Details

Time bar (total: 7.0s)

sample115.0ms

Algorithm
intervals
Results
37.0ms88×body1280valid
26.0ms89×body640valid
19.0ms245×body80valid
8.0ms35×body320valid
3.0ms21×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: 0.7b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* a1 a1) (* a2 a2))
0.6b
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
0.7b
(/ (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))
19.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
4.0ms
(/ (cos th) (sqrt 2.0))

series302.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(+ (* a1 a1) (* a2 a2))
209.0ms
(* (/ (cos th) (sqrt 2.0)) (+ (* a1 a1) (* a2 a2)))
61.0ms
(/ (cos th) (sqrt 2.0))

simplify53.0ms

Algorithm
egg-herbie
Counts
107 → 107
Iterations

Useful iterations: 2 (45.0ms)

IterNodesCost
0490872
12426805
25003791

prune283.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.3b

localize15.0ms

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)))
0.6b
(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

rewrite90.0ms

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:
10.0ms
(+ (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))

series330.0ms

Counts
3 → 9
Calls
3 calls:
33.0ms
(+ (pow a2 2) (pow a1 2))
206.0ms
(* (cos th) (/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0)))
91.0ms
(/ (+ (pow a2 2) (pow a1 2)) (sqrt 2.0))

simplify47.0ms

Algorithm
egg-herbie
Counts
131 → 131
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
03441118
115571023
250011018

prune287.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.3b

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)))
0.6b
(/ (* (cos th) (+ (pow a2 2) (pow a1 2))) (sqrt 2.0))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
11×add-sqr-sqrt
10×add-exp-log add-cbrt-cube
9×add-cube-cbrt
6×times-frac associate-/r* sqrt-prod
5×pow1 associate-*r* add-log-exp
4×unpow-prod-down associate-*r/ distribute-lft-out
3×flip3-+ 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 → 66
Calls
3 calls:
9.0ms
(+ (pow a2 2) (pow a1 2))
37.0ms
(* (cos th) (+ (pow a2 2) (pow a1 2)))
14.0ms
(/ (* (cos th) (+ (pow a2 2) (pow a1 2))) (sqrt 2.0))

series341.0ms

Counts
3 → 9
Calls
3 calls:
31.0ms
(+ (pow a2 2) (pow a1 2))
104.0ms
(* (cos th) (+ (pow a2 2) (pow a1 2)))
205.0ms
(/ (* (cos th) (+ (pow a2 2) (pow a1 2))) (sqrt 2.0))

simplify42.0ms

Algorithm
egg-herbie
Counts
75 → 75
Iterations

Useful iterations: 2 (35.0ms)

IterNodesCost
0277562
11443488
25001484

prune197.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ (sqrt (+ (pow a2 2) (pow a1 2))) (/ (sqrt 2.0) (sqrt (+ (pow a2 2) (pow a1 2)))))
0.4b
(/ (sqrt 2.0) (sqrt (+ (pow a2 2) (pow a1 2))))
6.9b
(sqrt (+ (pow a2 2) (pow a1 2)))
6.9b
(sqrt (+ (pow a2 2) (pow a1 2)))

rewrite354.0ms

Algorithm
rewrite-expression-head
Rules
912×times-frac
881×*-un-lft-identity
833×sqrt-prod
411×add-sqr-sqrt
409×add-cube-cbrt
236×unpow-prod-down distribute-lft-out
62×associate-/r*
26×sqrt-div
21×associate-/r/
14×associate-/l*
13×flip3-+ flip-+
11×add-exp-log add-cbrt-cube div-inv
6×pow1
4×cbrt-undiv div-exp add-log-exp
3×sqrt-undiv
2×rem-sqrt-square frac-2neg sqrt-pow1 pow1/2 clear-num associate-/l/
Counts
4 → 623
Calls
4 calls:
242.0ms
(/ (sqrt (+ (pow a2 2) (pow a1 2))) (/ (sqrt 2.0) (sqrt (+ (pow a2 2) (pow a1 2)))))
19.0ms
(/ (sqrt 2.0) (sqrt (+ (pow a2 2) (pow a1 2))))
19.0ms
(sqrt (+ (pow a2 2) (pow a1 2)))
15.0ms
(sqrt (+ (pow a2 2) (pow a1 2)))

series242.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(/ (sqrt (+ (pow a2 2) (pow a1 2))) (/ (sqrt 2.0) (sqrt (+ (pow a2 2) (pow a1 2)))))
76.0ms
(/ (sqrt 2.0) (sqrt (+ (pow a2 2) (pow a1 2))))
39.0ms
(sqrt (+ (pow a2 2) (pow a1 2)))
35.0ms
(sqrt (+ (pow a2 2) (pow a1 2)))

simplify130.0ms

Algorithm
egg-herbie
Counts
635 → 635
Iterations

Useful iterations: 1 (26.0ms)

IterNodesCost
099912109
1500210810

prune850.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 0.3b

regimes202.0ms

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

sample3.0s

Algorithm
intervals
Results
1.0s2509×body1280valid
674.0ms7918×body80valid
613.0ms2065×body640valid
234.0ms1063×body320valid
80.0ms500×body160valid