Details

Time bar (total: 8.9s)

sample183.0ms

Algorithm
intervals
Results
98.0ms87×body1280valid
36.0ms52×body640valid
13.0ms25×body320valid
11.0ms82×body80valid
3.0ms10×body160valid

simplify647.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
03250
17450
217650
354850
4175350
done500050

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize32.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.8b
(- (cos x) (cos y))

rewrite62.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt
15×*-un-lft-identity
11×add-exp-log add-cbrt-cube
9×add-cube-cbrt
8×add-log-exp
6×pow1 associate-*r/ associate-*r* associate-*l*
5×sqrt-prod difference-of-squares
4×sub-neg times-frac associate-/r/
3×flip3-- flip3-+ flip-- flip-+ associate-/l* distribute-lft-out--
2×cbrt-undiv distribute-rgt-in distribute-lft-in diff-log div-exp associate-*l/ frac-add prod-exp cbrt-unprod associate-/l/ unswap-sqr
1×frac-2neg pow-prod-down clear-num associate-/r* *-commutative div-inv diff-cos
Counts
4 → 88
Calls
4 calls:
23.0ms
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
30.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
3.0ms
(- 3.0 (sqrt 5.0))
3.0ms
(- (cos x) (cos y))

series1.5s

Counts
4 → 10
Calls
4 calls:
1.3s
(/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (* 3.0 (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
93.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
54.0ms
(- (cos x) (cos y))

simplify857.0ms

Counts
98 → 98
Iterations

Useful iterations: 2 (260.0ms)

IterNodesCost
03112970
18532897
231172544
done50002544

prune585.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

1.0b
(- 3.0 (sqrt 5.0))
1.0b
(- 3.0 (sqrt 5.0))
1.0b
(- 3.0 (sqrt 5.0))
2.8b
(- (cos x) (cos y))

rewrite15.0ms

Algorithm
rewrite-expression-head
Rules
18×add-sqr-sqrt
12×*-un-lft-identity add-log-exp
7×difference-of-squares
4×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out--
3×sqrt-prod
1×diff-cos
Counts
4 → 60
Calls
4 calls:
3.0ms
(- 3.0 (sqrt 5.0))
3.0ms
(- 3.0 (sqrt 5.0))
3.0ms
(- 3.0 (sqrt 5.0))
3.0ms
(- (cos x) (cos y))

series62.0ms

Counts
4 → 6
Calls
4 calls:
0.0ms
(- 3.0 (sqrt 5.0))
0.0ms
(- 3.0 (sqrt 5.0))
0.0ms
(- 3.0 (sqrt 5.0))
62.0ms
(- (cos x) (cos y))

simplify554.0ms

Counts
66 → 66
Iterations

Useful iterations: 3 (159.0ms)

IterNodesCost
0104711
1230680
2544646
31606638
done5000638

prune531.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

localize34.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (/ 1 3.0) (/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
0.4b
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
1.0b
(- 3.0 (sqrt 5.0))
2.8b
(- (cos x) (cos y))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
53×add-sqr-sqrt
29×*-un-lft-identity
28×add-exp-log
26×times-frac
23×associate-*r*
21×add-cube-cbrt
19×associate-*l*
18×add-cbrt-cube
9×prod-exp
8×pow1 div-exp add-log-exp unswap-sqr
5×sqrt-prod cbrt-unprod difference-of-squares
4×cbrt-undiv sub-neg associate-/r/
3×flip3-- associate-*r/ associate-*l/ flip-- distribute-lft-out--
2×distribute-rgt-in rec-exp distribute-lft-in flip3-+ diff-log 1-exp pow-prod-down frac-add *-commutative flip-+ div-inv
1×frac-times diff-cos
Counts
4 → 121
Calls
4 calls:
41.0ms
(* (/ 1 3.0) (/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
30.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
3.0ms
(- 3.0 (sqrt 5.0))
3.0ms
(- (cos x) (cos y))

series1.5s

Counts
4 → 10
Calls
4 calls:
1.4s
(* (/ 1 3.0) (/ (+ 2.0 (* (* (* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0))) (- (sin y) (/ (sin x) 16.0))) (- (cos x) (cos y)))) (+ (+ 1.0 (* (/ (- (sqrt 5.0) 1.0) 2.0) (cos x))) (* (/ (- 3.0 (sqrt 5.0)) 2.0) (cos y)))))
94.0ms
(* (sqrt 2.0) (- (sin x) (/ (sin y) 16.0)))
0.0ms
(- 3.0 (sqrt 5.0))
57.0ms
(- (cos x) (cos y))

simplify1.2s

Counts
131 → 131
Iterations

Useful iterations: 2 (346.0ms)

IterNodesCost
03705183
110455024
239074417
done50014417

prune730.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 0.0b

localize51.0ms

Local error

Found 4 expressions with local error:

1.0b
(- 3.0 (sqrt 5.0))
2.8b
(- (cos x) (cos y))
2.8b
(- (cos x) (cos y))
2.8b
(- (cos x) (cos y))

rewrite17.0ms

Algorithm
rewrite-expression-head
Rules
14×add-sqr-sqrt
12×*-un-lft-identity add-log-exp
5×difference-of-squares
4×pow1 add-exp-log add-cube-cbrt sub-neg flip3-- diff-log add-cbrt-cube flip-- distribute-lft-out--
3×diff-cos
1×sqrt-prod
Counts
4 → 60
Calls
4 calls:
3.0ms
(- 3.0 (sqrt 5.0))
3.0ms
(- (cos x) (cos y))
6.0ms
(- (cos x) (cos y))
3.0ms
(- (cos x) (cos y))

series173.0ms

Counts
4 → 10
Calls
4 calls:
0.0ms
(- 3.0 (sqrt 5.0))
59.0ms
(- (cos x) (cos y))
60.0ms
(- (cos x) (cos y))
54.0ms
(- (cos x) (cos y))

simplify35.0ms

Iterations

Useful iterations: 1 (14.0ms)

IterNodesCost
079666
1157645