp
5×distribute-rgt-in distribute-lft-in
4×associate-*r* pow-prod-down associate-*l/ unswap-sqr
3×rec-exp 1-exp associate-/l*
2×*-commutative
1×+-commutative frac-2neg clear-num sum-log
Counts
4 → 654
Calls
4 calls:
4.0ms
(+ (* a1 a1) (* a2 a2))
93.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))
14.0ms
(* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
6.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

series685.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(+ (* a1 a1) (* a2 a2))
226.0ms
(* (/ (/ 1 (sqrt (sqrt (sqrt 2.0)))) (sqrt (sqrt (sqrt 2.0)))) (* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2))))
320.0ms
(* (/ (cos th) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
106.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

simplify118.0ms

Algorithm
egg-herbie
Counts
666 → 666
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0178811355
1500110480

prune2.3s

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ (sqrt (sqrt 2.0)) (cos th))
0.4b
(* (/ (/ 1 (/ (sqrt (sqrt 2.0)) (cos th))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
0.6b
(/ (/ 1 (/ (sqrt (sqrt 2.0)) (cos th))) (sqrt (sqrt 2.0)))
0.6b
(/ 1 (/ (sqrt (sqrt 2.0)) (cos th)))

rewrite498.0ms

Algorithm
rewrite-expression-head
Rules
5367×times-frac
3501×sqrt-prod
2531×add-sqr-sqrt
2430×*-un-lft-identity
2418×add-cube-cbrt
886×associate-*l*
110×associate-/l*
84×div-inv
64×add-exp-log
43×associate-/r*
36×div-exp
34×add-cbrt-cube
28×unswap-sqr
20×associate-/r/
16×cbrt-undiv
8×prod-exp
7×pow1
6×rec-exp 1-exp
4×cbrt-unprod add-log-exp
3×frac-2neg associate-*r* clear-num
2×frac-times flip3-+ associate-*r/ flip-+
1×distribute-rgt-in pow-flip distribute-lft-in pow-prod-down associate-*l/ *-commutative associate-/l/ inv-pow
Counts
4 → 2154
Calls
4 calls:
6.0ms
(/ (sqrt (sqrt 2.0)) (cos th))
158.0ms
(* (/ (/ 1 (/ (sqrt (sqrt 2.0)) (cos th))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
42.0ms
(/ (/ 1 (/ (sqrt (sqrt 2.0)) (cos th))) (sqrt (sqrt 2.0)))
14.0ms
(/ 1 (/ (sqrt (sqrt 2.0)) (cos th)))

series457.0ms

Counts
4 → 12
Calls
4 calls:
76.0ms
(/ (sqrt (sqrt 2.0)) (cos th))
214.0ms
(* (/ (/ 1 (/ (sqrt (sqrt 2.0)) (cos th))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
65.0ms
(/ (/ 1 (/ (sqrt (sqrt 2.0)) (cos th))) (sqrt (sqrt 2.0)))
101.0ms
(/ 1 (/ (sqrt (sqrt 2.0)) (cos th)))

simplify324.0ms

Algorithm
egg-herbie
Counts
2166 → 2166
Iterations

Useful iterations: 0 (20.0ms)

IterNodesCost
0500137300

prune6.8s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

regimes188.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02217
12217

end0.0ms

sample2.3s

Algorithm
intervals
Results
799.0ms2492×body1280valid
465.0ms2157×body640valid
411.0ms7961×body80valid
158.0ms1004×body320valid
67.0ms572×body160valid