Details

Time bar (total: 12.6s)

sample134.0ms

Algorithm
intervals
Results
40.0ms79×body1280valid
36.0ms91×body640valid
22.0ms254×body80valid
13.0ms50×body320valid
3.0ms15×body160valid

simplify16.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0257
1507
2777
3967
41127
51277
61417
71417

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

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)))
0.6b
(/ (cos th) (sqrt 2.0))

rewrite29.0ms

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))

series48.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ (* a1 a1) (* a2 a2))
38.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
5.0ms
(/ (cos th) (sqrt 2.0))

simplify56.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0490872
12426805
25003791

prune747.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (pow a2 2) (pow a1 2))
0.2b
(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
0.4b
(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

rewrite89.0ms

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:
9.0ms
(+ (pow a2 2) (pow a1 2))
46.0ms
(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
28.0ms
(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

series56.0ms

Counts
3 → 9
Calls
3 calls:
5.0ms
(+ (pow a2 2) (pow a1 2))
40.0ms
(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
10.0ms
(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

simplify48.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03441118
115571023
250011018

prune737.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
0.6b
(/ (cos th) (sqrt 2.0))
6.5b
(sqrt (+ (* a1 a1) (* a2 a2)))
6.5b
(sqrt (+ (* a1 a1) (* a2 a2)))

rewrite36.0ms

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:
21.0ms
(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
4.0ms
(/ (cos th) (sqrt 2.0))
3.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
4.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

series51.0ms

Counts
4 → 12
Calls
4 calls:
32.0ms
(* (/ (cos th) (sqrt 2.0)) (sqrt (+ (* a1 a1) (* a2 a2))))
5.0ms
(/ (cos th) (sqrt 2.0))
8.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))
6.0ms
(sqrt (+ (* a1 a1) (* a2 a2)))

simplify41.0ms

Algorithm
egg-herbie
Counts
133 → 133
Iterations

Useful iterations: 2 (31.0ms)

IterNodesCost
03521093
112561042
250011028

prune1.1s

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0b

localize13.0ms

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))) (sqrt (sqrt 2.0)))
0.6b
(/ (cos th) (sqrt (sqrt 2.0)))

rewrite191.0ms

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:
3.0ms
(+ (* a1 a1) (* a2 a2))
104.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
18.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
5.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

series59.0ms

Counts
4 → 12
Calls
4 calls:
10.0ms
(+ (* a1 a1) (* a2 a2))
38.0ms
(* (/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0))) (+ (* a1 a1) (* a2 a2)))
5.0ms
(/ (/ (cos th) (sqrt (sqrt 2.0))) (sqrt (sqrt 2.0)))
6.0ms
(/ (cos th) (sqrt (sqrt 2.0)))

simplify113.0ms

Algorithm
egg-herbie
Counts
729 → 729
Iterations

Useful iterations: 1 (36.0ms)

IterNodesCost
0196110436
150019573

prune4.6s

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0b

regimes795.0ms

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
0147
1147

end0.0ms

sample3.6s

Algorithm
intervals
Results
1.4s2605×body1280valid
793.0ms2122×body640valid
721.0ms8075×body80valid
295.0ms1066×body320valid
98.0ms536×body160valid